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 NoQuestionsClass
168. If x= 6+
then the value of
* + 4 is
(1) 1448
(3) 1444
(2) 1442
(4) 1446
9
2Find the product of ( (boldsymbol{m}-mathbf{1})(boldsymbol{m}- )
2)( (m-3) )
9
360. 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
4Find 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
561. If 7x
= 14, then the value
2x
of x-
3 is :
8x
(1) 9
(3) 27
(2) 8
(4) 11
9
6If ( 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
7Find the cube of 499
860. 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
9When ( 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
1064. If m+
= 4, find the value
of (m – 2)2 + (m-22
(1) -2
(3) 2
(2) 0
(4) 4
9
11Which polynomial represents this plot?
A. cubic
D. linear
9
12The 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
13If ( 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
14Factorize:
( 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
15If ( 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
16Find 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
18Write the degree of each of the following polynomials:
( frac{1}{2} y^{7}-12 y^{6}+48 y^{5}-10 )
10
19Which 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
20What 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
21Which 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
22Write 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
23If ( 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
24If ( 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
25The degree of the equation, given by ( (x+2)(x-1)=(x+1)(x+3), ) is
( A cdot 2 )
B. 3
( c . )
D.
9
26Degree of polynomial 5 is
( A cdot 1 )
B. 2
( c cdot 0 )
D. Not defined
9
27Which one of the following is a
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
28Divide
( left(y^{3}-3 y^{2}+5 y-1right) div(y-1) )
10
2956. If 2x + 3y = 13 and xy = 6 then
the value of 8x + 27yº will be
(1) 799 (2) 797
(3) 795 (4) 793
9
30Find 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
32Solve:
( frac{m^{2}-3 m-108}{m+9}=0, ) then ( m=? )
10
33Which 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
3461. 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
35If ( 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
36Find the missing terms such that the given polynomial become a perfect square trinomial:
[
-12 x+9
]
10
37Simplify:
( (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
38What should be added to ( x^{5}-1 ) to be
completely divisible by ( x^{2}+3 x-1 ? )
10
39Show that ( (x-2) ) is a factor of ( x^{3}- )
( 3 x^{2}-10 x+24 )
10
4068. 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
41If ( 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
4258. 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
43Degree of the polynomials ( frac{x^{23}+x^{14}-x^{16}}{x^{2}} ) is
( A cdot 2 )
B . 23
c. 14
D. 21
9
44If 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
45If ( p(t)=t^{3}-1, ) find the values of
( boldsymbol{p}(mathbf{1}), boldsymbol{p}(-mathbf{2}) )
10
46The 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
47f ( a=3, b=-3, ) find the value of
( (a-2)^{2}+(b-2)^{2} )
9
48Substituting ( x=-3 ) in
( x^{2}-5 x+4 )
A . -2
B . 28
( c cdot 2 )
D. -1
10
49Classify the following polynomial based on their degrees:
( boldsymbol{y}^{2}-boldsymbol{4} )
10
50If 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
51Factorize ( 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
52Verify 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
5355.
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
54Perform division
( left(y^{2}+7 y+10right) div 6(y+5) )
10
557.
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
56If 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
57Carry out the following divisions ( -54 l^{4} m^{3} n^{2} ) by ( 9 l^{2} m^{2} n^{2} )10
5825.
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
59Prove if ( cot theta+frac{1}{cot theta}=2 ) then ( cot ^{2} theta+ )
( frac{1}{cot ^{2} theta}=2 )
9
60When ( 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
61Divide ( 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
62If ( 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
6361. If x + y2 + z = xy + y2 + zx, lx
# O). then the value of
4x + 2y – 32
is
2x
(2) 1
(1) o
9
64Say true or false:
The zeros of the polynomial ( x^{2}-14 x+ )
49 are equal to 7
A. True
B. False
10
65Write each of the following polynomials in the standard form. Also, write their
degree:
( left(x^{3}-1right)left(x^{3}-4right) )
9
66If ( x-y=7 ) and ( x^{3}-y^{3}=133 ; ) find:
the value of ( x y )
A . 12
B. – –
( c .-10 )
D. 5
9
6751. For real a, b, c if a + b + c
a+c
ab + bc + ca, the value of –
(1) 3
(3) 2
(2)
(40
9
68Divide: ( a^{4}+4 b^{4} ) by ( a^{2}+2 a b+b^{2} )10
69Simplify: ( (sqrt{2} x-2 y)^{2} )9
7067. If
5x
2×2 + 5x +1
then the
value of (x+2x is
of
X
+-
(1) 15
(3) 20
(2) 10
(4) 5
9
71Divide ( 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
72Factorise 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
7313.
