Polynomials Questions

We provide polynomials practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on polynomials skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

List of polynomials Questions

Question No Questions Class
1 68. If x= 6+
then the value of
* + 4 is
(1) 1448
(3) 1444
(2) 1442
(4) 1446
9
2 Find the product of ( (boldsymbol{m}-mathbf{1})(boldsymbol{m}- )
2)( (m-3) )
9
3 60. If x2 = y + z, y2 = 2 + x and z =
x + y. then the value of
1.11
1+x 1+ y 1+ z is
(1)-1
(2) 1
(3) 2
(4) O
9
4 Find the Quotient and the Remainder
when the first polynomial is divided by
the second.
( left(x^{4}-2 x^{3}+2 x^{2}+x+4right) ) by ( left(x^{2}+x+right. )
1)
A. Quotient ( =x^{2}+3 x+4 ), Remainder ( =0 )
B. Quotient= ( x^{2}-3 x-4 ), Remainder ( =0 )
c. Quotient ( =-x^{2}-3 x+4 ), Remainder ( =0 )
D. Quotient ( =x^{2}-3 x+4 ), Remainder ( =0 )
10
5 61. If 7x
= 14, then the value
2x
of x-
3 is :
8x
(1) 9
(3) 27
(2) 8
(4) 11
9
6 If ( frac{boldsymbol{a}}{boldsymbol{b}}=frac{boldsymbol{c}}{boldsymbol{d}}=frac{boldsymbol{e}}{boldsymbol{f}} ) and
( frac{2 a^{4} b^{2}+3 a^{2} c^{2}-5 e^{4} f}{2 b^{6}+3 b^{2} d^{2}-5 f^{5}}=left(frac{a}{b}right)^{n} ) then
the value if ( n ) is
( A )
B. 2
( c cdot 3 )
( D )
10
7 Find the cube of 49 9
8 60. If (x – 1) and (x + 3) are the fac-
tors of x2 + kx + k, then
(1) k, = -2, k, = -3
(2) k, = 2, k = -3
(3) k, = 2, k, = 3
(4) k, = -2, k, = 3
9
9 When ( x^{3}-2 x^{2}+a x-b ) is divided by
( x^{2}-2 x-3, ) the remainder is ( x-6 . ) The
values of ( a ) and ( b ) are respectively:
( A cdot-2 ) and -6
B. 2 and -6
c. -2 and 6
D. 2 and 6
10
10 64. If m+
= 4, find the value
of (m – 2)2 + (m-22
(1) -2
(3) 2
(2) 0
(4) 4
9
11 Which polynomial represents this plot?
A. cubic
B. biquadratic
c. quadratic
D. linear
9
12 The remainder in the division of ( 14 x^{2}- )
( 53 x+45 ) by ( 7 x-9 ) is
A . -3
B. ( 7 x )
c. 90
D.
10
13 If ( left(x^{2}+4 x-21right) ) is divided by ( x+7 )
then the quotient is
( mathbf{A} cdot x+3 )
B. ( x-3 )
c. ( x^{2}-2 )
D. ( x-4 )
10
14 Factorize:
( 4 a^{2} b-9 b^{3} )
( mathbf{A} cdot b(2 a+3 b)(2 a+3 b) )
B. ( b(2 a+3 b)(a-3 b) )
( mathbf{c} cdot b(a+3 b)(2 a-3 b) )
D. ( b(2 a+3 b)(2 a-3 b) )
9
15 If ( f(x)=x^{4}-2 x^{3}+3 x^{2}-a x+b ) is a
polynomial such that when it is divide by ( (x-1) ) and ( (x+1) ) the remainders
are 5 and 19 respectively the remainder when ( f(x) ) is divisible by ( (x-2) ) is
( A cdot 7 )
B. 8
c. 9
D. 10
9
16 Find the value of ( b ) for which the
polynomial ( 2 x^{3}-9 x^{2}-x-b ) is
divisible by ( 2 x+3 )
10
17 ( frac{x^{2}+9 x+14}{x+7}= )
( mathbf{A} cdot x+2 )
B. ( x+7 )
( c cdot 2 )
D.
10
18 Write the degree of each of the following polynomials:
( frac{1}{2} y^{7}-12 y^{6}+48 y^{5}-10 )
10
19 Which of the following is a
constant polynomial?
( mathbf{A} cdot p(x)=7+3 x )
B ( . p(x)=7 )
C ( . p(x)=7 x+7 )
D. ( p(x)=4 x+3 )
10
20 What is the degree of the given
monomial ( boldsymbol{x} boldsymbol{y}^{2} boldsymbol{z}^{2} ? )
( A cdot 3 )
B. 4
( c .5 )
D. 6
10
21 Which of the following is a cubic polynomial?
( mathbf{A} cdot p(x)=x^{2}-16 )
в. ( p(x)=x-16 )
C ( cdot p(x)=x^{3}-27 )
D ( cdot p(x)=27^{3} )
10
22 Write the polynomial in standard form and also write down their degree. ( left(frac{5}{6} z-frac{3}{4} z^{2}-frac{2}{3} z^{3}+1right) ) 10
23 If ( a+b+c=8 ) and ( a b+b c+c a=20 )
find the value of ( a^{3}+b^{3}+c^{3}-3 a b c )
9
24 If ( a=frac{1}{3-2 sqrt{2}}, b=frac{1}{3+2 sqrt{2}}, ) then the
value of ( a^{3}+b^{3} ) is
A ( cdot 194 )
в. 196
( c cdot 198 )
D. 200
9
25 The degree of the equation, given by ( (x+2)(x-1)=(x+1)(x+3), ) is
( A cdot 2 )
B. 3
( c . )
D.
9
26 Degree of polynomial 5 is
( A cdot 1 )
B. 2
( c cdot 0 )
D. Not defined
9
27 Which one of the following is a
quadratic polynomial?
A ( cdot x^{2}+3 )
B. ( x^{3}+x^{2}+4 )
( mathbf{c} cdot 2 x^{4}+4 x^{3}+3 x^{2}+6 )
D. None of the above
9
28 Divide
( left(y^{3}-3 y^{2}+5 y-1right) div(y-1) )
10
29 56. If 2x + 3y = 13 and xy = 6 then
the value of 8x + 27yº will be
(1) 799 (2) 797
(3) 795 (4) 793
9
30 Find the quotient the and remainder of the following division:
( left(5 x^{3}-8 x^{2}+5 x-7right) div(x-1) )
10
31 ( f(x+2) ) is a factor of ( left(x^{4}-x^{2}-aright) )
then find ( a )
10
32 Solve:
( frac{m^{2}-3 m-108}{m+9}=0, ) then ( m=? )
10
33 Which of the following is NOT a quadratic polynomial?
( mathbf{A} cdot p(x)=16-4 x )
в. ( p(x)=13-x )
C ( cdot p(x)=12 x^{3}-x )
D. All of the above
9
34 61. If x + y + z = 1, xy + yz + 2x
= -1, xyz = -1, then xy + y +
z is
(1)-2 (2)-1
(3) O
(4) 1
9
35 If ( boldsymbol{x} neq-mathbf{5}, ) then the expression ( frac{mathbf{3} boldsymbol{x}}{boldsymbol{x}+mathbf{5}} div )
( frac{6}{4 x+20} ) can be simplified to
A ( .2 x )
в. ( frac{x}{2} )
c. ( frac{9 x}{2} )
D. ( 2 x+4 )
10
36 Find the missing terms such that the given polynomial become a perfect square trinomial:
[
-12 x+9
]
10
37 Simplify:
( (7 m-8 n)^{2}+(7 m+8 n)^{2} )
A ( cdot 198 m^{2}+28 n^{2} )
B. ( 98 m^{2}+128 n^{2} )
( mathbf{c} .98 m+128 n )
D. ( 98 m^{2}-128 n^{2} )
9
38 What should be added to ( x^{5}-1 ) to be
completely divisible by ( x^{2}+3 x-1 ? )
10
39 Show that ( (x-2) ) is a factor of ( x^{3}- )
( 3 x^{2}-10 x+24 )
10
40 68. If x2 + y2 + 2 + 2 = 2(y-2), then
value of x + y + z is equal to
(1) 0
(2) 1
(4)
3
de
(3) 2
9
41 If ( m-frac{1}{m}=5, ) then find ( m^{2}+frac{1}{m^{2}} )
B. ( sqrt{27} )
c. ( 25 sqrt{29} )
D. ( 25 sqrt{27} )
9
42 58. If ab + bc + ca = 0, then the val-
ue of

+-
a? – bc b? – ac c2 – ab *
(1) 2
(2) -1
(3) O
(4) 1
9
43 Degree of the polynomials ( frac{x^{23}+x^{14}-x^{16}}{x^{2}} ) is
( A cdot 2 )
B . 23
c. 14
D. 21
9
44 If the polynomial ( boldsymbol{f}(boldsymbol{x})= )
( left(6 x^{4}+8 x^{2}+17 x^{2}+21 x+7right) ) is
divided by another polynomial ( g(x)= )
( 3 x^{2}+4 x+1 ) the remainder is ( (a x+b) )
Find ( a ) and ( b )
10
45 If ( p(t)=t^{3}-1, ) find the values of
( boldsymbol{p}(mathbf{1}), boldsymbol{p}(-mathbf{2}) )
10
46 The remainder obtained when ( t^{6}+ )
( 3 t^{2}+10 ) is divided by ( t^{3}+1 ) is
A ( cdot t^{2}-11 )
B . ( 3 t^{2}+11 )
( mathbf{c} cdot t^{3}-1 )
D. ( 1-t^{3} )
10
47 f ( a=3, b=-3, ) find the value of
( (a-2)^{2}+(b-2)^{2} )
9
48 Substituting ( x=-3 ) in
( x^{2}-5 x+4 )
A . -2
B . 28
( c cdot 2 )
D. -1
10
49 Classify the following polynomial based on their degrees:
( boldsymbol{y}^{2}-boldsymbol{4} )
10
50 If a zero of ( p(x)=x^{2}+3 x+g ) is ( 2, ) then
value of ( g ) is
A . -10
B. 10
( c .5 )
D. -5
10
51 Factorize ( 3 a^{5}-108 a^{3} )
A ( cdot 3 a^{3}(a-6)(2 a-6) )
В ( cdot 2 a^{3}(a+6)(7 a-6) )
c. ( 2 a^{3}(a-6)(3 a+6) )
D. ( 3 a^{3}(a+6)(a-6) )
9
52 Verify whether the following are zeros of the polynomial indicated against them:
( boldsymbol{g}(boldsymbol{x})=mathbf{5} boldsymbol{x}^{2}+mathbf{7} boldsymbol{x}, boldsymbol{x}=mathbf{0},-frac{mathbf{7}}{mathbf{5}} )
A. True
B. False
10
53 55.
If x = 1.75, y = 0.5, then find
the value of
4×2 + 4xy + y2.
(1) 15.75 (2) 16.00
(3) 16.25 (4) 16.75
9
54 Perform division
( left(y^{2}+7 y+10right) div 6(y+5) )
10
55 7.
The age of a man is same as his wife’s age with the digits
reversed. Then sum of their ages is 99 years and the man is
9 years older than his wife. The age of man and his wife is
(a) 50 years
(b) 45 years
(c) 54 years
(d) 44 years
10
56 If the polynomial ( left(x^{3}-3 x^{2}+a x+18right) )
is divided by ( (x-4), ) the reminder is 58
Find the value of a.
9
57 Carry out the following divisions ( -54 l^{4} m^{3} n^{2} ) by ( 9 l^{2} m^{2} n^{2} ) 10
58 25.
The
The real number k for which the equation, 2×3 + 3x +k=0
has two distinct real roots in [0, 1] [JEEM 2013]
(a) lies between 1 and 2
(6) lies between 2 and 3
© lies between-1 and 0
(d) does not exist.
10
59 Prove if ( cot theta+frac{1}{cot theta}=2 ) then ( cot ^{2} theta+ )
( frac{1}{cot ^{2} theta}=2 )
9
60 When ( p(x)=x^{3}+a x^{2}+2 x+a ) is
divided by ( (x+a), ) the remainder is
( mathbf{A} cdot mathbf{0} )
B. ( a )
( c .-a )
D. ( 2 a )
9
61 Divide ( 4 x^{2} y^{2}(6 x-24) div 4 x y(x-4) )
( mathbf{A} cdot 6 x y )
B. ( 4 x y )
c. ( x-4 )
D. ( x y(x-4) )
10
62 If ( left(x^{3 / 2}-x y^{1 / 2}+x^{1 / 2} y-y^{3 / 2}right) ) is
divided by ( left(x^{1 / 2}-y^{1 / 2}right), ) the quotient is:
( mathbf{A} cdot x+y )
в. ( x-y )
C ( cdot x^{1 / 2}-y^{1 / 2} )
D. ( x^{2}-y^{2} )
10
63 61. If x + y2 + z = xy + y2 + zx, lx
# O). then the value of
4x + 2y – 32
is
2x
(2) 1
(1) o
9
64 Say true or false:
The zeros of the polynomial ( x^{2}-14 x+ )
49 are equal to 7
A. True
B. False
10
65 Write each of the following polynomials in the standard form. Also, write their
degree:
( left(x^{3}-1right)left(x^{3}-4right) )
9
66 If ( x-y=7 ) and ( x^{3}-y^{3}=133 ; ) find:
the value of ( x y )
A . 12
B. – –
( c .-10 )
D. 5
9
67 51. For real a, b, c if a + b + c
a+c
ab + bc + ca, the value of –
(1) 3
(3) 2
(2)
(40
9
68 Divide: ( a^{4}+4 b^{4} ) by ( a^{2}+2 a b+b^{2} ) 10
69 Simplify: ( (sqrt{2} x-2 y)^{2} ) 9
70 67. If
5x
2×2 + 5x +1
then the
value of (x+2x is
of
X
+-
(1) 15
(3) 20
(2) 10
(4) 5
9
71 Divide ( left(frac{boldsymbol{y}}{boldsymbol{6}}+frac{boldsymbol{2} boldsymbol{y}}{boldsymbol{3}}right) divleft(boldsymbol{y}+frac{boldsymbol{2} boldsymbol{y}-mathbf{1}}{boldsymbol{3}}right) ) 10
72 Factorise the following: ( a^{6}-b^{6} )
( mathbf{A} cdot(a+b)(a-b)left(a^{2}+b^{2}+a bright)left(a^{2}-b^{2}+a bright) )
B ( cdot(a+b)(a-b)left(a^{2}+b^{2}+a bright)left(a^{2}+b^{2}-a bright) )
( mathbf{c} cdot(a+b)(a-b)left(a^{2}-b^{2}-a bright)left(a^{2}+b^{2}-a bright) )
D. None of these
9
73 13.
If a2 + b2 + c2=1, then ab + bc + ca lies in the interval
(1984 – 2 Marks
@ 15,2] (b) (-1,2]
@ 1-1 () [-1,]
9
74 The degree of the polynomial ( x^{2}- ) ( 5 x^{4}+frac{3}{4} x^{7}-73 x+5 ) is
A. 7
B. ( frac{3}{4} )
( c cdot 4 )
D. -73
9
75 (
10 UUIU
3.
D
.
Ratio of my present age to age twenty years ago is
(a) 3:2
(b) 2:1
(c) 3:1
(d) 1:2
10
76 Choose the correct options:
This question has multiple correct options
A. Remainder obtained on dividing ( p(x)=x^{3}+1 ) by ( (x+ )
1) is 0
B. ( x=1 ) and ( x=2 ) are zeroes of polynomial ( P(x)= )
( 5 x^{5}-20 x^{4}+5 x^{3}+50 x^{2}-20 x-40 )
C ( cdot 6 x^{7}-5 x^{4}+2 x+3 ) is a polynomial of degree 7
D. ( x+1 ) and ( 2 x-3 ) are factors of ( 2 x^{3}-9 x^{2}+x+12 )
9
77 If ( x^{3}-frac{1}{x^{3}}=14, ) then ( x-frac{1}{x}= )
( A cdot 2 )
B. 4
( c .5 )
D.
9
78 Divide and write the quotient and
remainder.
(a) ( left(y^{2}+10 y+24right) div(y+4) )
(b) ( left(p^{2}+7 p-5right) div(p+3) )
10
79 If ( a^{2}+10 b^{2}+5 c^{2}+6 a b+2 b c-16 c+ )
( mathbf{1 6}=mathbf{0} ) then the possible value of ( boldsymbol{a}- )
( b+c= )
A . 5
B. -3
( c cdot-2 )
D. 10
9
80 ( R_{1} ) and ( R_{2} ) are the reminders when the
polynomial ( a x^{3}+3 x^{2}-3 ) and ( 2 x^{3}- )
( 5 x+2 a ) are divided by ( (x-4) )
respectively. If ( 2 R_{1}-R_{2}=0, ) then find
the value of a
A ( cdot a=frac{1}{6} )
в. ( _{a=frac{1}{3}} )
c. ( _{a=frac{1}{7}} )
D. ( a=frac{1}{5} )
9
81 Find if polynomial ( x^{4}-3 x^{3}+7 x^{2}- )
( 8 x+12 ) is exactly divisible by ( x^{2}- )
( 2 x+2 )
10
82 The expansion of ( (2 x-3 y)^{2} ) is:
A ( cdot 2 x^{2}+3 y^{2}+6 x y )
B. ( 4 x^{2}+9 y^{2}-12 x y )
c. ( 2 x^{2}+3 y^{2}-6 x y )
D. ( 4 x^{2}+9 y^{2}+12 x y )
9
83 The quotient and remainder when
( 3 x^{4}+6 x^{3}-6 x^{2}+2 x-7 ) is divided by
( x-3 ) are
A. Quotient: ( 3 x^{3}+15 x^{2}+39 x+119 ) and Remainder: 350
B. Quotient: ( 3 x^{3}+10 x^{2}+39 x+119 ) and Remainder: 35
C . Quotient: ( 3 x^{3}+15 x^{2}+39 x+119 ) and Remainder: 50
D. Quotient: ( 3 x^{3}+15 x^{2}+119 ) and Remainder: 350
9
84 If ( frac{x^{a^{2}}}{x^{b^{2}}}=x^{16}, x>1, ) and ( a+b=2, ) what
is the value of ( a-b ? )
( A cdot 8 )
B. 14
( c cdot 16 )
D. 18
9
85 ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{4}+boldsymbol{2} boldsymbol{x}^{3}-boldsymbol{2} boldsymbol{x}^{2}+boldsymbol{x}-mathbf{1} ) and
( boldsymbol{q}(boldsymbol{x})=boldsymbol{x}^{2}+boldsymbol{2} boldsymbol{x}-boldsymbol{3} )
Then ( p(x) ) is divisible by ( q(x), ) if we
A. Add ( (x-2) )
B. Add ( (x-3) )
c. Add ( (2-x) )
D. Add ( (3-x) )
10
86 Solve: ( left(5 p^{2}-25 p+20right) div(p-1) ) 9
87 Divide the polynomial ( p(x) ) by the polynomial ( g(x) ) and find the quotient and remainder.
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{3}-boldsymbol{3} boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-boldsymbol{3} )
( g(x)=x^{2}-2 )
( mathbf{A} cdot q(x)=x-3, r(x)=7 x+9 )
в. ( q(x)=x+3, r(x)=-7 x-9 )
C ( . q(x)=x+3, r(x)=7 x-9 )
D. ( q(x)=x-3, r(x)=7 x-9 )
10
88 If ( x^{2}+frac{1}{x^{2}}=7 ) find the value of ( x^{3}+frac{1}{x^{3}} ) 9
89 Find the remainder when we divide
( boldsymbol{x}^{7} boldsymbol{y}-boldsymbol{x} boldsymbol{y}^{7} ) by ( (boldsymbol{x}+boldsymbol{y})left(boldsymbol{x}^{2}-boldsymbol{x} boldsymbol{y}+boldsymbol{y}^{2}right) )
10
90 Find the zeroes of the quadratic
polynomial ( x^{2}+14 x+48 ) and verify
them
9
91 Factorise the polynomial: ( a x^{2}+b x^{2}+ )
( a y^{2}+b y^{2} )
9
92 A cubic polynomial is a polynomial of degree
A .