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
74The 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
76Choose 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
77If ( x^{3}-frac{1}{x^{3}}=14, ) then ( x-frac{1}{x}= )
( A cdot 2 )
B. 4
( c .5 )
D.
9
78Divide 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
79If ( 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
81Find if polynomial ( x^{4}-3 x^{3}+7 x^{2}- )
( 8 x+12 ) is exactly divisible by ( x^{2}- )
( 2 x+2 )
10
82The 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
83The 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
84If ( 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
86Solve: ( left(5 p^{2}-25 p+20right) div(p-1) )9
87Divide 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
88If ( x^{2}+frac{1}{x^{2}}=7 ) find the value of ( x^{3}+frac{1}{x^{3}} )9
89Find 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
90Find the zeroes of the quadratic
polynomial ( x^{2}+14 x+48 ) and verify
them
9
91Factorise the polynomial: ( a x^{2}+b x^{2}+ )
( a y^{2}+b y^{2} )
9
92A cubic polynomial is a polynomial of degree
A .
B.
( c cdot 3 )
( D )
9
93Simplify ( (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
95Divide as directed ( 5(2 x+1)(3 x+5) div )
( (2 x+1) )
10
96Simplify: ( left(a^{2}-b^{2}right)^{2} )9
97( p(x)=25 ) is a
polynomial
A. linear
c. constant
D. cubic
9
98Divide 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
101Factorize:
( 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
102Find 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
1031 -b))2 + ab = p (a + b)2,
then the value of p is (assume
that a # -b)
(2) 1
(3) =
(4)
9
104If ( 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
105If ( a+frac{1}{a}=2, ) then find ( a^{4}+frac{1}{a^{4}} )9
106Divide 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
107Divide the polynomial ( 2 x^{4}-4 x^{3}- )
( 3 x-1 ) by ( (x-1) ) and verify the
remainder with zero of the divisor.
10
108Verify 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
109Degree of the polynomial ( boldsymbol{p}(boldsymbol{x})=-10 )
is
A . -10
B. 10
( c cdot 0 )
D.
10
110Factorise 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
11166. If a – b – – 3abc = 0, then
(1) a = b = c
(2) a + b + c = 0
(3) a + c = b
(4) a = b + c
9
112Arrange ( boldsymbol{x}^{8}+boldsymbol{x}+boldsymbol{x}^{12}-boldsymbol{3} boldsymbol{x}^{7}+boldsymbol{x}^{9}+1 ) in
descending powers of ( x )
10
113Using 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
114The degree of the term ( x^{3} y^{2} z^{2} ) is:
( A cdot 3 )
B. 2
c. 12
D.
9
115Using identity ( (a+b)^{2}=left(a^{2}+2 a b+right. )
( b^{2} ) ) Evaluate
(i) ( (609)^{2}left(text { ii) }(725)^{2}right. )
9
116Solve:
( left(y^{2}+10 y+24right) div(y+4) )
10
11751. The value of
[(0.87)2+(0.13)2 + (0.87) x (0.26)] 2013
(1) O
(3) 1
(2) 2013
(4) -1
9
118Divide ( 81 x^{3}left(50 x^{2}-98right) ) by ( 27 x^{2}(5 x+ )
7)
10
119If ( a^{2}+b^{2}+c^{2}=250 ) and ( a b+b c+ )
( c a=3 ), then find ( a+b+c )
9
120If ( 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
121Zeroes 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
122Obtain 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
123Find: ( (5 m+7 n)^{2} )9
124Perform the division ( left(a^{4}-a^{3}+a^{2}-right. )
( a+1) divleft(a^{3}-2right) )
10
125Write the polynomial in standard form and also write down their degree. ( left(p^{2}+2right)left(p^{2}+7right) )10
126State true or false:
If ( a+2 b=5 ; ) then
( a^{3}+8 b^{3}+30 a b=125 )
A. True
B. False
9
127f ( 2 x+y=14 ) and ( x y=6, ) Find the
value of ( 4 x^{2}+y^{2} )
9
128Find 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
129What 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
130ff ( 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
131If 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
132Find 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
133For ( 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
134Which 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
135Simplify the following.
( b^{4} div b^{5} )
10
136If ( boldsymbol{x}=mathbf{5}-mathbf{2} sqrt{mathbf{6}}, ) find the value of ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}} )9
137Tuu
5
-1
4.
Assertion : x +11=1 is a linear equation.
Reason: In a linear equation power ofx cannot be negati
10
138Expand: ( (x y+8)(x y-8) )9
139Given 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
140Find the polynomials whose zeroes are
three times the zeroes of ( 2 x^{2}-3 x+1 )
10
141If ( 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
142Prove 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
144Which type of polynomial is ( (2+x) ? )
A. Linear Polynomial
c. Cubic Polynomial
D. None of above
9
145Q 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
146Perform the following divisions and give the remainders.
( left(x^{2}+15 x+56right) div(x+8) )
10
147Carry out the following division. ( 28 x^{4} div 56 x )10
148The integral part of ( (sqrt{2}+1)^{2} ) is:
( A cdot 2 )
B. 3
( c cdot 4 )
D.
9
149Total 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
150Find 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
151The 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
152If ( x-frac{1}{x}=5, ) then ( x^{3}-frac{1}{x^{3}} ) equals
A . 125
в. 130
c. 135
D. 140
9
153Evaluate each of the following using suitable identities:
( (99)^{3} )
9
154State 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
155f ( 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
156The 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
157Find 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
158When ( 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
159Solve: ( 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
161If 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
162When 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
163Using 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
164Simplify:
( (8 a-5 b)^{2} )
9
165Write 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
166If ( p-frac{1}{p}=4, ) find the value of ( p^{4}+frac{1}{p^{4}} )
A . 16
B. 18
c. 324
D. 322
9
167Use 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
168Evaluate: ( 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
17051. 1fx–2, then the value of x’
(1) 15
(3) 14
(2) 2
(4) 11
9
171Find all zeroes of ( 2 x^{4}-3 x^{3}-3 x^{2}+ )
( 6 x-2 ) if 2 zeroes ( sqrt{2} ) and ( -sqrt{2} )
10
17269. If x + y = 15, then (x – 10)3 +
(y-5) is
(1) 25
(2) 125
(3) 625 (4) O
10
173Divide
( frac{x^{3}+x+1}{x^{2}-1} )
10
174Simplify :
¡) ( 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
175Shikhaa 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
176ff ( 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
178Factorise 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
17961. 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
180Find 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
181What is the type of polynomial ( 11= ) ( -4 x^{2}-x^{3} ? )
A. Cubic
c. Linear
D. None of these
10
182If ( 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
184If 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
185What 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
186A polynomial of 4 is called a
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
188Factorize ( (5 x-3 y)^{3}+(3 y-8 z)^{3}+ )
( (8 z-5 x)^{3} )
9
189What is the degree of the polynomial
( 2 a^{2}+4 b^{8} ? )
( A cdot 2 )
B. 10
c. 8
D.
10
1902
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
191The polynomial ( 4 x^{2}+2 x-2 ) is a
A. Linear polynomial
c. Cubic polynomial
D. constant polynomial
10
192The 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
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
194State 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
195Write the polynomial in standard form
and also write down their degree. ( 4 p+15 p^{6}-p^{5}+4 p^{2}+3 )
9
196Simplify:
( left(left(3 x^{2}-2 a xright)+3 a^{2}right)^{3} )
9
197Which 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
198If ( 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
199Simplify 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
200Which 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
201Consider 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
202By 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
203Find the remainder when the polynomial
( 4 y^{3}-3 y^{2}-5 y+1 ) is divided by ( 2 y+3 )
10
204Find the roots of equation ( x^{2}-3 x- )
( mathbf{1 0}=mathbf{0} )
10
205Find 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
206Divide 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
20855.-
=?
(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
209A number was divided successively in order by 4,5 and 6 The remainders were respectively 2,3 and 4 Then find out the number9
210Choose 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
211Which of the following is NOT a
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
212Find the degree of given polynomial:
( 4 x^{3}-1 )
9
213Divide ( 4left(2 x^{2}+5 x+3right) ) by ( 2(2 x+3) )10
214f ( p(x)=x^{42}-2 k ) is divided by ( (x+1) )
the remainder is ( 9, ) what is the value of
k?