B.
( c cdot 3 )
( D )
9
93 Simplify ( (7 a-5 b)left(49 a^{2}+35 a b+right. )
( left.25 b^{2}right) )
9
94 ( (3-sqrt{7})(3+sqrt{7})= )
( mathbf{A} cdot mathbf{4} )
B . 2
( c cdot 6 )
D. 8
9
95 Divide as directed ( 5(2 x+1)(3 x+5) div )
( (2 x+1) )
10
96 Simplify: ( left(a^{2}-b^{2}right)^{2} ) 9
97 ( p(x)=25 ) is a
polynomial
A. linear
B. quadratic
c. constant
D. cubic
9
98 Divide the polynomial ( p(x) ) by the
polynomial ( p(g) ) and find the quotient
an in each of the following:
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{3}-boldsymbol{3} boldsymbol{x}^{2}+boldsymbol{5} boldsymbol{x}-boldsymbol{3}, boldsymbol{g}(boldsymbol{x})= )
( x^{2}-2 )
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{4}-boldsymbol{3} boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x}+mathbf{5}, boldsymbol{g}(boldsymbol{x})= )
( boldsymbol{x}^{2}+mathbf{1}-boldsymbol{x} )
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{4}-boldsymbol{5} boldsymbol{x}+boldsymbol{6}, boldsymbol{g}(boldsymbol{x})=boldsymbol{2}-boldsymbol{x}^{2} )
10
99 ( (x)^{n}+(a)^{n} ) is completely divisible by
( x+a, ) then ( n ) can be
A . 7028
в. 861
c. 26
D. 782
9
100 ( boldsymbol{f}(boldsymbol{x})=mathbf{3} boldsymbol{x}^{5}+mathbf{1} mathbf{1} boldsymbol{x}^{4}+mathbf{9} mathbf{0} boldsymbol{x}^{2}-mathbf{1} mathbf{9} boldsymbol{x}+mathbf{5} mathbf{3} )
is divided by ( x+5, ) then the remainder
is:
A. 100
B . -100
( c cdot-102 )
D. 102
9
101 Factorize:
( a^{2}-(2 a+3 b)^{2} )
( mathbf{A} cdot-3(a+b)(a+3 b) )
B ( cdot 3(a+b)(a+3 b) )
( mathbf{c} cdot-3(a-b)(a-3 b) )
D. ( 3(a+b)(a-3 b) )
9
102 Find the degree of the given algebraic expression ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{c} )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. 3
9
103 1 -b))2 + ab = p (a + b)2,
then the value of p is (assume
that a # -b)
(2) 1
(3) =
(4)
9
104 If ( a^{2}=b^{2}+b c ) then ( b+c ) always equals
A ( cdot frac{a^{2}}{b} )
в. ( frac{1}{2} b c )
( c cdot 1 )
D. ( b c )
9
105 If ( a+frac{1}{a}=2, ) then find ( a^{4}+frac{1}{a^{4}} ) 9
106 Divide the polynomial ( p(x) ) by the
polynomial ( g(x) ) and find the quotient and remainder in each of the following:
(i) ( p(x)=x^{3}-3 x^{2}+5 x-3, g(x)= )
( x^{2}-2 )
(ii) ( p(x)=x^{4}-3 x^{2}+4 x+5, g(x)= )
( boldsymbol{x}^{2}+mathbf{1}-boldsymbol{x} )
(iii) ( p(x)=x^{4}-5 x+6, g(x)=2-x^{2} )
10
107 Divide the polynomial ( 2 x^{4}-4 x^{3}- )
( 3 x-1 ) by ( (x-1) ) and verify the
remainder with zero of the divisor.
10
108 Verify whether the following are zeroes of the polynomial, indicated against them. ( boldsymbol{p}(boldsymbol{x})=boldsymbol{l} boldsymbol{x}+boldsymbol{m}, boldsymbol{x}=-frac{boldsymbol{m}}{boldsymbol{l}} ) 10
109 Degree of the polynomial ( boldsymbol{p}(boldsymbol{x})=-10 )
is
A . -10
B. 10
( c cdot 0 )
D.
10
110 Factorise the following: ( (5 x-6 y)^{3}+ )
( (7 z-5 x)^{3}+(6 y-7 z)^{3} )
A. ( 3(5 x-6 y)(7 z-5 x)(6 y-7 z) )
в. ( (x-6 y)(7 z-x)(y-7 z) )
c. ( 3(x-6 y)(z+5 x)(8 y-z) )
D. ( (x-y)(7 z+5 x)(6 y-7 z) )
9
111 66. If a – b – – 3abc = 0, then
(1) a = b = c
(2) a + b + c = 0
(3) a + c = b
(4) a = b + c
9
112 Arrange ( boldsymbol{x}^{8}+boldsymbol{x}+boldsymbol{x}^{12}-boldsymbol{3} boldsymbol{x}^{7}+boldsymbol{x}^{9}+1 ) in
descending powers of ( x )
10
113 Using the reals ( a_{n} ;(n=1,2, dots, 5), ) if ( l, m, n in{1,2,3,4,5} m<n )
A ( cdotleft(sum a_{n}right)^{2}=sumleft(a_{l}^{2}right)+2left(sum a_{m} a_{n}right) )
B . ( 0=sumleft(a_{l}^{2}right)-sumleft(a_{m} a_{n}right) )
C ( cdotleft(sum a_{n}right)^{2}=sumleft(a_{l}^{2}right)-2left(sum a_{m} a_{n}right) )
D. ( left(sum a_{n}right)^{2}=sumleft(a_{l}^{2}right)+sumleft(a_{m} a_{n}right) )
9
114 The degree of the term ( x^{3} y^{2} z^{2} ) is:
( A cdot 3 )
B. 2
c. 12
D.
9
115 Using identity ( (a+b)^{2}=left(a^{2}+2 a b+right. )
( b^{2} ) ) Evaluate
(i) ( (609)^{2}left(text { ii) }(725)^{2}right. )
9
116 Solve:
( left(y^{2}+10 y+24right) div(y+4) )
10
117 51. The value of
[(0.87)2+(0.13)2 + (0.87) x (0.26)] 2013
(1) O
(3) 1
(2) 2013
(4) -1
9
118 Divide ( 81 x^{3}left(50 x^{2}-98right) ) by ( 27 x^{2}(5 x+ )
7)
10
119 If ( a^{2}+b^{2}+c^{2}=250 ) and ( a b+b c+ )
( c a=3 ), then find ( a+b+c )
9
120 If ( a neq 0 ) and ( a-frac{1}{a}=4, ) find:
( a^{4}+frac{1}{a^{4}} )
A .92
в. 112
( c .322 )
D. 122
9
121 Zeroes of polynomial ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{2}-boldsymbol{3} boldsymbol{x}+ )
2 are
This question has multiple correct options
( A cdot 3 )
B.
( c cdot 4 )
D. 2
9
122 Obtain all the zeroes of ( 3 x^{4}+6 x^{3}- ) ( 2 x^{2}-10 x-5, ) if of its zeroes are ( sqrt{frac{5}{3}} ) ( mathfrak{Q}-sqrt{frac{mathbf{5}}{mathbf{3}}} ) 10
123 Find: ( (5 m+7 n)^{2} ) 9
124 Perform the division ( left(a^{4}-a^{3}+a^{2}-right. )
( a+1) divleft(a^{3}-2right) )
10
125 Write the polynomial in standard form and also write down their degree. ( left(p^{2}+2right)left(p^{2}+7right) ) 10
126 State true or false:
If ( a+2 b=5 ; ) then
( a^{3}+8 b^{3}+30 a b=125 )
A. True
B. False
9
127 f ( 2 x+y=14 ) and ( x y=6, ) Find the
value of ( 4 x^{2}+y^{2} )
9
128 Find the number of zeroes of the
quadratic ( x^{2}+7 x+10 ) and verify the
relationship between the zeroes and the the co-efficients.
10
129 What must be added to ( f(x)=4 x^{4}+ )
( 2 x^{3}+2 x^{2}+x-1 ) so that the resulting
polynomial is divisible by ( g(x)=x^{2}+ )
( 2 x-3 )
A. ( -61 x+65 )
в. ( 2 x-15 )
c. ( -15 x+2 )
D. None of these
10
130 ff ( x+2 y+3 z=0 ) and ( x^{3}+4 y^{3}+ )
( mathbf{9} z^{3}=18 x y z ; ) evaluate:
( frac{(x+2 y)^{2}}{x y}+frac{(2 y+3 z)^{2}}{y z}+ )
( frac{(3 z+x)^{2}}{z x} )
A . 18
B. 23
c. 16
D. 11
9
131 If the product of two numbers is 21 and their difference is ( 4, ) then the ratio of the sum of their cubes to the difference of
their cubes is
( mathbf{A} cdot 185: 165 )
B . 165: 158
c. 185: 158
D. 158: 145
9
132 Find the roots of the following equation ( 2 y^{2}+frac{15}{y^{2}}=12, ) then
A ( cdot quad y=pm sqrt{frac{6+sqrt{6}}{4}}, y=pm sqrt{frac{6-sqrt{6}}{2}} )
в. ( quad y=pm sqrt{frac{6+sqrt{6}}{2}}, y=pm sqrt{frac{6-sqrt{5}}{2}} )
c. ( y=pm sqrt{frac{6+sqrt{6}}{2}}, y=pm sqrt{frac{6-sqrt{6}}{2}} )
D. ( y=pm sqrt{frac{6+sqrt{5}}{2}}, y=pm sqrt{frac{6-sqrt{6}}{2}} )
10
133 For ( frac{boldsymbol{x}^{mathbf{3}}+mathbf{2} boldsymbol{x}+mathbf{1}}{mathbf{5}}-frac{mathbf{7}}{mathbf{2}} boldsymbol{x}^{2}-boldsymbol{x}^{mathbf{6}}, ) write
i) the degree of the polynomial
ii) the coefficient of ( x^{3} )
iii) the coefficient of ( x^{6} )
iv) the constant term
10
134 Which of the following is INCORRECT?
( mathbf{A} cdot p(x)=5 x+5, ) degree ( =1 )
B ( cdot p(x)=4 x^{4}+4, ) degree ( =4 )
( mathbf{C} cdot p(x)=x^{8}, ) degree ( =8 )
D ( . p(x)=9, ) degree ( =9 )
9
135 Simplify the following.
( b^{4} div b^{5} )
10
136 If ( boldsymbol{x}=mathbf{5}-mathbf{2} sqrt{mathbf{6}}, ) find the value of ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}} ) 9
137 Tuu
5
-1
4.
Assertion : x +11=1 is a linear equation.
Reason: In a linear equation power ofx cannot be negati
10
138 Expand: ( (x y+8)(x y-8) ) 9
139 Given that ( a(a+b)=36 ) and ( b(a+ )
( b)=64, ) where ( a ) and ( b ) are positive,
( (a-b) ) equals:
A . 2.8
B. 3.2
( c .-2.8 )
D. – 2.5
9
140 Find the polynomials whose zeroes are
three times the zeroes of ( 2 x^{2}-3 x+1 )
10
141 If ( a, b, c ) are the roots of the equation
( boldsymbol{x}^{3}+boldsymbol{p} boldsymbol{x}^{2}+boldsymbol{q} boldsymbol{x}+boldsymbol{r}=boldsymbol{0}, ) form the
equation whose roots are ( a-frac{1}{b c}, b-frac{1}{c a}, c-frac{1}{a b} )
10
142 Prove the following identities:
( boldsymbol{a b c}left(sum boldsymbol{a}right)^{3}-left(sum boldsymbol{b c}right)^{3}=boldsymbol{a b c} sum boldsymbol{a}^{3}- )
( sum b^{3} c^{2}=left(a^{2}-b cright)left(b^{2}-c aright)left(c^{2}-a bright) )
9
143 ( f(alpha, beta, gamma ) are the zeros of the polynomial
( boldsymbol{x}^{3}+boldsymbol{p} boldsymbol{x}^{2}+boldsymbol{q} boldsymbol{x}+boldsymbol{2} ) such that ( boldsymbol{alpha} boldsymbol{beta}+mathbf{1}= )
( 0, ) find the value of ( 2 p+q+5 )
10
144 Which type of polynomial is ( (2+x) ? )
A. Linear Polynomial
B. Quadratic Polynomial
c. Cubic Polynomial
D. None of above
9
145 Q 1 ) If the polynomial ( a z^{3}+4 z^{2}+3 z- )
4 and ( z^{3}-4 z+a ) leave the same
remainder when divided by ( z-3, ) find
the value of ( a )
( Q ) 2) If both ( x-2 ) and ( x-frac{1}{2} ) are the
factors of ( p x^{2}+5 x+r, ) show that ( p=r )
Q 3) Without actually division prove that ( 2 x^{4}-5 x^{3}+2 x^{2}-x+2 ) is
divisible by ( x^{2}-3 x+2 )
9
146 Perform the following divisions and give the remainders.
( left(x^{2}+15 x+56right) div(x+8) )
10
147 Carry out the following division. ( 28 x^{4} div 56 x ) 10
148 The integral part of ( (sqrt{2}+1)^{2} ) is:
( A cdot 2 )
B. 3
( c cdot 4 )
D.
9
149 Total number of pencils required are ( operatorname{given} operatorname{by} 4 x^{4}+2 x^{3}-2 x^{2}+62 x-66 . ) If
each box contains ( x^{2}+2 x-3 ) pencils,
then find the number of boxes to be
purchased.
10
150 Find all zeroes of polynomial ( 3 x^{4}+ ) ( 6 x^{3}-2 x^{2}-10 x-5 ) if two zeroes
( operatorname{are} sqrt{5 / 3} ) and ( -sqrt{5 / 3} )
10
151 The degree of the differential equation ( left(frac{d^{2} y}{d x^{2}}right)^{2}+left(frac{d y}{d x}right)^{2}=x sin left(frac{d^{2} y}{d x^{2}}right) )
( A cdot 1 )
B. 2
( c .3 )
D. None of these
10
152 If ( x-frac{1}{x}=5, ) then ( x^{3}-frac{1}{x^{3}} ) equals
A . 125
в. 130
c. 135
D. 140
9
153 Evaluate each of the following using suitable identities:
( (99)^{3} )
9
154 State whether the statement is True or
False.

The square of ( (x+3 y) ) is equal to ( x^{2}+ )
( 6 x y+9 y^{2} )
A. True
B. False

9
155 f ( 3 x+y+z=0 ) show that ( 27 x^{3}+ )
( boldsymbol{y}^{3}+boldsymbol{z}^{3}=mathbf{9} boldsymbol{x} boldsymbol{y} boldsymbol{z} )
9
156 The value of
( frac{(0.31)^{3}-(0.21)^{3}}{0.0961+0.0651+0.0441} ) is
( mathbf{A} cdot mathbf{0} )
B. ( 0 . )
c. 0.2
D. 0.04
9
157 Find the value of ( (a+b)^{2}-(a-b)^{2} )
( mathbf{A} cdot a b )
в. ( 2 a )
( c cdot 3 a b )
D. ( 4 a )
9
158 When ( 4 g^{3}-3 g^{2}+g+k ) is divided by
( g-2, ) the remainder is ( 27 . ) Find the
value of ( k )
( mathbf{A} cdot mathbf{3} )
B. 5
c. 8
D. 12
E . 10
9
159 Solve: ( frac{x^{2}-(y-z)^{2}}{(x+z)^{2}-y^{2}}+frac{y^{2}-(x-z)^{2}}{(x+y)^{2}-z^{2}}+ )
( frac{z^{2}-(x-y)^{2}}{(y+z)^{2}-x^{2}}= )
( A )
B.
( c cdot 1 )
( D )
9
160 ( left(2 m^{2}-3 m+10right) div(m-5) ) 10
161 If the polynomials ( 2 x^{3}+m x^{2}+3 x-5 )
and ( x^{3}+x^{2}-4 x+m ) leaves the same
remainder when divided by ( x-2, ) then
the value of ( m ) is
A ( cdot-frac{3}{13} )
B. ( -frac{13}{3} )
( c cdot frac{3}{13} )
D. ( frac{13}{3} )
9
162 When a positive integer ( y ) is divided by
( 47, ) the remainder is ( 11 . ) Therefore, when
( y^{2} ) is divided by ( 47, ) the remainder will
be
( A cdot 7 )
B. 17
c. 27
D. 37
9
163 Using remainder theorem, find the
remainder when ( 2 x^{3}-3 x^{2}+4 x-5 ) is
divided by ( boldsymbol{x}+mathbf{3} )
( mathbf{A} cdot 204 )
B . -136
( c .-98 )
D. 42
9
164 Simplify:
( (8 a-5 b)^{2} )
9
165 Write the degree of the following polynomials.
(i) ( boldsymbol{p}+boldsymbol{p}^{mathbf{3}}+boldsymbol{p}^{boldsymbol{7}} )
(ii) ( a+a^{3}-a^{0} )
(iii) ( boldsymbol{m}+boldsymbol{a}^{4} boldsymbol{m}+boldsymbol{a}^{5} boldsymbol{m}^{3}-boldsymbol{m}^{2}-boldsymbol{a}^{4} boldsymbol{m}^{boldsymbol{7}} )
10
166 If ( p-frac{1}{p}=4, ) find the value of ( p^{4}+frac{1}{p^{4}} )
A . 16
B. 18
c. 324
D. 322
9
167 Use remainder theorem to find
remainder when ( p(x) ) is divided by ( q(x) ) in the following questions: ( p(x)=x^{4}+ )
( boldsymbol{x}^{3}+boldsymbol{x}^{2}-mathbf{5} boldsymbol{x}+mathbf{1}, boldsymbol{q}(boldsymbol{x})=boldsymbol{x}+mathbf{1} )
9
168 Evaluate: ( frac{xleft(8 x^{2}-32right)}{8 x(x-4)} )
( mathbf{A} cdot x+2 )
B. ( x+4 )
c. ( frac{x^{2}-4}{x-4} )
D. ( x^{2}-4 )
10
169 ( frac{6 a b-b^{2}+12 a c-2 b c}{b+2 c} ) 10
170 51. 1fx–2, then the value of x’
(1) 15
(3) 14
(2) 2
(4) 11
9
171 Find all zeroes of ( 2 x^{4}-3 x^{3}-3 x^{2}+ )
( 6 x-2 ) if 2 zeroes ( sqrt{2} ) and ( -sqrt{2} )
10
172 69. If x + y = 15, then (x – 10)3 +
(y-5) is
(1) 25
(2) 125
(3) 625 (4) O
10
173 Divide
( frac{x^{3}+x+1}{x^{2}-1} )
10
174 Simplify :
¡) ( frac{-14 x^{8} y^{5}+21 x^{10} y-28 x^{7} y^{6}}{7 x^{7} y^{8}} )
ii) ( frac{15 a^{4} x^{8}-30 a^{7} x^{5}-45 a^{6} x^{6}}{20 a^{14} x^{5}} )
iii) ( frac{-60 x^{4} a^{5}-75 x^{3} a^{6}+8 x^{5} a^{4}}{-20 x^{8} a^{4}} )
10
175 Shikhaa has Piggy bank. It is full of one-rupee and fifty-
paise coins. It contains 3 times as many fifty paise coins as
one rupee coins. The total amount of the money in the
bank is 35. How many coins of each kind are there in the
bank?