9
215Find the remainder when ( p(x)=2 x^{2}- )
( 5 x-1 ) is divided by ( x-3 )
A .
B.
( c cdot 2 )
D. 3
9
216State True Or False, if the following expression is a quadratic polynomial:
( boldsymbol{x}^{2}+boldsymbol{x} )
A . True
B. False
9
217Multiply:
( left(m^{2}-5right) timesleft(m^{3}+2 m-2right) )
10
218Solve ( left(4 x^{4}-5 x^{3}-7 x+1right) div(4 x-1) )10
219The 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
220Find the degree of following polynomial ( 4 x-sqrt{5} )
A ( cdot frac{1}{2} )
B.
( c cdot 2 )
D.
9
221The polynomial ( 3 x-2 ) is a.
A. Linear polynomial
c. Cubic polynomial
D. constant polynomial
10
222Divide ( p(x)=x^{3}-3 x^{2}+5 x- )
( mathbf{3} ) by ( boldsymbol{g}(boldsymbol{x})=boldsymbol{x}^{2}-mathbf{2} )
10
223In 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
224Find and correct errors of the following mathematical expressions:
( frac{3 x}{3 x+2}=frac{1}{2} )
10
225Factors 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
226Find the remainder obtained on dividing
( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{3}+mathbf{1} ) by ( boldsymbol{x}+mathbf{1} )
10
227Prove 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
228When 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
229If ( 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
23068. 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
231Find the value of ( 52^{2} ) using standard
identity.
A . 2604
в. 2704
c. 2804
D. 2904
9
23257.
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
233Find 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
234If 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
23563. 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
236Find the value of ( 99 times 101 ) using
standard identity
A . 9999
B. 9989
( mathrm{c} .9979 )
D. 1009
9
237If ( x+frac{1}{x}=3, ) then ( x^{4}+frac{1}{x^{4}}= )
A. 81
B . 23
c. 25
D. 47
9
238Find 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
239Find the degree of the polynomial ( left(x^{2}+right. )
( mathbf{9})left(mathbf{5}-boldsymbol{x}^{2}right) )
9
240Factorise: ( (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
241If ( x^{2}+frac{1}{x^{2}}=83 . ) Find the value of ( x^{3}- )
( frac{1}{m^{3}} )
9
242Perform the division.
( (10 x-25) div 5 )
10
243Which 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
244Expand ( left[boldsymbol{x}-frac{boldsymbol{2}}{boldsymbol{3}} boldsymbol{y}right]^{boldsymbol{3}} )9
245What should be added to ( 1+2 x-3 x^{2} )
to get ( x^{2}-x-1 ? )
9
246For 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
247The 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
248f ( 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
249Find 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
250The 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
251If 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
252If ( 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
253Evaluate the following:
( (7 x-2 y)^{2} )
( (3 x+7 y)^{2} )
9
254What 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
256If 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
258The 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
260Write a polynomial of degree 5 using variable ( x )10
261Find the product ( (3+sqrt{2})(3-sqrt{2}) )9
26258. 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
263What is the degree of the given
monomial ( -11 y^{2} z^{2} ? )
( mathbf{A} cdot mathbf{0} )
B . 2
( c cdot 4 )
D.
10
264Using 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
266The value of ( 7 x-42 ) is
A. ( 7(x-6) )
B. ( 7(x+6) )
( c cdot-7(x-6) )
D. ( -7(x+6) )
9
267Verify whether ( x=3 ) is a zero of the
polynomial ( boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}-mathbf{1 5} )
10
268Two 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
269Evaluate ( (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
270Write 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
271Simplify:
( 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
272Find the product of ( (a-3)(a-5)(a-7) )9
273If ( 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
274Find 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
275What 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
276Assertion : Vx+9x = 3 is not a linear equation.
Reason: Linear equation involves only linear polynomials.
10
277Find 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
278The degree of ( 3 x^{2} y^{4} z^{6} ) is
( A cdot 2 )
B. 12
( c cdot 4 )
D. 6
10
279Factorize:
( (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
280If 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
281Find the degree of the following polynomial
( boldsymbol{x}^{2}-mathbf{9} boldsymbol{x}+mathbf{2 0} )
10
282If ( 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
283Find 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
284Perform the division: ( 2 x^{2}+2 x+11 ) by
( boldsymbol{x}+mathbf{3} )
10
285Using 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
287Divide ( (10 x-25) div(2 x-5) )10
288Factorise:
( 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
289What 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
290Divide ( boldsymbol{a}+boldsymbol{b} ) by ( boldsymbol{a}^{1 / 3}+boldsymbol{b}^{1 / 3} )10
291If ( 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
292Solve:
( 8 l^{3}-36 l^{2} m+54 l m^{2}-27 m^{3} )
10
293Divide 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
294Using 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
295Factorise 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
296Factorize:
( 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
297Find the degree of the polynomial given
below:
( boldsymbol{x}^{5}-boldsymbol{x}^{4}+mathbf{3} )
9
298Find the degree of the following polynomial ( 2 x+4+6 x^{2} )10
299Decide using factor theorem, whether
( (x-2) ) is a factor of ( x^{3}-4 x^{2}-4 )
9
300Check 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
301If ( 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
303Expand ( (k+4)^{3} )10
304The 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
305Which 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
306If ( 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
307What is the degree of the given
monomial ( -x y^{2} ? )
( A cdot 2 )
B. 3
( c cdot 4 )
D. none
9
308If ( 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
309Use 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
310Evaluate 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
311Write 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
313Verify ( t=1 ) is a zero of the polynomial
( 2 t^{3}-3 t^{2}+7 t-6 )
10
314Assertion
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
315For 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
316Evaluate ( frac{(-40+80 a)}{8 a} )10
317UCHUU U
UU ULULLAH
3.
a 8 6x -2
Assertion : 4x + = is a linear equation.
Reason: Solution of the equation is-2.
10
318Which of the following is NOT a
( 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
319Expand ( (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
320Simplify ( -3 x y z div z^{2} )10
321Evaluate ( left(x^{2}-8 x+12right) div(x-6) )
A. ( x-2 )
B. ( x+2 )
c. ( x )
D. None
10
322Factorize
( 2 x^{2}+4 x+2=0 )
9
323Find 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
324If ( 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
325Find the product ( :(x-3)(x+3)left(x^{2}+right. )
( mathbf{9} )
9
326If ( a^{2}+b^{2}=29 ) and ( a b=10, ) then find
( a-b )
A . 10
B. 3
( c cdot 9 )
D. 19
9
327The degree of a polynomial ( 2 x^{5}-5 x^{3}- )
( 10 x+9 ) is
A . 5
B. 3
c. 1
D.
9
328f ( x+a ) is one of the factors of ( p(x)= )
( 2 x^{2}+2 a x+5 x+10, ) then find ( a )
9
329The 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
331If 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
333Let ( 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
33454. ( + ) simplifies to9
3354.
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
33661.
If x + y = z, then the expression
x + y – 2+ 3xyz will be equal
to :
(1) O
(2) 3xyz
(3) -3xyz (4) z
9
337If ( 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
338Classify the following as linear, quadratic and cubic polynomials
( x-1 )
10
339If ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{7}, ) find ( boldsymbol{x}^{mathbf{3}}+frac{mathbf{1}}{boldsymbol{x}^{mathbf{3}}} )9
340Write 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
341Which 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
34264. 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
343Show that:
( (a-b)(a+b)+(b-c)(b+c)+(c- )
( boldsymbol{a})(boldsymbol{c}+boldsymbol{a})=mathbf{0} )
9
344Test whether ( x^{5}+5 x^{3}+3 x ) is divisible
by ( (x-1) )
9
345Find the degree of the following polynomial ( x^{3}+2 x^{2}-5 x-6 )9
346Shew 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
347Find the degree of the given polynomials.
( x^{0} )
9
348Find the quotient the and remainder of the following division:
( left(2 x^{2}-3 x-14right) div(x+2) )
10
349If ( 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
350Use 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
351Find the cube of 1089
352If 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
353Divide 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
354Without finding the cubes, factorise the following:
( (x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3} )
9
355If ( 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
356Following 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
357Factorise 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
358Factorise :
( (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
359If ( 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
360Assertion :=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
361Simplify: ( (boldsymbol{x}+boldsymbol{y})^{2}+(boldsymbol{x}-boldsymbol{y})^{2} )9
362If ( 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
363The degree of constant polynomial is
A .