(a) 14
(b) 16
(c) 48
(d) 42
10
176 ff ( a+b-12=0 ) and ( a b=27 ), then find
( boldsymbol{a}^{boldsymbol{3}}+boldsymbol{b}^{boldsymbol{3}} )
9
177 ( frac{sqrt{a^{2}-b^{2}}+a}{sqrt{a^{2}+b^{2}}+b} div frac{sqrt{a^{2}+b^{2}}-b}{a-sqrt{a^{2}-b^{2}}} ) 10
178 Factorise the following ( : 27(a-b)^{3}+ )
( (2 a-b)^{3}+(4 b-5 a)^{3} )
A ( cdot(a-b)(a-b)(4 b-8 a) )
В. ( 9(a-b)(2 a-b)(4 b-5 a) )
c. ( 9(a-b)(a-2 b)(4 b-a) )
D. ( 94-b)(2 a-b)(b-a) )
9
179 61. If x is a rational number and
(x + 1)3 – (x – 13
(x + 1)2 –(x – 1)2
sum of numerator and denomi-
nator of x is
-101(1) 3
(2) 400
(3) 5
(4) 7100
9
180 Find the values of polynomial ( 3 x^{3}- ) ( 4 x^{2}+7 x-5 ) when ( x=3 ) & ( x=-3 )
A. 61,-143
В. -61,142
c. 61,142
D. -61,-142
10
181 What is the type of polynomial ( 11= ) ( -4 x^{2}-x^{3} ? )
A. Cubic
B. Quadratic
c. Linear
D. None of these
10
182 If ( x=sqrt{6}+sqrt{5}, ) then ( x^{2}+frac{1}{x^{2}}-2=? )
A ( cdot 2 sqrt{6} )
B. ( 2 sqrt{5} )
( c cdot 24 )
D. 20
9
183 ( (x+y-z)^{2}= )
A ( cdot x^{2}+y^{2}-z^{2}+2 x y+2 x z-2 y z )
B ( cdot x^{2}+y^{2}+z^{2}+2 x y-2 x z-2 y z )
C ( cdot x^{2}+y^{2}-z^{2}-2 x y+2 x z+2 y z )
D. None of the above
9
184 If the polynomial ( 6 x^{4}+8 x^{3}-5 x^{2}+ )
( a x+b ) is exactly divisible by the
polynomial ( 2 x^{2}-5, ) then find the
product of the values of ( a ) and ( b )
10
185 What is the degree of the following polynomial expression:
( frac{4}{3} x^{7}-3 x^{5}+2 x^{3}+1 )
A. 7
B. 4
( c cdot 5 )
D.
10
186 A polynomial of 4 is called a
A. quadratic polynomial
B. biquadratic polynomial
c. cubic polynomial
D. none of these
9
187 ( frac{boldsymbol{x}-boldsymbol{y}}{sqrt{boldsymbol{x}}+sqrt{boldsymbol{y}}}=ldots ldots )
( mathbf{A} cdot sqrt{x-y} )
B. ( sqrt{x}+sqrt{y} )
c. ( -(sqrt{x}+sqrt{y}) )
D. ( sqrt{x}-sqrt{y} )
9
188 Factorize ( (5 x-3 y)^{3}+(3 y-8 z)^{3}+ )
( (8 z-5 x)^{3} )
9
189 What is the degree of the polynomial
( 2 a^{2}+4 b^{8} ? )
( A cdot 2 )
B. 10
c. 8
D.
10
190 2
2.
Divide 34 into two parts in such a way that
of one
part is equal to
of the other.
(a)
(c)
10
14
(b) 24
(d) 20
10
191 The polynomial ( 4 x^{2}+2 x-2 ) is a
A. Linear polynomial
B. Quadratic polynomial
c. Cubic polynomial
D. constant polynomial
10
192 The zeros of the polynomial ( n^{3}+9 n^{2}+ )
( 23 n+15 ) are ( a-d, a ) and ( a+d . ) What
is the value of ‘a’?
A . 4
B. -3
( c .6 )
D. 3
9
193 The quadratic polynomial
A. has the highest power equal to 2
B. has the highest power equal to 1
C. has the highest power equal to 3
D. None of the above.
9
194 State whether the statement is True or
False. The cube of ( left(2 x+frac{1}{x}right) ) is equal to ( 8 x^{3}+ ) ( 12 x+frac{6}{x}+frac{1}{x^{3}} )
A. True
B. False
9
195 Write the polynomial in standard form
and also write down their degree. ( 4 p+15 p^{6}-p^{5}+4 p^{2}+3 )
9
196 Simplify:
( left(left(3 x^{2}-2 a xright)+3 a^{2}right)^{3} )
9
197 Which of the following should be added to ( 9 x^{3}+6 x^{2}+x+2 ) so that the sum is
divisible by ( (3 x+1) ? )
A . -4
B. –
( c cdot-2 )
D. –
9
198 If ( boldsymbol{x}-frac{mathbf{1}}{boldsymbol{x}}=mathbf{9}, ) the value of ( boldsymbol{x}^{2}+frac{mathbf{1}}{boldsymbol{x}^{2}} ) is
A. 83
B. 79
c. 11
D.
9
199 Simplify the following into their lowest form: ( frac{6 x^{2}+9 x}{3 x^{2}-12 x} )
A ( cdot frac{2 x+3}{x-4} )
в. ( frac{2 x-3}{x-4} )
c. ( frac{2 x+3}{x+4} )
D. None of these
10
200 Which of the following represents a linear polynomial?
A ( cdot p(x)=3 x+4 )
В ( cdot p(x)=3 x^{3}+4 )
C ( cdot p(x)=4 x^{3}+3 )
D ( cdot p(x)=2 x^{2} )
9
201 Consider the polynomial ( frac{x^{3}+2 x+1}{5}-frac{7}{2} x^{2}-x^{6} )
Write the degree of the above polynomial
( mathbf{A} cdot mathbf{6} )
B. 3
c. 1
D.
9
202 By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial:
( boldsymbol{x}^{4}+mathbf{1} ; boldsymbol{x}-mathbf{1} )
A ( cdot x^{3}+x^{2}+x+1,3 )
B. ( x^{3}+x^{2}+x+1,1 )
c. ( x^{3}+x^{2}+x+1,5 )
D. ( x^{3}+x^{2}+x+1,2 )
10
203 Find the remainder when the polynomial
( 4 y^{3}-3 y^{2}-5 y+1 ) is divided by ( 2 y+3 )
10
204 Find the roots of equation ( x^{2}-3 x- )
( mathbf{1 0}=mathbf{0} )
10
205 Find the quotient and remainder when ( x^{5}-5 x^{4}+9 x^{3}-6 x^{2}-16 x+13 ) is
divided by ( x^{2}-3 x+2 )
10
206 Divide the following and write your answer in lowest terms: ( frac{3 x^{2}-x-4}{9 x^{2}-16} div ) ( frac{4 x^{2}-4}{3 x^{2}-2 x-1} )
A ( frac{3 x+1}{4(3 x+4)} )
В. ( frac{3 x-1}{4(3 x+4)} )
c. ( frac{3 x+1}{4(3 x-4)} )
D. None of these
10
207 ( 25 x^{2}-left(x^{2}-36right)^{2}= )
A ( cdot(x-4)(x+4)(x+9)(x-9) )
B ( cdot(x-4)(4+x)(x+9)(9-x) )
( mathbf{c} cdot(x+4)(x+4)(x-9)(x-9) )
D ( cdot(x-4)(4-x)(x+9)(9+x) )
9
208 55.-
=?
(0.87)4 -(0.13)
0.87% 0.87 +0.13×0.13
(1) 1 (2) 0.87
(3) 0.13 (4) 0.74
9
209 A number was divided successively in order by 4,5 and 6 The remainders were respectively 2,3 and 4 Then find out the number 9
210 Choose the correct answer from the
alternatives given
If the expression ( 2 x^{2}+14 x-15 ) is divided
by ( (x-4) ). then the remainder is
A . 65
B. 0
( c cdot 73 )
D. 45
10
211 Which of the following is NOT a
quadratic polynomial?
A ( cdot p(x)=x^{2}+4 x-16 )
( mathbf{B} cdot p(y)=y^{2}+8 y-10 )
( mathbf{c} cdot p(x)=73 x-84 )
( mathbf{D} cdot p(y)=2 y^{2}-x^{2} )
9
212 Find the degree of given polynomial:
( 4 x^{3}-1 )
9
213 Divide ( 4left(2 x^{2}+5 x+3right) ) by ( 2(2 x+3) ) 10
214 f ( p(x)=x^{42}-2 k ) is divided by ( (x+1) )
the remainder is ( 9, ) what is the value of
k?
9
215 Find the remainder when ( p(x)=2 x^{2}- )
( 5 x-1 ) is divided by ( x-3 )
A .
B.
( c cdot 2 )
D. 3
9
216 State True Or False, if the following expression is a quadratic polynomial:
( boldsymbol{x}^{2}+boldsymbol{x} )
A . True
B. False
9
217 Multiply:
( left(m^{2}-5right) timesleft(m^{3}+2 m-2right) )
10
218 Solve ( left(4 x^{4}-5 x^{3}-7 x+1right) div(4 x-1) ) 10
219 The remainder of
( frac{(5 m+1)(5 m+3)(5 m+4)}{5} ) is
( mathbf{A} cdot mathbf{1} )
B. 2
( c cdot 3 )
( D )
9
220 Find the degree of following polynomial ( 4 x-sqrt{5} )
A ( cdot frac{1}{2} )
B.
( c cdot 2 )
D.
9
221 The polynomial ( 3 x-2 ) is a.
A. Linear polynomial
B. Quadratic polynomial
c. Cubic polynomial
D. constant polynomial
10
222 Divide ( p(x)=x^{3}-3 x^{2}+5 x- )
( mathbf{3} ) by ( boldsymbol{g}(boldsymbol{x})=boldsymbol{x}^{2}-mathbf{2} )
10
223 In the following case, use the remainder
theorem and find the remainder when
( boldsymbol{p}(boldsymbol{x}) ) is divided by ( boldsymbol{g}(boldsymbol{x}) cdot boldsymbol{p}(boldsymbol{x})=boldsymbol{4} boldsymbol{x}^{3}- )
( 12 x^{2}+14 x-3 g(x)=2 x-1 )
9
224 Find and correct errors of the following mathematical expressions:
( frac{3 x}{3 x+2}=frac{1}{2} )
10
225 Factors of ( a^{2}+4 a+4 ) are:
A ( cdot(a+2)^{2} )
в. ( (a+1)^{2} )
c. ( (a-2)^{2} )
D. ( (a-1)^{2} )
9
226 Find the remainder obtained on dividing
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{3}+mathbf{1} ) by ( boldsymbol{x}+mathbf{1} )
10
227 Prove the following identities:
[
begin{array}{l}
frac{boldsymbol{a}^{3}(boldsymbol{b}+boldsymbol{c})}{(boldsymbol{a}-boldsymbol{b})(boldsymbol{a}-boldsymbol{c})}+frac{boldsymbol{b}^{3}(boldsymbol{c}+boldsymbol{a})}{(boldsymbol{b}-boldsymbol{c})(boldsymbol{b}-boldsymbol{a})}+ \
frac{boldsymbol{a}^{3}(boldsymbol{a}+boldsymbol{b})}{(boldsymbol{c}-boldsymbol{a})(boldsymbol{c}-boldsymbol{b})}=boldsymbol{b} boldsymbol{c}+boldsymbol{c} boldsymbol{a}+boldsymbol{a} boldsymbol{b}
end{array}
]
9
228 When the polynomial ( a^{3}+2 a^{2}- )
( 5 a x-7 ) is divided by ( a+1, ) the
remainder is ( R_{1} . ) If ( R_{1}=14 ), find the
value of ( boldsymbol{x} )
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D.
9
229 If ( boldsymbol{a}+boldsymbol{b}=mathbf{7} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{a} boldsymbol{b}=boldsymbol{6}, boldsymbol{f} boldsymbol{i} boldsymbol{n} boldsymbol{d} boldsymbol{a}^{2}-boldsymbol{b}^{2} )
( mathbf{A} cdot pm 35 )
B. ±12
( c .pm 22 )
( mathrm{D} cdot pm 39 )
9
230 68. If the sum of and its recipro-
cal is 1 and a # O, b# 0, then
the value of a + b3 is
(1) 2
(2) –
1 0
(3)
(4) 1
9
231 Find the value of ( 52^{2} ) using standard
identity.
A . 2604
в. 2704
c. 2804
D. 2904
9
232 57.
If 3 (a + b + c) = (a + b + c)2
and a, b, care non-zero real num-
bers, then
(1) a + b = c (2) a + c = b
(3) b + c = a (4) a = b = c
9
233 Find the zeroes of the polynomial in
each of the following:
( h(y)=2 y )
( mathbf{A} cdot mathbf{0} )
B. ( 2 y )
c. ( y )
D. –
10
234 If a polynomial ( a z^{3}+4 z^{2}+2 z-4 ) and
( z^{2}+4 z+a ) leave the same remainder
divide by ( (z-3) . ) Find the value of a.
A . 1
в. ( frac{-17}{26} )
c. -1
D. 17
9
235 63. If a = 2.234, b= 3.121 and c =
-5.355, then the value of a+b3
+ c3-3 abc is
(1)-1
(2) O
(3) 1
(4) 2Y
9
236 Find the value of ( 99 times 101 ) using
standard identity
A . 9999
B. 9989
( mathrm{c} .9979 )
D. 1009
9
237 If ( x+frac{1}{x}=3, ) then ( x^{4}+frac{1}{x^{4}}= )
A. 81
B . 23
c. 25
D. 47
9
238 Find the value of ( left(frac{a}{b-1}right)+ ) ( left(frac{a}{b-1}right)^{2}+left(frac{a}{b-1}right)^{3} ) if ( a+2 b=2 )
A . -6
B. 8
c. 10
D. -12
E . 14
10
239 Find the degree of the polynomial ( left(x^{2}+right. )
( mathbf{9})left(mathbf{5}-boldsymbol{x}^{2}right) )
9
240 Factorise: ( (boldsymbol{a}+mathbf{2 b}-mathbf{3 c})^{mathbf{3}}-boldsymbol{a}^{mathbf{3}}-mathbf{8 b}^{mathbf{3}}+ )
( mathbf{2 7 c}^{mathbf{3}} )
9
241 If ( x^{2}+frac{1}{x^{2}}=83 . ) Find the value of ( x^{3}- )
( frac{1}{m^{3}} )
9
242 Perform the division.
( (10 x-25) div 5 )
10
243 Which of the following is a rational function?
A ( cdot frac{1}{3} sqrt{4 x^{3}+4 x+7} )
в. ( frac{3 x^{3}-7 x+1}{x-2}, x neq 2 )
c. ( frac{3 x^{5}+5 x^{3}+2 x+7}{x^{3 / 2}}, x>0 )
D. ( frac{sqrt{1+x}}{2+5 x}, x neq-2 / 5 )
9
244 Expand ( left[boldsymbol{x}-frac{boldsymbol{2}}{boldsymbol{3}} boldsymbol{y}right]^{boldsymbol{3}} ) 9
245 What should be added to ( 1+2 x-3 x^{2} )
to get ( x^{2}-x-1 ? )
9
246 For polynomial ( boldsymbol{P}(boldsymbol{x})=mathbf{6} boldsymbol{x}^{mathbf{3}}+mathbf{2} mathbf{9} boldsymbol{x}^{mathbf{2}}+ )
( mathbf{4 4} boldsymbol{x}+mathbf{2 1}, ) find ( mathbf{P}(-mathbf{2}) )
9
247 The value of the expression ( frac{left(x^{2}-y^{2}right)^{3}+left(y^{2}-z^{2}right)^{3}+left(z^{2}-x^{2}right)^{3}}{(x-y)^{3}+(y-z)^{3}+(z-x)^{3}} ) is
A ( cdotleft(x^{2}-y^{2}right)left(y^{2}-z^{2}right)left(z^{2}-x^{2}right) )
B. ( 3(x-y)(y-z)(z-x) )
C. ( (x+y)(y+z)(z+x) )
D. ( 3(z+y)(y+z)(z+x) )
9
248 f ( p=5+2 sqrt{6} ) and ( q=frac{1}{p}, ) find ( p^{2}+q^{2} )
is :
A .49
B. 98
( c .100 )
D. None of these
9
249 Find the Quotient and the Remainder when the first polynomial is divided by the second.
( left(6 x^{2}-31 x+47right) ) by ( (2 x-5) )
A. Quotient ( =3 x-8, ) Remainder ( =7 )
B. Quotient = 3x + 8, Remainder = 7
c. Quotient ( =-3 x-8, ) Remainder ( =7 )
D. Quotient ( =-3 x+8, ) Remainder ( =7 )
10
250 The factors of ( 1-p^{3} ) are
A ( cdot(1-p)left(1+p+p^{2}right) )
B ( cdot(1+p)left(1-p-p^{2}right) )
C . ( (1+p)left(1+p^{2}right) )
D. ( (1+p)left(1-p^{2}right) )
9
251 If the quotient obtained on dividing
( x^{4}+10 x^{3}+35 x^{2}+50 x+29 ) by ( (x+ )
4) is ( x^{3}-a x^{2}+b x+6 ) then find ( a ) and
b. Also find the remainder
9
252 If ( boldsymbol{y}=mathbf{3}, ) then ( boldsymbol{y}^{3}left(boldsymbol{y}^{3}-boldsymbol{y}right)= )
A. 300
в. 459
( c cdot 648 )
D. 999
E . 1099
10
253 Evaluate the following:
( (7 x-2 y)^{2} )
( (3 x+7 y)^{2} )
9
254 What is the degree of the polynomial ( boldsymbol{p}(boldsymbol{x})=mathbf{5} boldsymbol{x}^{3}-boldsymbol{8} boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x} ? )
( A cdot 3 )
B . 2
( c cdot 1 )
D.
9
255 ( f(alpha, beta, gamma ) are the zeroes of the cubic
polynomial ( x^{3}+4 x+2, ) then find the
value of:
( frac{1}{alpha+beta}+frac{1}{beta+gamma}+frac{1}{gamma+alpha} )
10
256 If the sum and difference of two
numbers are 20 and 8 respectively then the difference of their squares is :
A ( cdot 12 )
B. 28
( c cdot 160 )
D. 180
9
257 ( mu^{2}+frac{1}{mu^{2}}=79 )
find ( mu+frac{1}{mu} )
9
258 The difference of the degrees of the
polynomials ( 3 x^{2} y^{3}+5 x y^{7}-x^{6} ) and
( 3 x^{5}-4 x^{3}+2 ) is
( A cdot 2 )
B. 3
( c )
D. None
10
259 ( operatorname{Let} fleft(x+frac{1}{x}right)=x^{2}+frac{1}{x^{2}}(x neq 0), ) then
( boldsymbol{f}(boldsymbol{x}) ) equals:
A ( cdot x^{2}-2 )
B . ( x^{2}-1 )
( mathbf{c} cdot x^{2} )
D. None of these
9
260 Write a polynomial of degree 5 using variable ( x ) 10
261 Find the product ( (3+sqrt{2})(3-sqrt{2}) ) 9
262 58. If a2 + b2+ c2-ab-bc- ca = 0
then
(1) a = b c (2) a = b = c
(3) a +b= c (4) a= buc
9
263 What is the degree of the given
monomial ( -11 y^{2} z^{2} ? )
( mathbf{A} cdot mathbf{0} )
B . 2
( c cdot 4 )
D.