B. 2
c. 0
( D )
10
36480. 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
365On 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
367Evaluate the following (using identities):
( (11)^{3} )
9
368OLOT
57. If 2x + 3y = and xy =
then the value of 8×3 + 27yº is
(1) 583
(2) 583
(3) 187
(4) 671
9
369Evaluate:
( left(y^{3}-216right) div(y-6) )
10
370Find 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
371Factors 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
372Calculate ( 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
373Use suitable identities to find the
product of
( (x+5)(x+2) )
9
374Use Remainder theorem to factorize the
following polynomial. ( 2 x^{3}+3 x^{2}-9 x- )
( mathbf{1 0} )
9
375Evaluate ( 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
376Read 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
377Factorise 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
378What 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
379Say true or false:
The degree of the sum of two polynomials each of degree 5 is always
( mathbf{5} )
A . True
B. False
9
380Find the volume of the cuboid with
dimensions ( (x-1),(x-2) ) and ( (x- )
( mathbf{3}) )
9
381Determine whether the following polynomial has ( (x+1) ) as a factor.
( boldsymbol{x}^{4}-boldsymbol{x}^{3}+boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1} )
9
382If ( 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
383Divide 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
384Perform the division: ( 6 x^{3}-23 x+x^{2}+ )
12 by ( 2 x-3 )
10
385Solve:
( x^{4}+frac{1}{x^{4}} )
9
386On 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
387Find 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
388The zero polynomial is the identity of the additive group of polynomials.
A. multiplicative
c. multiplicative inverse
9
389Find the degree of the following polynomial ( x^{3}+17 x-21-x^{2} )9
390Expand ( (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
39156. 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
392Identify 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
393What is the degree of the polynomial
( (x+1)left(x^{2}-x-x^{4}+1right) ? )
9
394Divide :
( 15 x^{3} y^{3} ) by ( 3 x y^{2} )
10
39562. If * (3-2)-3
x # o, then
the value of x? +
(2)23
(1) 25
(3) 2
(427
9
396ff ( x=2 ) and ( y=-8 ) find the value of
( (x-y)^{3} )
10
397Evaluate:
( (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
398Expand using suitable identities
( (-2 a+5 b-3 c)^{2} )
9
399Which type of polynomial is ( 5 t-sqrt{7} ? )
A. Linear Polynomial
c. cubic Polynomial
D. None of above
10
400When ( 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
401Zero of the zero polynomial is
( mathbf{A} cdot mathbf{0} )
B. 1
C . Any real number
D. Not defined
10
402Determine whether the following polynomial has ( (x+1) ) as a factor. ( x^{3}-x^{2}-(3-sqrt{3}) x+sqrt{3} )9
403State 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
405The 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
406Let ( 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
407Write 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
410The degree of a polynomial ( x^{3}-27 ) is
( mathbf{A} cdot mathbf{3} )
B.
c. 26
D. 27
10
411Solve: ( frac{5 a^{3}-4 a^{2}+3 a+18}{a^{2}-2 a+3} )10
412Divide 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
413The 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
41467. 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
416Polynomials 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
417The 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
41859. If a = 11 and b = 9, then the
la? +62 + ab
value of 23 – 63 is
(1)
(2) 2
(3) 2
(4) 20
9
419Classify the following as a constant, linear, quadratic and cubic polynomials
( sqrt{2} x-1 )
A. Linear
c. cubic
D. None of these
9
420Given 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
421Find the value of ( 1.05 times 0.95 ) using
standard identity
A . 0.9985
B. 0.9975
c. 0.9875
D. 0.9995
9
422Expand the following using identities ( (x+7)(y+5) )9
423Perform the division: ( x^{4}-16 ) by ( x-2 )10
424Find 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
425The polynomial having atmost 3 zero
A. constant polynomial
B. linear polynomial
D. cubic polynomial
10
426If ( a-b-2=0 ) and ( a^{3}-b^{3}-6 a b=k )
then find the value of ( k )
9
427The 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
428Factorise ( : 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
429Factorize:
( 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
431Workout 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
432If ( 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
433What 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
434Divide and write the quotient and the remainder.
( left(p^{2}+7 p-5right) div(p+3) )
10
435Find the zeroes of polynomial ( boldsymbol{p}(boldsymbol{x})= )
( 6 x^{2}-3 )
10
436How to divide the equation in algebraic expression9
43771. I x*)2, then the value of
(1) 212
(3) 25
(2) 2
(4) 27
9
438Write 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
439Evaluate :
( frac{6 x^{2}-x-2}{3 x-2} )
10
440Classify the following as linear, quadratic and cubic polynomials:
( boldsymbol{x}^{boldsymbol{3}}-boldsymbol{4} )
A. Cubic
B. Linear
D. None of the above
9
441Write each of the following polynomials in the standard form. Also, write their
degree:
( a^{2}+4+5 a^{6} )
9
442If ( 3 x-frac{1}{3 x}=5, ) then find ( 81 x^{4}+frac{1}{81 x^{4}} )9
443Simplify:
( 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
444boty
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
445State whether the following expressions are polynomials in one variable or not. Give reasons for your answer. ( sqrt[3]{t}+2 t )10
446Find ( y^{2}+frac{1}{y^{2}} ) and ( y^{4}+frac{1}{y^{4}} ) if ( y+frac{1}{y}=9 )9
447The variable in the quadratic
polynomial ( t^{2}+4 t+5 ) is
( mathbf{A} cdot mathbf{1} )
B. 4
( c cdot t )
D. 5
10
448Solve ( :left[left(4 x^{4}-3 x^{3}-2 x^{2}+4 x-3right)right. )
divide by ( (x-1) )
10
449Degree of the polynomial
( left(a^{2}+1right)(a+2)left(a^{3}+3right) ) is
( A cdot 3 )
B. 6
( c cdot 2 )
( D )
10
450Evaluate: ( 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
452The 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
453According 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
454Evaluate 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
456Find 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
457Find the degree of the polynomial: 5
( boldsymbol{x}^{2} )
10
458Simplify: ( (3 a-5 b)^{3}-(3 a+5 b)^{3} )9
45969. If x + y +
5+= 4, then
the value of x + y2 is
(1) 2
(2) 4
(3) 8
(4) 16
9
460Factorise 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
461The 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
462The 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
463Simplify:
( (2 x+3 y)^{2} )
9
464If ( 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
466If ( 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
467A quadratic polynomial has at the most zero(es).
A . zero
B. one
c. three
D. two
10
468Evaluate:
( (a-3 b)^{2}-4(a-3 b)-21 )
9
469If ( 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
470The 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
471If ( frac{a}{b}+frac{b}{a}=1, ) then the value of ( a^{3}+b^{3} )
is-
A .
B. ( a )
( c cdot b )
D.
9
472Show 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
474Simplify: ( (3 m+5 n)^{2}-(2 n)^{2} )9
475Simplify:
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
476Remainder 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
47758. 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
478If ( 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
479Determine 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
480f ( 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
48152. 9×2 +25-30xcan be expressed
as the square of
(1) -3x-5 (2) 3x + 5
(3) 3x – 5 (4) 3×2 – 25
9
482Say 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
484Factorise: ( 7 y^{3}+12 z^{3} )9
48566.
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
48658. If p= 102 then the value of
p (p2 – 6p + 12) is
(1) 1000008 (2) 10000008
(3) 999992 (4) 9999992
9
487Evaluate using expansion of ( (a+b)^{2} ) or
( (a-b)^{2}: )
( (45)^{2} )
9
488Which 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
489The 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
490Give 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
491The quotient when
( left(2 x^{4}-3 x^{3}-x^{2}+4 x-2right) ) divided by
is:
10
49262. The value of 204 x 197 is
(1) 40218 (2) 40188
(3) 40212 (4) 39812
9
493If ( 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
494If ( 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
495f ( x=3, ) then the value of ( 20 x^{7}+x^{5} 3 )9
496Classify 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
497Find 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
499Expand ( frac{1}{x^{4}-5 x^{3}+7 x^{2}+x-8} ) in
descending powers of ( x ) to four terms, and find remainder.
10
500Identify zero polynomial among the following.