10
264 Using remainder theorem, find the reminder when ( x^{3}-a x^{2}+2 x-a ) is
divided by ( boldsymbol{x}-boldsymbol{a} )
( A cdot a )
B. ( a+2 )
( mathbf{c} cdot a+1 )
D. ( a-2 )
9
265 ( a^{12}-1 ) can be factorised as:
( mathbf{A} cdot(a-1)(a-2)(a-3)(a-4) )
B ( cdot(a-1)left(a^{2}+a+1right)(a+1)left(a^{2}+a+1right) )
C ( cdotleft(a^{2}+a+1right)left(a^{2}-a+1right) )
D ( cdot(a-1)left(a^{2}+a+1right)(a+1)left(a^{2}-a+1right)left[left(a^{2}+1right)left(a^{4}-right.right. )
( left.a^{2}+1right) )
9
266 The value of ( 7 x-42 ) is
A. ( 7(x-6) )
B. ( 7(x+6) )
( c cdot-7(x-6) )
D. ( -7(x+6) )
9
267 Verify whether ( x=3 ) is a zero of the
polynomial ( boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}-mathbf{1 5} )
10
268 Two number differ by 5. If their product is ( 336, ) then the sum of the two numbers
is :
A . 21
B . 28
( c .37 )
D. 51
9
269 Evaluate ( (4 a+3 b)^{2}-(4 a-3 b)^{2}+ )
( 48 a b )
A . ( 76 a b )
B. ( 96 a b )
( c .46 a b )
D. ( 106 a b )
9
270 Write the degree of the following polynomial :
( 5 x^{2} y z^{3}+x y^{4} z^{2} )
( A cdot 3 )
B. 2
( c cdot 7 )
D.
10
271 Simplify:
( mathbf{2 0}(boldsymbol{y}+mathbf{4})left(boldsymbol{y}^{2}+mathbf{5} boldsymbol{y}+mathbf{3}right) div mathbf{5}(boldsymbol{y}+mathbf{4}) )
A ( cdot 5left(y^{2}+5 y+3right) )
B ( cdot 4left(y^{2}-5 y+3right) )
( mathbf{c} cdot 4left(y^{2}+5 y-3right) )
D. ( 4left(y^{2}+5 y+3right) )
10
272 Find the product of ( (a-3)(a-5)(a-7) ) 9
273 If ( boldsymbol{x}=mathbf{2}, boldsymbol{x}=mathbf{0} ) are roots of the
polynomials ( f(x)=2 x^{3}-5 x^{2}+a x+ )
( b, ) then find the values of ( a ) and ( b )
A ( cdot a=2, b=0 )
В. ( a=7, b=0 )
c. ( a=3, b=0 )
D. ( a=1, b=0 )
10
274 Find the degree of the given algebraic
expression ( 2 y^{2} z+10 y z )
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D. 10
9
275 What is the quotient when ( left(x^{3}+8right) ) is
divided by ( left(x^{2}-2 x+4right) ? )
( mathbf{A} cdot x-2 )
B. ( x+2 )
c. ( x+1 )
D. ( x-1 )
10
276 Assertion : Vx+9x = 3 is not a linear equation.
Reason: Linear equation involves only linear polynomials.
10
277 Find the remainder when ( 10 x-4 x^{2}-3 )
is divided by ( x+2 ) using remainder
theorem.
A . -60
B. 39
( c .-39 )
D. None of these
9
278 The degree of ( 3 x^{2} y^{4} z^{6} ) is
( A cdot 2 )
B. 12
( c cdot 4 )
D. 6
10
279 Factorize:
( (x-y)^{3}-8 x^{3} )
( mathbf{A} cdot-2(x+y)left(7 x^{2}-4 x y+y^{2}right) )
B . ( -(x-y)left(x^{2}-4 x y+6 y^{2}right) )
( mathbf{c} cdot-(x+2 y)left(x^{2}-4 x y+y^{2}right) )
( mathbf{D} cdot-(x+y)left(7 x^{2}-4 x y+y^{2}right) )
9
280 If two of the zeros of equation ( 2 x^{4}- ) ( 3 x^{3}-3 x^{2}+6 x-2, ) are ( sqrt{2} ) and ( -sqrt{2} )
and other two are ( ^{prime} a^{prime} ) and ( ^{prime} b^{prime}, ) then ( a b= )
0. ( P ), then the value of ( p= )
10
281 Find the degree of the following polynomial
( boldsymbol{x}^{2}-mathbf{9} boldsymbol{x}+mathbf{2 0} )
10
282 If ( a=2 overline{3}+2 overline{3}, ) then
A. ( a^{3}-6 a-6=0 )
В . ( a^{3}-6 a+6=0 )
c. ( a^{3}+6 a-6=0 )
D. ( a^{3}+6 a+6=0 )
9
283 Find the value of ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1} ) at
( boldsymbol{x}=mathbf{2} )
( A cdot 3 )
B. – –
( c )
D. –
10
284 Perform the division: ( 2 x^{2}+2 x+11 ) by
( boldsymbol{x}+mathbf{3} )
10
285 Using the identity ( (boldsymbol{a}-boldsymbol{b})^{2}=boldsymbol{a}^{2}- )
( 2 a b+b^{2} ) compute ( (5 a-4 b)^{2} )
9
286 ( boldsymbol{p}(boldsymbol{y})=mathbf{5} boldsymbol{y}^{3}-boldsymbol{2} boldsymbol{y}^{2}+boldsymbol{y}+mathbf{1 0} ) is a
polynomial in ( y ) of degree
( A cdot 0 )
B.
( c cdot 2 )
D. 3
9
287 Divide ( (10 x-25) div(2 x-5) ) 10
288 Factorise:
( boldsymbol{p}^{3}(boldsymbol{q}-boldsymbol{r})^{3}+boldsymbol{q}^{3}(boldsymbol{r}-boldsymbol{p})^{3}+boldsymbol{r}^{3}(boldsymbol{p}-boldsymbol{q})^{3} )
9
289 What is ( frac{x^{2}-3 x+2}{x^{2}-5 x+6} div frac{x^{2}-5 x+4}{x^{2}-7 x+12} )
equal to
A. ( frac{x+3}{x-3} )
B.
c. ( frac{x+1}{x-1} )
D.
10
290 Divide ( boldsymbol{a}+boldsymbol{b} ) by ( boldsymbol{a}^{1 / 3}+boldsymbol{b}^{1 / 3} ) 10
291 If ( a^{3}-3 a^{2} b+3 a b^{2}-b^{3} ) is divided by
( (a-b), ) then the remainder is
A ( cdot a^{2}-a b+b^{2} )
B ( cdot a^{2}+a b+b^{2} )
( c )
D.
10
292 Solve:
( 8 l^{3}-36 l^{2} m+54 l m^{2}-27 m^{3} )
10
293 Divide the following and write your answer in lowest terms: ( frac{x}{x+1} div ) ( frac{x^{2}}{x^{2}-1} )
A ( cdot frac{x-1}{x} )
в. ( frac{x+1}{x} )
c. ( frac{x-1}{x^{2}} )
D. None of these
10
294 Using appropriate identity, factorise the following:
( (1) 49 a^{2}+70 a b+25 b^{2} )
( (2) 9 a^{2}-30 a b+25 b^{2} )
9
295 Factorise and then divide the given
algebraic expressions.
1. ( left(12 r^{2}+8 r^{2}-4 r^{2}right) b yleft(-4 r^{2}right) )
2. ( left(frac{4}{9} x^{2}-49 z^{2}right) b y(2 x+21 z) )
( 3 cdotleft(5 a^{2} b^{2}+15 a^{2} b^{2}-20 a^{4} bright) b y 25 a b^{2} )
4. ( left(49 a^{2}-56 aright) b y(21 a-24) )
10
296 Factorize:
( 4 a^{2}-12 a+9-49 b^{2} )
A ( cdot(2 a+7 b-3)(8 a-7 b-3) )
в. ( (2 a-7 b-3)(8 a-7 b+3) )
c. ( (2 a-7 b-3)(2 a-7 b+3) )
D. ( (2 a+7 b-3)(2 a-7 b-3) )
9
297 Find the degree of the polynomial given
below:
( boldsymbol{x}^{5}-boldsymbol{x}^{4}+mathbf{3} )
9
298 Find the degree of the following polynomial ( 2 x+4+6 x^{2} ) 10
299 Decide using factor theorem, whether
( (x-2) ) is a factor of ( x^{3}-4 x^{2}-4 )
9
300 Check whether the first polynomial is a factor of the second polynomial by
applying the division algorithm. ( x^{3}- )
( mathbf{3} boldsymbol{x}+mathbf{1}, boldsymbol{x}^{mathbf{5}}-mathbf{4} boldsymbol{x}^{mathbf{3}}+boldsymbol{x}^{mathbf{2}}+mathbf{3} boldsymbol{x}+mathbf{1} )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
301 If ( a+b+2 c=0, ) then the value of ( a^{3}+ )
( b^{3}+8 c^{3} ) is equal to
A . ( 3 a b c )
B. ( 4 a b c )
( c cdot a b c )
D. ( 6 a b c )
9
302 ( left(5 x^{2}-9 x+3right),left(10 x^{4}+17 x^{3}-right. )
( left.62 x^{2}+30 x-3right) )
10
303 Expand ( (k+4)^{3} ) 10
304 The polynomial ( boldsymbol{p}(boldsymbol{x})=boldsymbol{a} boldsymbol{x}^{3}+boldsymbol{4} boldsymbol{x}^{2}+ )
( 3 x-4 ) and ( q(x)=x^{3}-4 x+a ) leave
same remainder when divided by
( (x-3) . ) Find ( a ) and hence find the
remainder when ( p(x) ) is divided by
( (x-2) )
9
305 Which of the following is a cubic polynomial?
A. ( x^{3}+3 x^{2}-4 x+3 )
B. ( x^{2}+4 x-7 )
( c cdot 3 x^{2}+4 )
D. ( 3left(x^{2}+x+1right) )
10
306 If ( a^{2}+b^{2}=34 ) and ( a b=12 ; ) find
( 7(a-b)^{2}-2(a+b)^{2} )
A . 48
B. -46
c. -45
D. 46
9
307 What is the degree of the given
monomial ( -x y^{2} ? )
( A cdot 2 )
B. 3
( c cdot 4 )
D. none
9
308 If ( a^{2}+b^{2}=34 ) and ( a b=12 ; ) find :
( 7(a-b)^{2}-2(a+b)^{2} )
A. 186
B . 46
c. -46
D. -186
9
309 Use the identity ( (x+a)(x+b)=x^{2}+ )
( (a+b) x+a b ) to find the following
product.
( left(2 a^{2}+9right)left(2 a^{2}+5right) )
9
310 Evaluate using expansion of ( (a+b)^{2} ) or
( (a-b)^{2}: )
( (20.7)^{2} ) is 428.49
If true then enter 1 and if false then
enter 0
9
311 Write the degree of the following polynomial. ( 12-x+4 x^{3} ) 10
312 ( 1+5 x ) is a quadratic polynomial
A. True
B. False
9
313 Verify ( t=1 ) is a zero of the polynomial
( 2 t^{3}-3 t^{2}+7 t-6 )
10
314 Assertion
Degree of a zero polynomial is not
defined.
Reason
Degree of a non-zero constant
polynomial is 0
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
10
315 For a polynomial, dividend is ( x^{4}+4 x- )
( 2 x^{2}+x^{3}-10, ) quotient is ( x^{2}+3 x- )
( 3 x^{2}+4 x+12 ) and remainder is 14
then divisor is equal to
A. ( x^{2}+2 )
B . ( x^{2}-2 )
c. ( x+2 )
D. None of these
10
316 Evaluate ( frac{(-40+80 a)}{8 a} ) 10
317 UCHUU U
UU ULULLAH
3.
a 8 6x -2
Assertion : 4x + = is a linear equation.
Reason: Solution of the equation is-2.
10
318 Which of the following is NOT a
quadratic polynomial?
( mathbf{A} cdot p(x)=p x^{2}+q x+r )
B ( cdot p(x)=a x^{2}+b x+c )
( mathbf{c} cdot p(x)=x cdot x^{2}+x cdot x+x )
D ( cdot p(x)=m x^{2}+n x+l )
10
319 Expand ( (boldsymbol{p}-boldsymbol{2} boldsymbol{q}+boldsymbol{r})^{2} )
( mathbf{A} cdot p^{2}+4 q^{2}+r^{2}-4 p q-4 q r+2 r p )
B ( cdot p^{2}-4 q^{2}+r^{2}-4 p q-4 q r+2 r p )
C ( cdot p^{2}+4 q^{2}-r^{2}-4 p q-4 q r+2 r p )
D. None of these
9
320 Simplify ( -3 x y z div z^{2} ) 10
321 Evaluate ( left(x^{2}-8 x+12right) div(x-6) )
A. ( x-2 )
B. ( x+2 )
c. ( x )
D. None
10
322 Factorize
( 2 x^{2}+4 x+2=0 )
9
323 Find the cube of ( 3 a-2 b )
B . ( a^{3}-54 a^{2} b+6 a b^{2}-b^{3} )
( mathbf{c} cdot 27 a^{3}-54 a^{2} b+6 a b^{2}-8 b^{3} )
D. ( a^{3}-54 a^{2} b-36 a b^{2}-8 b^{3} )
9
324 If ( x^{2}-(a+b) x+a b=0, ) then the
value of ( (x-a)^{2}+(x-b)^{2} ) is
( mathbf{A} cdot a^{2}+b^{2} )
B. ( (a+b)^{2} )
c. ( (a-b)^{2} )
D. ( a^{2}-b^{2} )
9
325 Find the product ( :(x-3)(x+3)left(x^{2}+right. )
( mathbf{9} )
9
326 If ( a^{2}+b^{2}=29 ) and ( a b=10, ) then find
( a-b )
A . 10
B. 3
( c cdot 9 )
D. 19
9
327 The degree of a polynomial ( 2 x^{5}-5 x^{3}- )
( 10 x+9 ) is
A . 5
B. 3
c. 1
D.
9
328 f ( x+a ) is one of the factors of ( p(x)= )
( 2 x^{2}+2 a x+5 x+10, ) then find ( a )
9
329 The degree of the polynomial ( 2 x-1 ) is
A. 0
B. ( frac{1}{2} )
( c cdot-1 )
D.
10
330 ( x^{2}+frac{1}{x^{2}}=6 )
Find
(i) ( x^{3}-frac{1}{x^{3}} )
(i) ( x^{6}+frac{1}{x^{6}} )
9
331 If the degree of ( 12 x^{3} y^{8} z^{n} ) is ( 14, ) then
( boldsymbol{n}= )
9
332 ( 4 r^{3} ) is a quadratic polynomial
A. True
B. False
9
333 Let ( Q(x) ) denotes the quotient which results from the division of the
polynomial ( x^{5}+3 x^{4}-x^{3}+8 x^{2}-x+ )
( 8 mathrm{by} x^{2}+1 ) The sum of the square of the coefficient of ( Q(x) ) is
A . 36
B. 37
c. 38
D. 39
10
334 54. ( + ) simplifies to 9
335 4.
Let a>0, b>0 and c>0. Then the roots of the equation
ax2 + bx+c=0
(1979)
(a) are real and negative (b) have negative real parts
(c) both (a) and (b) (d) none of these
10
336 61.
If x + y = z, then the expression
x + y – 2+ 3xyz will be equal
to :
(1) O
(2) 3xyz
(3) -3xyz (4) z
9
337 If ( x^{3}+6 x^{2}+4 x+k ) is exactly divisible
by ( x+2, ) then ( k ) is equal to
A . – 6
B. – –
( c cdot-8 )
D. -10
9
338 Classify the following as linear, quadratic and cubic polynomials
( x-1 )
10
339 If ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{7}, ) find ( boldsymbol{x}^{mathbf{3}}+frac{mathbf{1}}{boldsymbol{x}^{mathbf{3}}} ) 9
340 Write the degree of each of the following polynomials:
(i) ( 5 x^{3}+4 x^{2}+7 x )
(ii) ( 4-y^{2} )
(iii) ( 5 t-sqrt{7} )
(iv) 3
10
341 Which of the following expressions are polynomials in one variable and which
are not? State reasons for your answer
(i) ( 4 x^{2}-3 x+7 )
(ii) ( y^{2}+sqrt{2} )
(iii) ( 3 sqrt{t}+t sqrt{2} )
(iv) ( boldsymbol{y}+frac{mathbf{2}}{boldsymbol{y}} )
(v) ( x^{10}+y^{3}+t^{50} )
10
342 64. If x = 2 – 21/3 + 22/3, then the
value of x-6×2 + 18x + 18 is
(1) 22
(2) 33
(3) 40
(4) 45
(1) 22
(2) 23
9
343 Show that:
( (a-b)(a+b)+(b-c)(b+c)+(c- )
( boldsymbol{a})(boldsymbol{c}+boldsymbol{a})=mathbf{0} )
9
344 Test whether ( x^{5}+5 x^{3}+3 x ) is divisible
by ( (x-1) )
9
345 Find the degree of the following polynomial ( x^{3}+2 x^{2}-5 x-6 ) 9
346 Shew that ( left(a^{2}+b^{2}+c^{2}-b c-c a-right. )
( boldsymbol{a b})left(boldsymbol{x}^{2}+boldsymbol{y}^{2}+boldsymbol{z}^{2}-boldsymbol{z}^{2}-boldsymbol{y} boldsymbol{z}-boldsymbol{z} boldsymbol{x}-boldsymbol{x} boldsymbol{y}right) )
may be put into the form ( A^{2}+B^{2}+ )
( C^{2}-B C-C A-A B )
9
347 Find the degree of the given polynomials.
( x^{0} )
9
348 Find the quotient the and remainder of the following division:
( left(2 x^{2}-3 x-14right) div(x+2) )
10
349 If ( f(x)=a x^{2}+b x+c ) is divided by
( (b x+c), ) then the remainder is:
This question has multiple correct options
A ( cdot frac{a c^{2}}{b^{2}} )
B. ( frac{a c^{2}}{b^{2}}+2 c )
c. ( fleft(-frac{c}{b}right) )
D. ( frac{a c^{2}+2 b^{2} c}{b^{2}} )
9
350 Use remainder theorem to find
remainder when ( p(x) ) is divided by ( q(x) ) in the following questions:
( boldsymbol{p}(boldsymbol{x})=mathbf{2} boldsymbol{x}^{2}-mathbf{5} boldsymbol{x}+mathbf{7}, boldsymbol{q}(boldsymbol{x})=boldsymbol{x}-mathbf{1} )
9
351 Find the cube of 108 9
352 If the quotient on dividing, ( 8 x^{4}-2 x^{2}+ )
( 6 x-7 ) by ( 2 x+1 ) is ( 4 x^{3}+p x^{2}-q x+3 )
then find ( boldsymbol{q}-boldsymbol{p} )
10
353 Divide the polynomial ( p(x) ) by the polynomial ( g(x) ) and find the quotient and remainder in each of the following. ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{3}-boldsymbol{3} boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-boldsymbol{3} quad boldsymbol{g}(boldsymbol{x})= )
( x^{2}-2 )
10
354 Without finding the cubes, factorise the following:
( (x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3} )
9
355 If ( boldsymbol{x}+boldsymbol{y}+boldsymbol{z}=mathbf{0} ) then what is the value
of ( frac{x^{2}}{y z}+frac{y^{2}}{z x}+frac{z^{2}}{x y} ? )
A ( cdot(x y z)^{2} )
B. ( x^{2}+y^{2}+z^{2} )
c. 9
D. 3
9
356 Following polynomars write the degree
of each.
1). ( 6 x^{2}+x+1 )
2). ( y^{9}-3 y^{7}+frac{3}{2} y^{2}+4 )
3). ( 2 x+1 )
4). ( 5 t-sqrt{11} )
9
357 Factorise the expression: ( (x-2 y+ )
( 3 z)^{2} )
( mathbf{A} cdot x^{2}+y^{2}+9 z^{2}-4 x y+12 y z+6 z x )
B . ( x^{2}+y^{2}+9 z^{2}-4 y-12 y z+6 z x )
( mathbf{c} cdot x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+5 z x )
D. ( x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x )
9
358 Factorise :
( (2 a+b)^{3}-(a+3 b)^{3} )
A ( cdot(a+b)left(7 a^{2}+13 a b+13 b^{2}right) )
B . ( (a-2 b)left(7 a^{2}+17 a b+13 b^{2}right) )
C ( cdot(a-b)left(7 a^{2}+13 a b+17 b^{2}right) )
D. ( (2 a-b)left(7 a^{2}+17 a b+17 b^{2}right) )
9
359 If ( boldsymbol{x}^{mathbf{3}}-boldsymbol{a} boldsymbol{x}^{mathbf{2}}+boldsymbol{b} boldsymbol{x}- )
( boldsymbol{6} ) is exactly divisible by ( boldsymbol{x}^{2}- )
( mathbf{5 x + 6 . t h e n} frac{a}{b} ) is
A. an integer
B. an irrational number
( c cdot frac{6}{11} )
D.
9
360 Assertion :=x+4= -x is a linear equation.
Reason: Four-fifth of a number is more than three fourth of
the number by 4 is a statement of linear equation.
10
361 Simplify: ( (boldsymbol{x}+boldsymbol{y})^{2}+(boldsymbol{x}-boldsymbol{y})^{2} ) 9
362 If ( sqrt{boldsymbol{x}}-sqrt{mathbf{1 2}}=sqrt{mathbf{4}}-sqrt{boldsymbol{x}}, ) then find ( boldsymbol{x} )
A. ( 1+sqrt{3} )
B. ( 2+2 sqrt{3} )
c. ( 4+sqrt{3} )
D. ( 4+2 sqrt{3} )
9
363 The degree of constant polynomial is
A .
B. 2
c. 0
( D )
10
364 80. If x + = 1, then the value of
then the value of
is
x²+x+2
*(1-x)
(1) 1
(3) 2
(2) -1
(4) -2
9
365 On dividing the polynomial ( 9 x^{4}- ) ( 4 x^{2}+5 ) by another polynomial ( 3 x^{2}+ )
( x-1, ) the remainder comes out to be
( a x-b, ) Find ( ^{prime} a^{prime} ) and ( ^{prime} b^{prime} )
9
366 ( left(frac{4}{3} x-frac{3}{4} yright)^{3} ) is equal to
A ( cdot frac{64}{27} x^{3}+frac{27}{64} y^{3}+4 x^{2} y+frac{9}{4} x y^{2} )
B. ( frac{64}{27} x^{3}+frac{27}{64} y^{3}-4 x^{2} y-frac{9}{4} x y^{2} )
C ( frac{64}{27} x^{3}-frac{27}{64} y^{3}-4 x^{2} y+frac{9}{4} x y^{2} )
D. ( frac{64}{27} x^{3}-frac{27}{64} y^{3}+4 x^{2} y-frac{9}{4} x y^{2} )
9
367 Evaluate the following (using identities):
( (11)^{3} )
9
368 OLOT
57. If 2x + 3y = and xy =
then the value of 8×3 + 27yº is
(1) 583
(2) 583
(3) 187
(4) 671
9
369 Evaluate:
( left(y^{3}-216right) div(y-6) )
10
370 Find the quotient and remainder on dividing ( p(x) ) by ( g(x) ) in the following case, without actual division.
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{3}+boldsymbol{4} boldsymbol{x}^{2}-boldsymbol{6} boldsymbol{x}+boldsymbol{2} ; boldsymbol{g}(boldsymbol{x})=boldsymbol{x}- )
3
10
371 Factors of ( (boldsymbol{a}+boldsymbol{b})^{3}-(boldsymbol{a}-boldsymbol{b})^{3} ) are
A ( cdot 2 a bleft(3 a^{2}+b^{2}right) )
B . ( a bleft(3 a^{2}+b^{2}right) )
c. ( 2 bleft(3 a^{2}+b^{2}right) )
D. ( 3 a^{2}+b^{20} )
9
372 Calculate ( left(frac{mathbf{3} boldsymbol{x}}{boldsymbol{x}+mathbf{5}}right) divleft(frac{mathbf{6}}{mathbf{4} boldsymbol{x}+mathbf{2 0}}right) )
given that ( boldsymbol{x} neq-mathbf{5} )
( mathbf{A} cdot 2 x )
в. ( frac{x}{2} )
c. ( frac{9 x}{2} )
D. ( 2 x+4 )
10
373 Use suitable identities to find the
product of
( (x+5)(x+2) )
9
374 Use Remainder theorem to factorize the
following polynomial. ( 2 x^{3}+3 x^{2}-9 x- )
( mathbf{1 0} )
9
375 Evaluate ( left(frac{7}{8} x+frac{4}{5} yright)^{2} )
A. ( frac{49}{64} x^{2}+frac{6}{25} y^{2}+frac{7}{5} x y )
B ( cdot frac{18}{77} x^{2}+frac{16}{5} y^{2}+frac{1}{5} x y )
c. ( frac{13}{22} x^{2}+frac{16}{25} y^{2}+frac{1}{5} x y )
D. ( frac{49}{64} x^{2}+frac{16}{25} y^{2}+frac{7}{5} x y )
9
376 Read the following statements
(a) ( x^{2}-5 x+sqrt{2} ) is a polynomial in ( x )
(b) ( 4 x^{2}-3 sqrt{x}+7 ) is not a polynomial
in ( x )
(c) ( frac{x^{2}+2 x+5}{x+3}(x neq-3) ) is a rational
expression.
(d) ( frac{x^{3}-5 sqrt{x}-1}{x^{2}+x+4} ) is not a rational expression.
Correct options is –
A . acd
B. abc
( c cdot a b d )
D. abcd
9
377 Factorise the expressions and divide
them as directed.5pq ( left(p^{2}-q^{2}right) div )
( mathbf{2} p(boldsymbol{p}+boldsymbol{q}) )
A ( cdot frac{5}{2} q(p-q) )
в. ( frac{3}{2} p q )
c. ( frac{5}{2} q(p+q) )
D ( cdot frac{2}{5} q(p q) )
10
378 What must be added to ( x^{3}-3 x^{2}- )
( 12 x+19 ) so that the result is exactly
divisible by ( x^{2}+x-6 ? )
A ( .2 x-5 )
B. ( 2 x+5 )
c. ( -2 x-5 )
D. ( x+5 )
9
379 Say true or false:
The degree of the sum of two polynomials each of degree 5 is always
( mathbf{5} )
A . True
B. False
9
380 Find the volume of the cuboid with
dimensions ( (x-1),(x-2) ) and ( (x- )
( mathbf{3}) )
9
381 Determine whether the following polynomial has ( (x+1) ) as a factor.
( boldsymbol{x}^{4}-boldsymbol{x}^{3}+boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1} )
9
382 If ( x ) is real, then find the solution of
( sqrt{x+1}+sqrt{x-1}=1 )
A ( cdot frac{5}{4} )
B. ( frac{4}{5} )
( c cdot frac{3}{5} )
D. No such ( x ) exists
9
383 Divide the first expression by the
second. Write the quotient and the
remainder.
( a^{2}-b^{2} ; a-b )
A. Quotient ( =b ), Remainder ( =0 )
B. Quotient ( =a+b ), Remainder ( =0 )
c. Quotient ( =a b ), Remainder ( =a )
D. Quotient ( =a-b ), Remainder ( =a )
10
384 Perform the division: ( 6 x^{3}-23 x+x^{2}+ )
12 by ( 2 x-3 )
10
385 Solve:
( x^{4}+frac{1}{x^{4}} )
9
386 On dividing the polynomial ( 3 x^{3}+ ) ( 4 x^{2}+5 x-13 ) by a polynomial ( g(x), ) the
quotient and the remainder were ( (3 x+ )
10) and ( (16 x-43) ) respectively. Find
( boldsymbol{g}(boldsymbol{x}) )
10
387 Find the remainder when ( p(x)= )
( -3 x^{3}-4 x^{2}+10 x-7 ) is divided by
( boldsymbol{x}-mathbf{2} )
A . -26
в. -27
c. 26
D. 27
9
388 The zero polynomial is the identity of the additive group of polynomials.
A. multiplicative
B. additive
c. multiplicative inverse
D. additive inverse
9
389 Find the degree of the following polynomial ( x^{3}+17 x-21-x^{2} ) 9
390 Expand ( (4 x-3 y)^{3} )
( mathbf{A} cdot 64 x^{3}-144 x^{2} y+108 x y^{2}-27 y^{3} )
B. ( 64 x^{3}+144 x^{2} y+108 x y^{2}-27 y^{3} )
( mathbf{c} cdot 64 x^{3}-144 x^{2} y-108 x y^{2}-27 y^{3} )
D. None of these
9
391 56. If (x + 1) and (x-2) be the fac-
tors of x + (a + 1)x2 – (b-2)x-6,
then the values of a and b will be
(1) 2 and 8 (2) 1 and 7
(3) 5 and 3 (4) 3 and 7
9
392 Identify the cubic polynomial.
A ( cdot x^{5}+y^{3}-x^{3}+x^{4} )
В. ( x^{3}+y^{3}-x^{2} )
c. ( 2 x^{3}+8 y^{3}-9 x^{5} )
D. ( -7 x^{7}+x^{3} )
10
393 What is the degree of the polynomial
( (x+1)left(x^{2}-x-x^{4}+1right) ? )
9
394 Divide :
( 15 x^{3} y^{3} ) by ( 3 x y^{2} )
10
395 62. If * (3-2)-3
x # o, then
the value of x? +
(2)23
(1) 25
(3) 2
(427
9
396 ff ( x=2 ) and ( y=-8 ) find the value of
( (x-y)^{3} )
10
397 Evaluate:
( (a+b)(a-b)left(a^{2}+b^{2}right) ) is ( a^{4}-b^{4} )
If true then enter 1 and if false then
enter 0
9
398 Expand using suitable identities
( (-2 a+5 b-3 c)^{2} )
9
399 Which type of polynomial is ( 5 t-sqrt{7} ? )
A. Linear Polynomial
B. Quadratic polynomial
c. cubic Polynomial
D. None of above
10
400 When ( x^{3}-6 x^{2}+12 x-4 ) is divided by
( x-2, ) the remainder is
A .4
B. 0
( c .5 )
D. 6
9
401 Zero of the zero polynomial is
( mathbf{A} cdot mathbf{0} )
B. 1
C . Any real number
D. Not defined
10
402 Determine whether the following polynomial has ( (x+1) ) as a factor. ( x^{3}-x^{2}-(3-sqrt{3}) x+sqrt{3} ) 9
403 State whether the statement is True or
False.
Evaluate: ( (a+b c)(a-b c)left(a^{2}+b^{2} c^{2}right) ) is
equal to ( a^{4}-b^{4} c^{4} )
A. True
B. False
9
404 ( mathbf{f} boldsymbol{p}(boldsymbol{x})=boldsymbol{a} boldsymbol{x}^{3}+boldsymbol{3} boldsymbol{x}-mathbf{1} boldsymbol{3} ) and ( boldsymbol{q}(boldsymbol{x})= )
( 2 x^{3}-5 x+1 ) are divided by ( x+2 )
remainder is same in each case. find
the value of ( a )
9
405 The term, that should be added
to (4×2 + 8xd so that resulting ex-
pression be a perfect square, is
(1) 2
(2) 4
(3) 2x
(4) 1
9
406 Let ( boldsymbol{f}(boldsymbol{x}) ) be polynomial in ( boldsymbol{x} ) of degree
not less than 1 and ( ^{prime} a^{prime} ) be a real number.
If ( f(x) ) is divided by ( (x-a), ) then the
remainder is ( boldsymbol{f}(boldsymbol{a}) ). If ( (boldsymbol{x}-boldsymbol{a}) ) is a factor
of ( f(x), ) then ( f(a)=0 . ) Find the remainder of ( x^{4}+x^{3}-x^{2}+2 x+3 )
when divided by ( boldsymbol{x}-mathbf{3} )
A. 108
B. 98
c. 165
D. 170
9
407 Write the degree of the following polynomial:
( mathbf{7} p^{2} boldsymbol{q}^{3} boldsymbol{t}-mathbf{1} mathbf{1} boldsymbol{p}^{4} boldsymbol{t}+mathbf{2} boldsymbol{p}^{8} )
( A cdot 3 )
B. 5
( c cdot 7 )
( D )
10
408 ( 20 a^{2}-45= )
( mathbf{A} cdot 5(3-2 a)(3+2 a) )
B. ( 5(2 a-3)(2 a-3) )
( mathbf{c} cdot 3(5+2 a)(5-2 a) )
D. ( 3(2 a+5)(2 a-5) )
9
409 ( frac{a^{2}-b^{2}-2 b c-c^{2}}{a^{2}+b^{2}+2 a b-c^{2}} ) is equivalent to
A ( cdot frac{a+b+c}{a-b+c} )
в. ( frac{a-b-c}{a+b-c} )
c. ( frac{a-b-c}{a-b+c} )
D. ( frac{a-b+c}{a+b+c} )
10
410 The degree of a polynomial ( x^{3}-27 ) is
( mathbf{A} cdot mathbf{3} )
B.
c. 26
D. 27
10
411 Solve: ( frac{5 a^{3}-4 a^{2}+3 a+18}{a^{2}-2 a+3} ) 10
412 Divide the first expression by the second. Write the quotient and the remainder.
( x^{2}-frac{1}{4 x^{2}} ; x-frac{1}{2 x} )
A ( cdot ) Quotient ( =x+frac{2}{2 x}, ) Remainder ( =1 )
B. Quotient ( =2 x+frac{1}{2 x} ), Remainder = 0
c. quotient ( =x-frac{1}{2 x}, ) Remainder ( = )
D. Quotient ( =x+frac{1}{2 x}, ) Remainder ( =0 )
10
413 The remainder obtained when ( t^{6}+ ) ( 3 t^{2}+10 ) is divided by ( t^{3}+1 ) is:
A ( cdot t^{2}-11 )
B . ( t^{3}-1 )
( c cdot 3 t^{2}+11 )
D. none of these
9
414 67. The LCM of two numbers is 495
and their HCF is 5. If the sum of
the numbers is 100, then their
difference is :
(1) 10 (2) 46
(3) 70 (4) 90
9
415 ( frac{0.86 times 0.86 times 0.86+0.14 times 0.14 times 0.1}{0.86 times 0.86-0.86-0.14+0.14 times 0.1} )
is equal to
A . 1
B. 0
c. 2
D. 10
9
416 Polynomials of degrees 1,2 and 3 are called
polynomials respectively.
A. cubic, linear, quadratic
B. linear, quadratic, cubic
c. quadratic, linear, cubic
D. none of the above
10
417 The value of ( (a+b)^{2}-2(a-b)^{2}+ )
( (a-b)(a+b) ) is
A ( cdot 4 a b-b^{2} )
B . ( 2 a b-b^{2} )
( c cdot 3 a b-b^{2} )
D. ( 6 a b-2 b^{2} )
9
418 59. If a = 11 and b = 9, then the
la? +62 + ab
value of 23 – 63 is
(1)
(2) 2
(3) 2
(4) 20
9
419 Classify the following as a constant, linear, quadratic and cubic polynomials
( sqrt{2} x-1 )
A. Linear
B. Quadratic
c. cubic
D. None of these
9
420 Given a function ( f ) such that ( f(4)=5 )
then which of the following is/are true
for ( boldsymbol{f} ? )
A ( . f(x) neq x+1 )
в. ( f(x) neq 2 x-3 )
c. ( f(x) neq 3 x-2 )
D. ( f(x) neq 4 x-11 )
10
421 Find the value of ( 1.05 times 0.95 ) using
standard identity
A . 0.9985
B. 0.9975
c. 0.9875
D. 0.9995
9
422 Expand the following using identities ( (x+7)(y+5) ) 9
423 Perform the division: ( x^{4}-16 ) by ( x-2 ) 10
424 Find the degree of the expression ( left[x+left(x^{3}-1right)^{frac{1}{2}}right]^{5}+left[x-left(x^{3}-1right)^{frac{1}{2}}right]^{5} ) 9
425 The polynomial having atmost 3 zero
A. constant polynomial
B. linear polynomial
C. quadratic polynomial
D. cubic polynomial
10
426 If ( a-b-2=0 ) and ( a^{3}-b^{3}-6 a b=k )
then find the value of ( k )
9
427 The greatest index of a variable in the
polynomial ( 5 x^{2}+3 x+1 ) is
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D. 4
9
428 Factorise ( : 8 x^{3}-27 y^{3}-2 x+3 y )
A ( cdot(2 x+3 y)left(4 x^{2}-x y+9 y^{2}+1right) )
В ( cdot(2 x+y)left(4 x^{2}-6 x y-9 y^{2}right) )
C ( cdot(x-3 y)left(4 x^{2}-3 x y+9 y^{2}right) )
D ( cdot(2 x-3 y)left(4 x^{2}+6 x y+9 y^{2}-1right) )
9
429 Factorize:
( 4 x y-x^{2}-4 y^{2}+z^{2} )
( mathbf{A} cdot(z+x-2 y)(z-x+2 y) )
B . ( (z-x-2 y)(z-x+2 y) )
( mathbf{c} cdot(z+x-2 y)(z-x-2 y) )
D. ( (z+x-2 y)(z-x+y) )
9
430 ( (5 x+2 y+3 z)^{2} )
( mathbf{A} cdot 25 x^{2}+4 y^{2}+9 z^{2}+20 x y+12 y z+30 z x )
B ( cdot 25 x^{2}-4 y^{2}+9 z^{2}+20 x y+12 y z+30 z x )
( mathbf{c} cdot 25 x^{2}+4 y^{2}-9 z^{2}+20 x y+12 y z+30 z x )
D. None of these
9
431 Workout the following divisions
( mathbf{3 6}(boldsymbol{x}+mathbf{4})left(boldsymbol{x}^{2}+mathbf{7} boldsymbol{x}+mathbf{1 0}right) div mathbf{9}(boldsymbol{x}+mathbf{4}) )
( mathbf{A} cdotleft(x^{2}+7 x+10right) )
B. ( 4left(x^{2}+7 x+6right) )
c. ( 4left(x^{2}+7 x+10right) )
D. None
10
432 If ( alpha ) and ( beta ) are the zeroes of a polynomial
( x^{2}-4 sqrt{3} x+3, ) then find the value of
( boldsymbol{alpha}+boldsymbol{beta}-boldsymbol{alpha} boldsymbol{beta} )
10
433 What must be added to ( x^{3}-3 x^{2}- )
( 12 x+19, ) so that the result is exactly
divisible by ( x^{2}+x-6 ? )
A ( .2 x+5 )
в. ( 4 x-4 )
c. ( 2 x+3 )
D. ( -2 x-5 )
9
434 Divide and write the quotient and the remainder.
( left(p^{2}+7 p-5right) div(p+3) )
10
435 Find the zeroes of polynomial ( boldsymbol{p}(boldsymbol{x})= )
( 6 x^{2}-3 )
10
436 How to divide the equation in algebraic expression 9
437 71. I x*)2, then the value of
(1) 212
(3) 25
(2) 2
(4) 27
9
438 Write down the degree of the following polynomial:
( 7 x^{3}-5 x^{3} y^{2}+4 y^{4}-9 )
( A cdot 3 )
B. 4
( c cdot 5 )
( D )
9
439 Evaluate :
( frac{6 x^{2}-x-2}{3 x-2} )
10
440 Classify the following as linear, quadratic and cubic polynomials:
( boldsymbol{x}^{boldsymbol{3}}-boldsymbol{4} )
A. Cubic
B. Linear
c. Quadratic
D. None of the above
9
441 Write each of the following polynomials in the standard form. Also, write their
degree:
( a^{2}+4+5 a^{6} )
9
442 If ( 3 x-frac{1}{3 x}=5, ) then find ( 81 x^{4}+frac{1}{81 x^{4}} ) 9
443 Simplify:
( left[3 a^{2}-2 a^{2}+9 a^{2}-left{6 a^{2}-right.right. )
( left.left(-2 a^{2}+3 a^{2}right)right} )
9
444 boty
26. For the equation 3×2 + px +3 = 0,p>0, if one of the root is
square of the other, then p is equal to
(2000)
(a) 1/3
(b) 1
(C) 3
(d) 2/3
10
445 State whether the following expressions are polynomials in one variable or not. Give reasons for your answer. ( sqrt[3]{t}+2 t ) 10
446 Find ( y^{2}+frac{1}{y^{2}} ) and ( y^{4}+frac{1}{y^{4}} ) if ( y+frac{1}{y}=9 ) 9
447 The variable in the quadratic
polynomial ( t^{2}+4 t+5 ) is
( mathbf{A} cdot mathbf{1} )
B. 4
( c cdot t )
D. 5
10
448 Solve ( :left[left(4 x^{4}-3 x^{3}-2 x^{2}+4 x-3right)right. )
divide by ( (x-1) )
10
449 Degree of the polynomial
( left(a^{2}+1right)(a+2)left(a^{3}+3right) ) is
( A cdot 3 )
B. 6
( c cdot 2 )
( D )
10
450 Evaluate: ( 96 a b c(3 a-12)(5 b-30) div )
( mathbf{1 4 4}(boldsymbol{a}-mathbf{4})(boldsymbol{b}-mathbf{6}) )
( mathbf{A} cdot 10 a b c )
B. 2abc
( c cdot 2 a b )
D. ( 2 b c )
10
451 ( boldsymbol{p}(boldsymbol{x})=left(boldsymbol{x}^{2}-mathbf{1 0} boldsymbol{x}-mathbf{2 4}right), ) when divided
by ( x+2 ) and ( x neq-2 ) gives the quotient
Q. Find ( Q )
A . ( x-22 )
B. ( x-12 )
c. ( x+12 )
D. ( x+22 )
10
452 The value of a polynomial
A. changes with the change in variable
B. doesn”t change with the change in variable
C. many or may not change with the change in variable
D. all of the above
10
453 According to the remainder theorem when we divide a polynomial ( f(x) ) by
( (x-c), ) the remainder equals
A ( . f(c) )
в. ( f(-c) )
c. 0
D. None of the above
9
454 Evaluate using expansion of ( (a+b)^{2} ) or
( (a-b)^{2}: )
( (9.4)^{2} )
A . 88.36
B. 88.46
c. 89.16
D. 89.56
9
455 ( left(x^{2}+3 x+1right)=(x-2)^{2} ) is an
equation of degree
A. three
B. one
c. four
D. two
9
456 Find the reduced form of the expression ( frac{20 u^{3} v^{2}-15 u^{2} v}{10 u^{4} v+30 u^{3} v^{3}} )
A ( cdot frac{5 u v}{40 u^{7} v^{4}} )
в. ( frac{2 v-1}{u+2 u v^{2}} )
c. ( frac{4 u v-3}{2 u^{2}+6 u v^{2}} )
D. ( frac{2 u v-3 u v^{2}}{u^{2}+6} )
10
457 Find the degree of the polynomial: 5
( boldsymbol{x}^{2} )
10
458 Simplify: ( (3 a-5 b)^{3}-(3 a+5 b)^{3} ) 9
459 69. If x + y +
5+= 4, then
the value of x + y2 is
(1) 2
(2) 4
(3) 8
(4) 16
9
460 Factorise the expression and divide them as directed.
( 12 x yleft(9 x^{2}-16 y^{2}right) div 4 x y(3 x+4 y) )
10
461 The polynomial ( a x^{3}+b x^{2}+x-6 ) has
( (x+2) ) as a factor and leaves a
remainder 4 when divided by ( (x-2) )
Find ( a ) and ( b )
This question has multiple correct options
( mathbf{A} cdot a=0 )
в. ( b=2 )
( mathbf{c} cdot a=2 )
( mathbf{D} cdot b=0 )
9
462 The product of two numbers is 120 and the sum of their squares is ( 289 . ) The sum of the numbers is :
A . 20
B. 23
( c cdot 16 )
D. None of these
9
463 Simplify:
( (2 x+3 y)^{2} )
9
464 If ( p^{2}-6 p+7 ) is divided by ( (p-1) ) the
remainder will be
A. positive
B. zero
c. negative
D. none of these
9
465 ( boldsymbol{f}(boldsymbol{x})=mathbf{2} boldsymbol{x}^{3}-mathbf{5} boldsymbol{x}^{2}+boldsymbol{a} boldsymbol{x}+boldsymbol{a} )
Given that ( (x+2) ) is a factor of ( f(x) )
find the value of the constant ( a )
A . -16
B. 32
( c .-36 )
D. 42
10
466 If ( a x^{3}+b x^{2}+c x+d ) is divided by ( x )
2, then the remainder is equal
A ( . d )
B. ( a-b+c-d )
c. ( 8 a+4 b+2 c+d )
D. ( -8 a+4 b-2 c+d )
9
467 A quadratic polynomial has at the most zero(es).
A . zero
B. one
c. three
D. two
10
468 Evaluate:
( (a-3 b)^{2}-4(a-3 b)-21 )
9
469 If ( x^{3}+a x^{2}+b x+6 ) divided by ( x-2 ) as
factor then remainder becomes ( 0, ) and
leaves remainder 3 when divided by
( x-3 ) find the values of a and ( b )
9
470 The sum of two numbers is 9 and their
product is 20. Find the sum of their
cubes
A . 189
в. 130
c. 76
D. 39 9
9
471 If ( frac{a}{b}+frac{b}{a}=1, ) then the value of ( a^{3}+b^{3} )
is-
A .
B. ( a )
( c cdot b )
D.
9
472 Show that ( x+1 ) and ( 2 x-3 ) are factors of
( 2 x^{3}-9 x^{2}+x+12 )
10
473
23. Ifa and B(a<B) are the roots of the equation x2 + bx+c=0.
where c<0<b, then
(20005)
(a) 0<a<B
(b) a<0<B<l al
(c) a<B<0
(d) a<0<al<B
0<a<e
a<<$<la
10
474 Simplify: ( (3 m+5 n)^{2}-(2 n)^{2} ) 9
475 Simplify:
Find ( boldsymbol{x}(boldsymbol{x}+mathbf{1})(boldsymbol{x}+mathbf{2})(boldsymbol{x}+boldsymbol{3}) div boldsymbol{x}(boldsymbol{x}+mathbf{1}) )
A ( cdot(x+2)(x+3) )
B. ( x+2 )
c. ( x+3 )
D. None of these
10
476 Remainder when ( p(x)=x^{4}-5 x+6 ) is
divided by ( g(x)=2-x^{2} ) is ( -m x+2 m )
Find ( boldsymbol{m} )
10
477 58. If a, b, c are real and
al + b2 + 2 = 2 (a – b -c) – 3,
then the value of 2a – 3b + 4c is
(1) -1
(2) O
(3) 1
(4) 2
9
478 If ( n ) is an integer,what is the remainder when ( 5 x^{2 n+1}-10 x^{2 n}+3 x^{2 n-1}+5 ) is
divided by ( x+1 ? )
A .
B. 2
( c cdot 4 )
( D cdot-8 )
( E cdot-13 )
9
479 Determine the factors of ( 216 u^{3}+1 )
A ( cdot(6 u-1)left(36 u^{2}-6 u+1right) )
B . ( (6 u+1)left(36 u^{2}-6 u+1right) )
c. ( (6 u+1)left(6 u^{2}-6 u+1right) )
D. ( (u+1)left(6 u^{2}-6 u+1right) )
9
480 f ( a=x(y-z), b=y(z-x) ) and ( c= )
( z(x-y) . ) What is the value of
( frac{x y z}{a b c}left(frac{a^{3}}{x^{3}}+frac{b^{3}}{y^{3}}+frac{c^{3}}{z^{3}}right) ? )
9
481 52. 9×2 +25-30xcan be expressed
as the square of
(1) -3x-5 (2) 3x + 5
(3) 3x – 5 (4) 3×2 – 25
9
482 Say true or false:
For polynomials ( p(x) ) and any non-zero
polynomial ( g(x), ) there are polynomials ( boldsymbol{q}(boldsymbol{x}) ) and ( boldsymbol{r}(boldsymbol{x}) ) such that ( boldsymbol{p}(boldsymbol{x})= )
( boldsymbol{g}(boldsymbol{x}) boldsymbol{q}(boldsymbol{x})+boldsymbol{r}(boldsymbol{x}), ) where ( boldsymbol{r}(boldsymbol{x})=mathbf{0} ) or
( operatorname{degree} r(x)<operatorname{degree} g(x) . ) This
statement is correctly explains the remainder theorem.
A . True
B. False
9
483 ( frac{x^{-1}}{x^{-1}+y^{-1}}+frac{x^{-1}}{x^{-1}-y^{-1}} ) is equal to
A. ( frac{2 y^{2}}{y^{2}-x^{2}} )
в. ( frac{2 x^{2}}{y^{2}-x^{2}} )
c. ( frac{2 y^{2}}{y^{2}+x^{2}} )
D. none
10
484 Factorise: ( 7 y^{3}+12 z^{3} ) 9
485 66.
If a + b2 + 4c2 = 2 (a + b – 2c) –
3 and a, b, c are real, then the
value of (a + b + c) is
(1) 3
(2) 3-
(3) 2
(4) 2-
9
486 58. If p= 102 then the value of
p (p2 – 6p + 12) is
(1) 1000008 (2) 10000008
(3) 999992 (4) 9999992
9
487 Evaluate using expansion of ( (a+b)^{2} ) or
( (a-b)^{2}: )
( (45)^{2} )
9
488 Which of the following is not a constant polynomial?
A ( cdot p(x)=3^{3} )
B ( cdot p(x)=2^{3} )
( mathbf{c} cdot p(x)=x^{3} )
D ( cdot p(x)=4^{3} )
9
489 The value of
( frac{(mathbf{1 1 9})^{2}+(mathbf{1 1 9})(mathbf{1 1 1})+(mathbf{1 1 1})^{mathbf{2}}}{(mathbf{1 1 9})^{mathbf{3}}-(mathbf{1 1 1})^{mathbf{3}}} ) is
( A )
B. ( frac{1}{8} )
( c cdot 230 )
D. ( frac{1}{23} )
9
490 Give examples of polynomials ( boldsymbol{p}(boldsymbol{x}), boldsymbol{g}(boldsymbol{x}), boldsymbol{q}(boldsymbol{x}) ) and ( boldsymbol{r}(boldsymbol{x}), ) which satisfy
the division algorithm and
(i) ( operatorname{deg} p(x)=operatorname{deg} q(x) )
(ii) ( operatorname{deg} boldsymbol{q}(boldsymbol{x})= )
( operatorname{deg} r(x) ) (iii) ( operatorname{deg} r(x)=0 )
10
491 The quotient when
( left(2 x^{4}-3 x^{3}-x^{2}+4 x-2right) ) divided by
is:
10
492 62. The value of 204 x 197 is
(1) 40218 (2) 40188
(3) 40212 (4) 39812
9
493 If ( x^{2}+y^{2}+10=(2 sqrt{2 x}+4 sqrt{2} y) ) then
the value of ( (x+y) ) is
A ( .4 sqrt{2} )
B. ( 3 sqrt{2} )
( c cdot 6 sqrt{2} )
D. ( 9 sqrt{2} )
9
494 If ( sqrt{2 x-1}-sqrt{2 x+1}+4=0, ) then
( 128 x ) is equal to
A . 120
в. 260
c. 165
D. 200
10
495 f ( x=3, ) then the value of ( 20 x^{7}+x^{5} 3 ) 9
496 Classify the following polynomials as monomials, binomials and trinomials:
( 3 x^{2}, 3 x+2, x^{2}-4 x+2, x^{5}-7, x^{2}+ )
( mathbf{3} boldsymbol{x} boldsymbol{y}+boldsymbol{y}^{2}, boldsymbol{s}^{2}+boldsymbol{3} boldsymbol{s} boldsymbol{t}-boldsymbol{2} boldsymbol{t}^{2}, boldsymbol{x} boldsymbol{y}+boldsymbol{y} boldsymbol{z}+ )
( z x, a^{2} b+b^{2} c, 2 l+2 m )
10
497 Find the cubic polynomial with three different variables.
A ( cdot x^{3}+y^{3}+2^{3}-5^{3} )
B ( cdot a^{3}+b^{3}-c^{2}+1 )
c. ( x^{3}+x^{2}+x )
D. ( x y^{2}+x y^{3}-x y+6^{3} )
9
498 ( f(x)=x^{3}-3 x^{2}+2 x ) then find the
value of ( p(x) ) at ( x=2 )
9
499 Expand ( frac{1}{x^{4}-5 x^{3}+7 x^{2}+x-8} ) in
descending powers of ( x ) to four terms, and find remainder.
10
500 Identify zero polynomial among the following.
A . 0
B. ( x )
( mathbf{c} cdot x^{2} )
D. None of the above
9
501 Find the degree of the expression ( [x+ ) ( left.left(x^{3}-1right)^{frac{1}{2}}right]^{5}+left[x-left(x^{3}-1right)^{frac{1}{2}}right]^{5} ) 10
502 Expand: ( left(a^{2}+4 b^{2}right)(a+2 b)(a-2 b) ) 9
503 The polynomials ( left(2 x^{3}-5 x^{2}+x+aright) )
and ( left(a x^{3}+2 x^{3}-3right) ) when divided by
( (x-2) ) leave the remainders ( R_{1} ) and ( R_{2} )
respectively. Find the value of ( ^{prime} a^{prime} ) in the
following case, if
( boldsymbol{R}_{1}-boldsymbol{2} boldsymbol{R}_{2}=mathbf{0} )
9
504 ( left{x^{2}+10 x+25right} div(x+5) ) 10
505 When ( left(x^{3}-2 x+p x-qright) ) is divided by
( left(x^{2}-2 x-3right), ) the remainder is ( (x-6) )
What are the values of ( p, q ) respectively.
A . -2,-6
в. 2,-6
c. -4,12
D. 2,6
9
506 The degree of the polynomial ( x^{2}- ) ( 5 x^{4}+frac{3}{4} x^{7}-73 x+5 ) is
A. 7
B. ( frac{3}{4} )
( c cdot 4 )
D. -73
10
507 If ( a+b=5 ) and ( a^{2}+b^{2}=13, ) find ab 9
508 What is the remainder, when
( left(4 x^{3}-3 x^{2}+2 x-1right) ) is divided by
( (x+2) ? )
A . – 49
B. 55
( c cdot-30 )
D. 37
10
509 ( (x-2) ) is a factor of the expression ( x^{3}+ )
( a x^{2}+b x+6 . ) when this expression is
divided by ( (x-3), ) it leaves the remainder ( 3 . ) find the values of a and ( b )
9
510 State True or False.
( mathbf{2} a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-2 c a= )
( left[(a-b)^{2}+(b-c)^{2}+(c-a)^{2}right] )
A. True
B. False
9
511 Choose the correct answer from the
alternatives given. If ( x-frac{1}{x}=3 ) then find the value of ( x^{3}+frac{1}{x^{3}} )
A. ( 10 sqrt{13} )
(3) 5
B. ( 100 sqrt{3} )
c. ( 13 sqrt{10} )
D. ( 130 sqrt{10} )
9
512 ( frac{x^{3}+x^{2}+2 x-12}{x-3} ) 10
513 If ( A(x) ) and ( B(x) ) be two polynomials
and ( boldsymbol{f}(boldsymbol{x})=boldsymbol{A}left(boldsymbol{x}^{3}right)+boldsymbol{x} boldsymbol{B}left(boldsymbol{x}^{3}right) . ) If ( boldsymbol{f}(boldsymbol{x}) ) is
divisible by ( x^{2}+x+1 ) then show that it
is divisible by ( x-1 ) also.
10
514 Write the quadratic polynomial with zeros -2 and ( frac{1}{3} ) 10
515 Find the last digit of ( 1^{5}+2^{5}+ldots+99^{5} ) 9
516 Find the cube of ( :left(2 a+frac{1}{2 a}right) ; a neq 0 )
A ( cdot 8 a^{3}+6 a+frac{3}{2 a}+frac{1}{8 a^{3}} )
в. ( 8 a^{3}+3 a+frac{3}{a}+frac{1}{8 a^{3}} )
c. ( 8 a^{3}+3 a+frac{6}{a}+frac{1}{8 a^{3}} )
D. ( 8 a^{3}+6 a+frac{6}{a}+frac{1}{8 a^{3}} )
9
517 Find the remainder when ( x^{3}+p x^{2}+ )
( boldsymbol{q} boldsymbol{x}+boldsymbol{r} ) is divided by ( boldsymbol{x}^{2}+boldsymbol{p} boldsymbol{x}+boldsymbol{q} )
10
518 The least positive value of ( x ) satisfying ( frac{sin ^{2} 2 x+4 sin ^{4} x-4 sin ^{2} x cos ^{2} x}{4-sin ^{2} 2 x-4 sin ^{2} x}=frac{1}{9} )
is
A ( cdot frac{pi}{3} )
B. ( frac{pi}{6} )
c. ( frac{2 pi}{3} )
D. ( frac{5 pi}{6} )
10
519 Find the degree of :
a) ( x^{3}-3 x^{3} y^{6}+8 y^{3} )
b) ( 6 x^{4}-9 x^{3} y^{2}-6 y^{6} )
9
520 ( left(x^{2}-9 x-10right) div(x+1)= )
A . ( x-10 )
B. ( x+10 )
( mathbf{c} cdot x-8 )
D. ( x+8 )
10
521 Which of the following is NOT a constant polynomial?
A ( cdot p(y)=y^{circ} )
В . ( p(x)=x^{o} )
c. ( p(y)=frac{y}{y} )
D. ( p(x)=y x )
9
522 Evaluate the following using suitable
identities
( (999)^{3} )
9
523 Perform the division ( frac{left(x^{2}+1right)left(x^{2}+2right)}{left(x^{2}+3right)left(x^{2}+4right)} ) 10
524 Find a quadratic polynomial each with the give numbers as the sum and product of its zeros respectively. ( sqrt{mathbf{2}}, frac{mathbf{1}}{mathbf{3}} ) 10
525 Solve by using suitable identity: ( a^{4}- )
( b^{4}+2 b^{2}-1 )
9
526 f ( p=2-a ) then prove that ( a^{3}+6 a p+ )
( boldsymbol{p}^{3}-boldsymbol{8}=boldsymbol{0} )
9
527 On dividing ( 3 x^{3}+x^{2}+2 x+5 ) by a
polynomial ( g(x), ) the quotient and
remainder are ( (3 x-5) ) and ( (9 x+10) )
respectively. Find ( g(x) )
10
528 If ( boldsymbol{x}-boldsymbol{y}=-boldsymbol{6} ) and ( boldsymbol{x} boldsymbol{y}=mathbf{4}, ) find the
value of ( boldsymbol{x}^{mathbf{3}}-boldsymbol{y}^{mathbf{3}} )
( mathbf{A} cdot-288 )
в. 288
( c cdot-28 )
D. None of these
9
529 Factorize :
( (2 a+1)^{3}+(a-1)^{3} )
9
530 Twenty years ago, my age was one-third of what it is now
1. My present age is
(a) 66 years
(b) 30 years
(c) 33 years
(d) 36 years
10
531 Factorise:
( 27 a^{2}-75 b^{2} )
( mathbf{A} cdot(3 a+5 b)(3 a-5 b) )
B. ( 3(3 a+5 b)(3 a+5 b) )
( mathbf{c} cdot(3 a+5 b)(a-b) )
D. ( 3(3 a+5 b)(3 a-5 b) )
9
532 There are ( x^{4}+57 x+15 ) pens to be
distributed in a class of ( x^{2}+4 x+2 )
students. Each student should get the minimum possible number of pens. Find the number of pens received by each student and the number of pens
left undistributed ( (boldsymbol{x} epsilon boldsymbol{N}) )
в. ( 9 x-15 )
c. ( 9 x-20 )
D. ( 9 x+13 )
10
533 85. If x y
1
then the value of x
f-
z
1 1
+-+-
y z
is
(1) 9
(3) 4
(2) 3
(4) 6
10
534 Find the degree of the given algebraic
expression
( 3 x-15 )
( mathbf{A} cdot mathbf{1} )
B. 3
( c cdot 2 )
D. -15
10
535 3.
Ifx,y and z are real and different and
(1979)
u=x2 + 4y2 +9z2 – 6yz – 3zx – 2xy, then u is always.
(a) non negative
(b) zero
c) non positive
(d) none of these
9
536 ( boldsymbol{p}(boldsymbol{x})=mathbf{7} boldsymbol{x}^{2}-boldsymbol{9} ) is a
polynomial
A. quadratic
B. linear
c. constant
D. cubic
10
537 Solve ( (boldsymbol{a}+boldsymbol{b}+boldsymbol{c})^{3} ) 9
538 Find the product of ( (sqrt{2}+sqrt{3})(sqrt{2}+sqrt{5})(sqrt{2}+sqrt{7}) ) 9
539 ( operatorname{Let} p(x)=a x^{2}+b x+c ) be a quadratic
polynomial. It can have at most
A. One zero
B. Two zeros
c. Three zeros
D. None of these
10
540 If ( alpha ) and ( beta ) are the zeroes of the
polynomial ( 2 y^{2}+7 y+5, ) write the
values of ( boldsymbol{alpha}+boldsymbol{beta}+boldsymbol{alpha} boldsymbol{beta} )
10
541 ( x^{3}-15 x^{2}+59 x-45=0 ) solve for ( x ) 10
542 State the following statement is True or
False

The zero of the polynomial ( x^{3}-27 ) is 3
A. True
B. False

9
543 If ( a-b=7, a b=8, ) find ( a^{2}+b^{2} ) 9
544 What are the solution(s) to the system
of equations ( boldsymbol{y}=boldsymbol{x}^{2}-mathbf{9} ) and ( boldsymbol{y}-boldsymbol{3}= )
( x ? )
A. -3,0 and 4,7
в. -3,0
c. 4,7
D. 4,-3
10
545 Divide ( p(x) ) by ( g(x) ) in the following case
and verify division algorithm
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x}+boldsymbol{4} ; boldsymbol{g}(boldsymbol{x})=boldsymbol{x}+boldsymbol{2} )
10
546 Simplify: ( (boldsymbol{p}-boldsymbol{q})^{2}+mathbf{4} boldsymbol{p} boldsymbol{q} )
A ( cdot p^{2}-q^{2} )
в. ( (p+q)^{2} )
c. ( (2 p-q)^{2} )
D. ( (2 p-2 q)^{2} )
9
547 The value of ( boldsymbol{p}(boldsymbol{x})=boldsymbol{3} boldsymbol{x}-boldsymbol{2}-boldsymbol{x}^{2} ) at ( boldsymbol{x}= )
3
( A cdot 0 )
B. – 1
( c cdot-2 )
D. – 3
10
548 Write whether the following statements are True or False. Justify your answer The degree of ( x^{2}+2 x y+y^{2} ) is 2
A . True
B. False
10
549 Simplify: ( left(boldsymbol{m}^{2}+boldsymbol{2} boldsymbol{n}^{2}right)^{2}-boldsymbol{4} boldsymbol{m}^{2} boldsymbol{n}^{2} ) 9
550 Simplify: ( (boldsymbol{a}+boldsymbol{b})^{boldsymbol{3}} ) 9
551 Find the polynomial which represents the perimeter of the rectangle whose length is 2 more than its breadth. 10
552 If 1 is zero of the polynomial ( p(x)= )
( a x^{2}-3(a-1) x-1 ) then the value of
‘a’ is
A .
B. –
( c cdot-2 )
D.
10
553 If the quotient on dividing ( 2 x^{4}+x^{3}- )
( 14 x^{2}-19 x+6 ) by ( 2 x+1 ) is ( x^{3}+ )
( a x^{2}-b x-6 )
Find the values of a and ( b ), also the remainder
10
554 7.
(1980)
If(x2 + px + 1) is a factor of (ax3 + bx+c), then
(a) a² + c = – ab
(b) al-c2 = – ab
(c) a2-c2 = ab
(d) none of these
10
555 Which of the following does NOT
represent a zero polynomial?
( mathbf{A} cdot p(x)=0 )
B ( cdot p(x)=0 . x^{0} )
( mathbf{C} cdot p(x)=x^{0} )
D ( cdot p(x)=x^{0}-1 )
9
556 Find the degree of following polynomial ( -frac{3}{2} )
A .
B. 2
c. 0
D. Cannot be determined
9
557 Use synthetic division to find the quotient ( Q ) and remainder ( R ) when
dividing ( f(x)=x^{2}+2 x+3 ) by ( x-i )
( i=sqrt{(}-1) ) the imaginary unit)
9
558 (0
JU JUU
My age twenty years ago is
(a) 40 years
(b) 15 years
(c) 22 years
(d) 10 years
D
10
559 Which type of polynomial is ( 3 x^{3} ? )
A. Cubic Polynomial
B. Linear Polynomial
c. square Polynomial
D. None of These
10
560 Evaluate ( (2 x+3 y+5 z)^{2} ) 9
561 Factorise the following: ( 2 a^{3}-54 b^{3} )
( mathbf{A} cdot 2(a b+3 b)left(a^{2}+3 b+9 a b^{2}right) )
B ( cdot 2(a+2 b)left(a^{3}+3 a b-9 b^{3}right) )
C ( cdot(a-3 b)left(a^{2}+3 b+9 a b^{2}right) )
D ( cdot 2(a-3 b)left(a^{2}+3 a b+9 b^{2}right) )
9
562 Simplify:
(i) ( left(a^{2}-b^{2}right)^{2} )
(ii) ( (2 x+5)^{2}-(2 x-5)^{2} )
(iii) ( (7 m-8 n)^{2}+(7 m+8 n)^{2} )
( (i v)(4 m+5 n)^{2}+(4 n+5 m)^{2} )
( (v)(2.5 p-1.5 q)^{2}-(1.5 p-2.5 q)^{2} )
( (v i)(a b+b c)^{2}-2 a b^{2} c )
( (v i i)left(m^{2}-n^{2} mright)^{2}+2 m^{3} n^{2} )
9
563 The remainder obtained when the
polynomial ( boldsymbol{x}^{4}-mathbf{3} boldsymbol{x}^{mathbf{3}}+mathbf{9} boldsymbol{x}^{2}-mathbf{2 7} boldsymbol{x}+mathbf{8 1} )
is divided by ( (x-3) ) is:
( mathbf{A} cdot mathbf{0} )
B. 3
c. 81
D. 27
9
564 The remainder when ( 4 a^{3}-12 a^{2}+ )
( 14 a-3 ) is divided by ( 2 a-1, ) is
A ( cdot frac{2}{3} )
в. ( frac{5}{3} )
( c cdot frac{6}{7} )
D. ( frac{3}{2} )
10
565 f ( p(x)=x+3, ) then ( p(3)+p(-3), ) is equal
to
( A cdot 3 )
B . 2
( c cdot 0 )
D. 6
10
566 ( left(3 a-frac{1}{a}right)^{3} ) 9
567 The polynomial
( left(a x^{2}+b x+cright)left(a x^{2}-d x-cright), a c neq 0 )
has?
10
568 5.
The sum of two numbers is 45 and their ratio is 7: 8. Find
the numbers.
(a) 21
(b) 24
(c) 25
(d) 20
10
569 The number of cubic polynomials ( boldsymbol{P}(boldsymbol{x}) ) satisfying ( P(1)=2, P(2)=4, P(3)=6 )
( P(4)=8 ) is
( mathbf{A} cdot mathbf{0} )
B.
c. more than one but finitely manyt
D. infinitely many
10
570 Simplify:
( -45 p^{3} div 9 p^{2} )
10
571 If the sum of squares of the zeroes of the polynomials ( 6 x^{2}+x+k ) is ( frac{25}{36} ) find
the value of k?
10
572 If -1 is a zero of the polynomial ( p(x)= ) ( a x^{3}-x^{2}+x+4, ) find the value of ( a ) 10
573 Divide:
( x^{7}-y^{7} ) by ( x-y )
10
574 If ( a+2 b=9 ) and ( a b=7 . ) Find the value
of ( a^{2}+4 b^{2} )
9
575 57. If xy (x + y) = 1, then the val-
ue of
-x- yº is :
(1) O
(3) 3
(2) 1
(4)-2
9
576 If ( a x^{n-1}+b x^{n-2}+c x^{n-3} ) is a cubic
polynomial where ( n in N, ) then find the
value of ( boldsymbol{n} )
9
577 Factorize:
( a^{4}-343 a )
( mathbf{A} cdot a(a-7)left(a^{3}+a+36right) )
B ( cdot a(a-7)left(a^{2}+7 a+49right) )
( mathbf{c} cdot a(4 a-7)left(a^{2}-a+49right) )
D. ( a(4 a-7)left(a^{3}+7 a-36right) )
9
578 Divide ( 3 x^{4}-5 x^{3} y+6 x^{2} y^{2}-3 x y^{3}+ )
( boldsymbol{y}^{4} ) by ( boldsymbol{x}^{2}-boldsymbol{x} boldsymbol{y}+boldsymbol{y}^{2} )
What should be subtracted from the
quotient to make it a perfect square?
A ( cdot 2 x^{2} )
В. ( x^{2} )
( c cdot y^{2} )
D. -xy
10
579 66. If x-1=1, then the value of
(1)
(2)
(4) O
10
580 If ( x+frac{1}{x}=5, ) then find the value of ( x^{3}+frac{1}{x^{3}} )
A . 110
B. 115
( c cdot 105 )
D. 100
9
581 Divide: ( left(6 a^{5}+8 a^{4}+8 a^{3}+2 a^{2}+right. )
( 26 a+35) ) by ( left(2 a^{2}+3 a+5right) )
Answer: ( 3 a^{3}-3 a^{2}+a+7 )
A . True
B. False
10
582 Give the zeros of polynomial and list their multiplicities:
( boldsymbol{P}(boldsymbol{x})=(boldsymbol{x}+mathbf{2})(boldsymbol{x}-mathbf{1}) )
10
583 ( 26 z^{3}left(32 z^{2}-18right) div 13 z^{2}(4 z-3) )
A ( cdot z(4 z+3) )
в. ( (4 z+3) )
c. ( 4 z(4 z+3) )
D. None
10
584 State if True or False
Check whether the polynomial ( p(y)= )
( 2 y^{3}+y^{2}+4 y-15 ) is a multiple of
( (2 y-3) )
A .
B. can not say
( c )
D. can not be determine
9
585 State whether True or False.
Divide: ( x^{6}-8 ) by ( x^{2}-2, ) then the
answer is ( x^{4}+2 x^{2}+4 )
A. True
B. False
10
586 State whether the statement is True or
False. The cube of ( left(x-frac{1}{2}right) ) is equal to ( x^{3}- )
( frac{3 x^{2}}{2}+frac{3 x}{4}-frac{1}{8} )
A . True
B. False
9
587 Find the zero of the polynomial given below:
( boldsymbol{p}(boldsymbol{x})=boldsymbol{9} boldsymbol{x}-boldsymbol{3} )
A ( cdot frac{6}{7} )
B. ( frac{1}{2} )
c. ( frac{1}{3} )
D. ( frac{7}{3} )
10
588 The value of
( frac{(1.5)^{2}+(4.7)^{3}+(3.8)^{3}-3 times 1 .}{(1.5)^{2}+(4.7)^{2}+(3.8)^{2}-1.5 times 4.7-4} )
( A cdot 8 )
B. 9
c. 10
( D )
9
589 Using the identity ( (boldsymbol{a}-boldsymbol{b})^{2}=boldsymbol{a}^{2}- )
( 2 a b+b^{2} ) compute ( (x-6)^{2} )
9
590 Solve:
( 4 x^{4}-5 x^{3}-7 x+1 div 4 x-1 )
10
591 Work out the following divisions:
( (10 x-25) div(2 x-5) )
10
592 Illustration 2.13
Plot a graph for the equation y = x2 – 4x.
CO3
10
593 Factorize ( 25 a^{2}-9 b^{2} )
A ( cdot(5 a+b)(5 a-3 b) )
B. ( (a+3 b)(5 a-3 b) )
c. ( (5 a+3 b)(5 a-3 b) )
D. ( (5 a-3 b)(5 a+3 b) )
9
594 Find the remainder when ( 4 x^{3}-3 x^{2}+ )
( 4 x-2 ) divided by ( (text { i) } x-1 )
(ii) ( x-2 )
10
595 If ( x+frac{1}{x}=7 ) the value of ( x^{4}+frac{1}{x^{4}} ) is
A .2401
в. 2023
c. 2209
D. 2207
9
596 If the polynomials ( left(2 x^{3}+a x^{2}+3 x-5right) )
and ( left(x^{3}+x^{2}-4 x-aright) ) leave the same
remainder when divided by ( (x-1), ) find
the value of ( a )
9
597 Is ( x^{8}+a^{8} ) divisible by ( x+a ? ) 10
598 Using remainder theorem, find the
remainder when ( 3 x^{2}+x+7 ) is divided
by ( boldsymbol{x}+mathbf{2} )
A . 17
B. -23
c. 13
D. -29
9
599 The polynomial ( p(x)=x^{4}-2 x^{3}+ )
( 3 x^{2}-a x+3 a-7 ) when divided by ( x+ )
1 leaves the remainder 19
Find the value of ( a ). Also find the
remainder when ( p(x) ) is divided by ( x+ )
2
A ( . a=5 ; 62 )
В. ( a=4 ; 62 )
c. ( a=5 ; 60 )
D. ( a=4 ; 60 )
9
600 ff ( x^{4}+2 x^{3}-3 x^{2}+x-1 ) is divided
by ( x-2 . ) then the remainder is
A . 12
B. 14
c. 16
D. 21
10
601 Degree of the polynomial ( left(x^{3}-2right)left(x^{2}+right. )
11) is
( mathbf{A} cdot mathbf{0} )
B. 5
( c .3 )
D.
10
602 If ( x=frac{1}{5-x} ) and ( x neq 5, ) find the value of ( x^{3}+frac{1}{x^{3}} )
A . 80
в. 240
c. 110
D. 530
9
603 Divide the polynomial ( 39 y^{3}left(50 y^{2}-98right) )
by ( 36 y^{2}(5 y+7) )
10
604 Expand using suitable identities
( (2 a-3 b)^{3} )
9
605 Divide ( (24 x-42) ) by ( (4 x-7) )
A ( .4 x-7 )
B. 3
( c cdot 6 )
D. 7
10
606 If ( P(x), q(x) ) and ( r(x) ) are three polynomials of degree 2 , then prove that
[
left|begin{array}{lll}
boldsymbol{p}(boldsymbol{x}) & boldsymbol{q}(boldsymbol{x}) & boldsymbol{r}(boldsymbol{x}) \
boldsymbol{p}^{prime}(boldsymbol{x}) & boldsymbol{q}^{prime}(boldsymbol{x}) & boldsymbol{r}^{prime}(boldsymbol{x}) \
boldsymbol{p}^{prime prime}(boldsymbol{x}) & boldsymbol{q}^{prime prime}(boldsymbol{x}) & boldsymbol{r}^{prime prime}(boldsymbol{x})
end{array}right| text { is independent }
]
of ( X )
10
607 Which type of polynomial, the given
expression ( 5 x^{2}+x-7 ) is?
9
608 Find a quadratic polynomial each with the give numbers as the sum and
product of its zeros respectively.
4,1
10
609 State whether the statement is True or
False. The square of ( left(5-x+frac{2}{x}right) ) is equal to ( 21+x^{2}+frac{4}{x^{2}}-10 x+frac{10}{x} )
A. True
B. False
9
610 Write the degree of each polynomial
given below:
( boldsymbol{x} boldsymbol{y}+boldsymbol{y} boldsymbol{z}-boldsymbol{z} boldsymbol{x}^{3} )
10
611 Perform the division: ( x^{3}-5 x^{2}+8 x-4 )
by ( boldsymbol{x}-mathbf{2} )
10
612 Simplify: ( frac{mathbf{6 x}^{2}+mathbf{9 x}}{mathbf{3 x}^{2}-mathbf{1 2 x}} ) 10
613 Factorize:
( 9 a^{2}+frac{1}{9 a^{2}}-2-12 a+frac{4}{3 a} )
A ( cdotleft(3 a-frac{1}{3 a}right)left(3 a-frac{1}{3 a}-4right) )
B. ( left(a-frac{1}{3 a}right)left(7 a-frac{1}{3 a}-1right) )
c. ( left(3 a-frac{1}{3 a}right)left(2 a-frac{1}{3 a}-4right) )
D. ( left(3 a-frac{1}{3 a}right)left(4 a-frac{1}{3 a}-1right) )
9
614 Which of the following is a polynomial
with only one zero?
( mathbf{A} cdot p(x)=2 x^{2}-3 x+4 )
B ( cdot p(x)=x^{2}-2 x+1 )
C ( . p(x)=2 x+3 )
D ( . p(x)=5 )
10
615 Write the polynomial in standard form and also write down their degree. ( left(x^{2}-frac{2}{3}right)left(x^{2}+frac{4}{3}right) ) 10
616 66. If p, q, r are all real numbers,
then (p-q) + (q-1)3 + (r-p)3
is equal to
(1) (p -q (q-) (r-p)
(2) 3(p-q) (9-) (r-p)
(3) O
(4) 1
9
617 Solve: ( x^{3}-(x+1)^{2}=2001 )
( A cdot 13 )
B. 16
c. 10
D. 21
10
618 Carry out the following divisions ( 11 x y^{2} z^{3} ) by ( 55 x y z ) 10
619 Evaluate the following using suitable identity:
( (10 x-1)^{2} )
( (x-8 y)^{2} )
9
620 Simplify : ( left(frac{3}{2} x-0.45 yright)^{2} )
A. ( 2.25 x^{2}-1.35 x y+0.2015 y^{2} )
B. ( 2.15 x^{2}-1.35 x y+0.2025 y^{2} )
c. ( 2.25 x^{2}-1.35 x y+0.2025 y^{2} )
D. ( 2.25 x^{2}-1.25 x y+0.2025 y^{2} )
9
621 Write the degree of the following polynomial:
( 5 y+sqrt{2} )
9
622 Degree of the polynomial ( 4 x^{4}+0 x^{3}+ )
( mathbf{0} boldsymbol{x}^{boldsymbol{5}}+mathbf{5} boldsymbol{x}+mathbf{7} ) is
A . 4
B. 5
( c cdot 3 )
D.
9
623 Solution:
( 10 a^{2}(0.1 a-0.5 b) )
9
624 ( (2 x+3 y)^{2}-16 z^{2} ) 9
625 The simplified form of the expression given below is 🙁 y^{4}-x^{4}-y^{3} )
( frac{x(x+y) x}{y^{2}-x y+x^{2}} )
A . 1
B.
( c cdot-1 )
D. 2
10
626 Simplify:
i) ( left(a^{2}-b^{2}right)^{2} )
ii) ( (2 x+5)^{2}-(2 x-5)^{2} )
9
627 59. If a and b are two odd positive
integers, by which of the follow-
ing integers is (a – b) always
divisible?
(2) 6
(3) 8
(4) 12
(1) 3
9
628 Use the identity and expand the following ( (2 x+y)^{2} ) 9
629 What is meant by division algorithm
give example?
10
630 If ( x+frac{1}{x}=sqrt{3}, ) find the value of ( x^{3}+ )
( frac{1}{x^{3}} )
9
631 The product of two zeroes of the polynomial ( p(x)=x^{3}-3 x^{2}-6 x+8 ) is
( (-2) . ) Find all the zeroes of the polynomial
10
632 Solve:
( left(y^{2}+10 y+24right) div(y+4) )
10
633 Find the degree of the following polynomial
( boldsymbol{x}^{9}-boldsymbol{x}^{4}+boldsymbol{x}^{12}+boldsymbol{x}-boldsymbol{2} )
A ( cdot 12 )
B.
( c cdot 4 )
D.
10
634 Factorise the following: ( y^{6}+32 y^{3}-64 )
A ( cdot(y+2)left(y^{4}-2 y^{3}+8 y^{3}+8 y+16right) )
B . ( left(y^{2}+2 y-4right)left(y^{4}-2 y^{3}+8 y^{2}+8 y+16right) )
C ( cdotleft(y^{2}+2 y-4right)left(y^{4}-2 y^{3}+8 y^{2}right) )
D. ( (y+2)left(y^{4}-2 y^{3}+8 y^{2}+8 yright) )
9
635 What is the degree of the following polynomial expression:
( boldsymbol{u}^{frac{-1}{2}}+boldsymbol{3} boldsymbol{u}+boldsymbol{2} )
( mathbf{A} cdot mathbf{1} )
B. 0
( c cdot frac{-1}{2} )
D. Not Defined
9
636 65. If x2 + y2 – 4x – 4y + 8 = 0, then
the value of x-y is
(1) 4
(2) 4
(3) O
(4) 8
9
637 Find the quotient and remainder when
( p(x)=x^{3}-3 x^{2}+5 x-3 ) is divided by
( g(x)=x^{2}-2 )
10
638 Find the remainder when ( p(x)=x^{2}+ )
( 3 x+4 ) is divided by ( x+1 )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. 3
9
639 Using remainder theorem, find the remainder when ( 4 x^{3}+5 x-10 ) is
divided by ( boldsymbol{x}-mathbf{3} )
A . 197
в. 113
( c cdot-1 )
D. 0
9
640 Find ( 302 times 308 ) 9
641 Divide the following polynomial ( p(x) p(x) ) by the polynomial ( S(x) 5(x) )
( boldsymbol{P}(boldsymbol{x})=frac{2}{3} boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}+boldsymbol{6}, boldsymbol{S}(boldsymbol{x})=boldsymbol{x}+boldsymbol{6} )
10
642 Find the remainder if ( x-1 ) is divided by
( 5 x^{3}-2 x^{2}+3 x-22 )
9
643 The factors of ( boldsymbol{x}^{mathbf{4}}+boldsymbol{y}^{mathbf{4}}+boldsymbol{x}^{mathbf{2}} boldsymbol{y}^{mathbf{2}} ) are
( mathbf{A} cdotleft(x^{2}+y^{2}right)left(x^{2}+y^{2}-x yright) )
( mathbf{B} cdotleft(x^{2}+y^{2}right)left(x^{2}-y^{2}right) )
C ( cdotleft(x^{2}+y^{2}+x yright)left(x^{2}+y^{2}-x yright) )
D. Factorization is not possible
9
644 Find the value of ( (2-sqrt{1-x})^{6}+(2+ )
( sqrt{1-x})^{6} )
9
645 Work out the following divisions.
( 96 a b c(3 a-12)(5 b+30) div 144(a- )
4)( (b+6) )
( mathbf{A} cdot 96 a b c )
B. ( 10 a b c )
c. ( 144 a b c(b-12) )
D. ( 24(a-b+c) )
10
646 Using the Remainder and Factor Theorem, factorise the following polynomial: ( x^{3}+10 x^{2}-37 x+26 ) 10
647 If ( a^{2}+b^{2}+c^{2}=35 ) and ( a b+b c+ )
( c a=23 ; ) find ( a+b+c )
( A cdot pm 7 )
B. ±2
( c .pm 9 )
( mathrm{D} cdot pm 14 )
9
648 Divide the first polynomial by the second polynomial in each of the following. Also, write the quotient and remainder:
( boldsymbol{y}^{4}+boldsymbol{y}^{2}, boldsymbol{y}^{2}-boldsymbol{2} )
10
649 If the zeros of the polynomial ( boldsymbol{f}(boldsymbol{x})= ) ( x^{3}-3 x^{2}+x+1 ) are ( a-b, a, a+b, ) find ( a )
and b.
10
650 Using long division method, divide the polynomial ( 4 p^{3}-4 p^{2}+6 p-frac{5}{2} ) by ( 2 p-1 )
A ( cdot 2 p^{2}-p-frac{5}{2} )
В ( cdot 2 p^{2}+p+frac{5}{2} )
c. ( _{2 p^{2}-p+frac{5}{2}} )
D. None of the above
10
651 Divide ( boldsymbol{x}(boldsymbol{x}+mathbf{1})(boldsymbol{x}+mathbf{2})(boldsymbol{x}+boldsymbol{3}) ) by
( (x+3)(x+2) )
A. ( x(x+3) )
в. ( x(x+2) )
c. ( (x+1) )
D. ( x(x+1) )
10
652 If ( a x^{3}+b x^{2}+c ) is divided by ( (x-3) )
then the remainder is:
A. ( -27 a+9 b+c )
B . ( -27 a-9 b )
c. ( 27 a+9 b+c )
D. ( 27 a+9 b )
E ( .-27 a+9 b )
9
653 Factorise the expression and divide them as directed.
( 5 p qleft(p^{2}-q^{2}right) div 2 p(p+q) )
10
654 If ( a+b=1 a n d a^{2}+b^{3}+3 a b=k, ) then
the value of k is
( mathbf{A} cdot mathbf{1} )
B. 3
( c .5 )
D.
9
655 Solve
( left(15 y^{4}+10 y^{3}-3 y^{2}right) div 5 y^{2} )
10
656 Evaluate ( 8.5 times 9.5 ) using suitable
standard identity.
9
657 ff both ( (x-2) ) and ( left(x-frac{1}{2}right) ) are factors of ( p x^{2}+5 x+r, ) show that ( p=r ) 9
658 Find the cube of 23 9
659 Which of the following is not a linear polynomial?
A ( . p(y)=8 y+6 )
В. ( p(x)=8 y+2 x )
c. ( p(x)=4+frac{5 x}{x}+8 x^{circ} )
D. ( p(x)=4+5 x )
9
660 Expand ( left(2 y-frac{3}{y}right)^{3} )
A ( cdot 8 y^{3}-36 y+frac{54}{y}-frac{27}{y^{3}} )
в. ( 8 y^{3}+36 y+frac{54}{y}-frac{27}{y^{3}} )
c. ( 8 y^{3}-36 y-frac{54}{y}-frac{27}{y^{3}} )
D. None of these
9
661 Find the degrees of the following polynomial
( 3-4 a b+5 b^{3}+2 a b^{2} )
9
662 Prove the following result by using suitable identities.
( (x-y)^{2}+(y-z)^{2}+(z-x)^{2}= )
( 2left(x^{2}+y^{2}+z^{2}-x y-y z-z xright) )
9
663 Which of the following is a factor of the
polynomial ( -2 x^{2}+7 x-6 ? )
A. ( -2 x-3 )
B. ( 2 x+2 )
c. ( x-6 )
D. ( 2 x-2 )
E . ( -2 x+3 )
10
664 Find the product. ( (3+sqrt{2})(2+sqrt{3})(3-sqrt{2})(2-sqrt{3}) ) 9
665 3+ x + V3 -X=2 then x is
66. V3+r
13 + x – 13-
equal to
9
666 Simplify:
( a^{6}-b^{6} )
9
667 Divide ( 4 x^{3}+3 x^{2}-2 x+8 ) by ( x-2 ) 10
668 Write the polynomial in standard form
and also write down their degree. ( 4 z^{3}-3 z^{5}+2 z^{4}+z+1 )
10
669 Find the remainder when ( x^{4}+x^{3}- )
( 2 x^{2}+x+1 ) is divided by ( x-1 )
( A cdot 2 )
B. –
( c cdot-2 )
D.
9
670 67. If a+b= 10 and a + b = 58,
then a + b3 will be equal to
(1) 340 (2) 540
(3) 270 (4) 370
9
671 Use the identity ( (a+b)(a-b)=a^{2}- )
( b^{2} ) to find the product of ( left(frac{2 x}{3}+1right)left(frac{2 x}{3}-right. )
( mathbf{1} )
9
672 Find the degree of the polynomial:
( mathbf{7} boldsymbol{x}^{mathbf{3}}+mathbf{2} boldsymbol{x}^{mathbf{2}}+boldsymbol{x} )
10
673 If ( b ) is zero of the polynomial ( p(x)= )
( a x^{2}-3(a-1) x-1, ) then find the
value of ( boldsymbol{a} )
9
674 Divide ( x^{4}-y^{4} ) by ( x-y ) 10
675 Factorize ( 27 m^{3}-216 n^{3} ) 9
676 Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial
(i) ( t^{2}-3,2 t^{4}+3 t^{3}-2 t^{2}-9 t-12 )
(ii) ( x^{2}+3 x+1,3 x^{4}+5 x^{3}-7 x^{2}+ )
( 2 x+2 )
(iii) ( x^{3}-3 x+1, x^{5}-4 x^{3}+x^{2}+3 x+ )
( mathbf{1} )
10
677 Find the remainder when ( p(x)=x^{3}- )
( 4 x^{2}+3 x+1 ) is divided by ( (x-1) )
9
678 Classify the following polynomial based on their degrees:
( boldsymbol{y}+mathbf{3} )
10
679 Two angles in a triangle are in the ratio 4:5. If the sum of
these angles is equal to the third angle, then the angles are
(a) 180°
(b) 40°
(c) 50°
(d) 90°
.
Ten
10
680 Divide
( left(2 a^{2}-13 a b+15 b^{2}right) b y(a-5 b) )
10
681 Factorise the expressions and divide them as directed.
( 12 x yleft(9 x^{2}-16 y^{2}right) div 4 x y(3 x+4 y) )
A. ( 3(3 x-4 y) )
B. ( 3(3 x+4 y) )
c. ( 4(3 x-4 y) )
D. ( 3(4 x-3 y) )
10
682 52.
If x + y + z = 6 and xy + y2 + 2x
= 10 then the value of x3 + y +
22 – 3.xyz is :
(1) 36
(2) 48
(3) 42
(4) 40
9
683 57. If xy (x + y) = 1, then the val-
ue of –
+3,3-*-y is :
(1) o
(3) 3
(2) 1
(4) -2
9
684 66. If a = 2-361, b = 3.263 and c =
5.624, then the value of
a + b3 – + 3abc is
(1) 35-621 (2)
(3) 19.277 (4) 1
9
685 70. If x
3 then the value of
x1 + x2 + x + 1 is
(1)
(2) 1
(3) 2
(4) 3
9
686 55. For what value of a, (x + a) is a
factor of polynomial f(x)= x + ax?
– 2x + a +6?
(1) 2
(2) 3
(3) – 2 (4) – 3
9
687 If ( a+frac{1}{a}=4 ) and ( a neq 0, ) find ( a^{2}+frac{1}{a^{2}} )
A . 14
B. 12
c. 17
D. 19
9
688 Convert into factors ( a^{2}+4 a+4-b^{2} ) 9
689 Evaluate ( (10 x-25) div(2 x-5) )
( mathbf{A} cdot mathbf{5} )
B. 4
( c cdot 3 )
D.
10
690 Write the constant term of each of the
following algebraic expressions: ( a^{3}- ) ( 3 a^{2}+7 a+5 )
9
691 If ( l^{2}+m^{2}+n^{2}=5, ) then ( (l m+m n+ )
( (n) ) is
( mathbf{A} cdot geq(-5 / 2) )
B ( cdot geq(-1) )
( c cdot leq 5 )
( D . leq 3 )
9
692 Find ( alpha ) in order that ( x^{3}-7 x+5 ) may be
a factor of ( x^{5}-2 x^{4}-4 x^{2}+19 x^{2}- )
( 31 x+12+alpha )
10
693 Find the value of ‘a’ ( operatorname{in} 4 x^{2}+a x+ )
( mathbf{9}=(mathbf{2} boldsymbol{x}+mathbf{3})^{2} )
A ( . a=34 )
B. ( a=11 )
c. ( a=12 )
D. ( a=33 )
9
694 If ( x=frac{4}{3} ) is a zeroes of the polynomial
( p(x)=6 x^{3}-11 x^{2}+k x-20, ) find the
value of ( k )
10
695 Divide
( 4 sqrt{2} y^{3} ) by ( 3 sqrt{2} y^{2} ) The answer is ( frac{m y}{3} )
Then ( m= )
10
696 If ( a-frac{1}{a}=5 ; ) find ( a^{2}+frac{1}{a^{2}}-3 a+frac{3}{a} )
A . 10
B. 14
( c cdot 6 )
D. 12
9
697 Which type of polynomial is ( 45 y^{2} ? )
A. Linear Polynomial
B. Bi-quadratic polynomial
c. Cubic Polynomial
D. Quadratic Polynomial
9
698 Find the missing terms such that the given polynomial become a perfect square trinomial:
( 81 x^{2}+dots-1 )
10
699 Factorise:
( mathbf{2} sqrt{mathbf{2}} boldsymbol{a}^{mathbf{3}}+mathbf{1 6} sqrt{mathbf{2}} boldsymbol{b}^{mathbf{3}}+boldsymbol{c}^{mathbf{3}}-mathbf{1 2 a b} boldsymbol{c} )
9
700 If ( (n+1)^{3}-(n)^{3}=n+1, ) then which
of the following can be the value of ( n ? )
( mathbf{A} cdot mathbf{0} )
B . 2
c. -2
D. Cannot be determined
9
701 Find the square of:
607
A. 368549
B. 368449
( c .368349 )
D. 368249
9
702 Zero of the polynomial ( p(x)=2-5 x ) is 10
703 Use synthetic division to find the quotient ( Q ) and remainder ( R ) when dividing ( boldsymbol{f}(boldsymbol{x})=boldsymbol{x}^{5}+boldsymbol{x}^{4}+boldsymbol{x}^{3}+boldsymbol{2} boldsymbol{x}-boldsymbol{5} ) by ( boldsymbol{x}+boldsymbol{i} )
( (i=sqrt{(}-1) text { imaginary unit }) )
9
704 Verify ( f(x)=2 x^{3}+11 x^{2}-7 x-6 ) is
the factor of ( (x-1) ) using factor
theorem.
10
705 Find the remainder by using remainder
theorem when polynomial ( x^{3}-3 x^{2}+ )
( x+1 ) is divided by ( x-1 )
( A cdot 8 )
B.
( c cdot-2 )
D. -7
9
706 State whether the statement is True or
False.
Expanding ( (a-b+c)^{2} ) we get ( a^{2}+ )
( b^{2}+c^{2}-2 a b-2 b c+2 c a )
A. True
B. False
9
707 Find the value of ( 87^{2}-13^{2} )
A . 7300
B. 7350
( c .7400 )
D. 7450
9
708 Divide ( 6 x^{4}+13 x^{3}+39 x^{2}+37 x+45 )
by ( 3 x^{2}+2 x+9 )
10
709 Degree of a constant term of a
polynomial is
A .
B. 0
( c cdot 2 )
D. Not defined
9
710 6.
Two numbers are such that the ratio between them is 3:5. If
each is increased by 10, the ratio between the new numbers
so formed is 5:7. Find the original numbers.
(a) 12
(b) 20
(c) 25
(d) 15
10
711 Using identity find the value of ( (4.7)^{2} ) 9
712 Divide ( left(36 x^{2}-4right) ) by ( (6 x-2) )
A. ( 3 x-1 )
B. ( 3 x+1 )
c. ( 6 x-2 )
D. ( 6 x+2 )
10
713 Find the remainder when ( p(x)=x^{3}+ )
( 3 x^{2}+3 x+1, ) is divided by ( x )
( A )
B.
( c cdot-1 )
D.
9
714 State true or false:
( frac{3}{4 x+3}=frac{1}{4} )
A. True
B. False
10
715 ( boldsymbol{p}(boldsymbol{x})=mathbf{2} boldsymbol{x}^{3}-mathbf{3} boldsymbol{x}^{2}-mathbf{5} ) is a
polynomial
A . linear
B. cubic
c. quadratic
D. constant
10
716 State whether True or False.
Divide: ( x^{2}+3 x-54 ) by ( x-6, ) then the
answer is ( x+9 )
A. True
B. False
10
717 Expand ( (sqrt{10} x-sqrt{5} y)^{2} ) using
appropriate identity
9
718 When ( 5 x^{13}+3 x^{10}-k ) is divided by ( x+ )
1, the remainder is 20. The value of k is
A . – 22
B . -12
( c cdot 8 )
D. 28
( E cdot 14 )
9
719 Find the degree of each of the polynomials given below ( 5 t-sqrt{3} ) 10
720 Divide and write the quotient and
remainder:
( left(4 x^{4}-5 x^{3}+0 x^{2}-7 x+1right) div(4 x-1) )
10
721 Find whether ( x-1 ) is a factor of ( 2 x^{2}- )
( mathbf{5} boldsymbol{x}+mathbf{3} )
10
722 What number should be added to ( x^{3}- )
( 9 x^{2}-2 x+3 ) so that the remainder
may be 5 when divided by ( (x-2) )
9
723 Find the product of ( left(frac{1}{2} m-frac{1}{3}right)left(frac{1}{2} m+right. )
( left.frac{1}{3}right)left(frac{1}{4} m^{2}+frac{1}{9}right) )
9
724 Degree of which of the following polynomial is zero?
( A cdot x )
B . 15
c. ( y )
D. ( _{x+frac{1}{x}} )
9
725 In each of the following two polynomials
find the value of ( a, ) if ( x+a ) is a factor.
( x^{4}-a^{2} x^{2}+3 x-a )
10
726 .
x² + 8
60. Simplify: x4 + 4×2 +16
x
+
2
021-
x+ 2
x² + 2
3 + 2×2 + 4
(3)
x² + 2
x3 + 3×2 +8
1
9

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