A . 0
B. ( x )
( mathbf{c} cdot x^{2} )
D. None of the above
9
501Find 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
502Expand: ( left(a^{2}+4 b^{2}right)(a+2 b)(a-2 b) )9
503The 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
505When ( 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
506The 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
507If ( a+b=5 ) and ( a^{2}+b^{2}=13, ) find ab9
508What 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
510State 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
511Choose 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
513If ( 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
514Write the quadratic polynomial with zeros -2 and ( frac{1}{3} )10
515Find the last digit of ( 1^{5}+2^{5}+ldots+99^{5} )9
516Find 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
517Find 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
518The 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
519Find 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
521Which 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
522Evaluate the following using suitable
identities
( (999)^{3} )
9
523Perform the division ( frac{left(x^{2}+1right)left(x^{2}+2right)}{left(x^{2}+3right)left(x^{2}+4right)} )10
524Find 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
525Solve by using suitable identity: ( a^{4}- )
( b^{4}+2 b^{2}-1 )
9
526f ( p=2-a ) then prove that ( a^{3}+6 a p+ )
( boldsymbol{p}^{3}-boldsymbol{8}=boldsymbol{0} )
9
527On 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
528If ( 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
529Factorize :
( (2 a+1)^{3}+(a-1)^{3} )
9
530Twenty 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
531Factorise:
( 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
532There 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
53385. 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
534Find the degree of the given algebraic
expression
( 3 x-15 )
( mathbf{A} cdot mathbf{1} )
B. 3
( c cdot 2 )
D. -15
10
5353.
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
B. linear
c. constant
D. cubic
10
537Solve ( (boldsymbol{a}+boldsymbol{b}+boldsymbol{c})^{3} )9
538Find 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
540If ( 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
542State the following statement is True or
False

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

9
543If ( a-b=7, a b=8, ) find ( a^{2}+b^{2} )9
544What 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
545Divide ( 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
546Simplify: ( (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
547The 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
548Write 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
549Simplify: ( left(boldsymbol{m}^{2}+boldsymbol{2} boldsymbol{n}^{2}right)^{2}-boldsymbol{4} boldsymbol{m}^{2} boldsymbol{n}^{2} )9
550Simplify: ( (boldsymbol{a}+boldsymbol{b})^{boldsymbol{3}} )9
551Find the polynomial which represents the perimeter of the rectangle whose length is 2 more than its breadth.10
552If 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
553If 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
5547.
(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
555Which 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
556Find the degree of following polynomial ( -frac{3}{2} )
A .
B. 2
c. 0
D. Cannot be determined
9
557Use 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
559Which type of polynomial is ( 3 x^{3} ? )
A. Cubic Polynomial
B. Linear Polynomial
c. square Polynomial
D. None of These
10
560Evaluate ( (2 x+3 y+5 z)^{2} )9
561Factorise 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
562Simplify:
(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
563The 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
564The 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
565f ( 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
567The polynomial
( left(a x^{2}+b x+cright)left(a x^{2}-d x-cright), a c neq 0 )
has?
10
5685.
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
569The 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
570Simplify:
( -45 p^{3} div 9 p^{2} )
10
571If 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
572If -1 is a zero of the polynomial ( p(x)= ) ( a x^{3}-x^{2}+x+4, ) find the value of ( a )10
573Divide:
( x^{7}-y^{7} ) by ( x-y )
10
574If ( a+2 b=9 ) and ( a b=7 . ) Find the value
of ( a^{2}+4 b^{2} )
9
57557. If xy (x + y) = 1, then the val-
ue of
-x- yº is :
(1) O
(3) 3
(2) 1
(4)-2
9
576If ( 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
577Factorize:
( 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
578Divide ( 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
57966. If x-1=1, then the value of
(1)
(2)
(4) O
10
580If ( 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
581Divide: ( 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
582Give 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
584State 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
585State 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
586State 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
587Find 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
588The 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
589Using the identity ( (boldsymbol{a}-boldsymbol{b})^{2}=boldsymbol{a}^{2}- )
( 2 a b+b^{2} ) compute ( (x-6)^{2} )
9
590Solve:
( 4 x^{4}-5 x^{3}-7 x+1 div 4 x-1 )
10
591Work out the following divisions:
( (10 x-25) div(2 x-5) )
10
592Illustration 2.13
Plot a graph for the equation y = x2 – 4x.
CO3
10
593Factorize ( 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
594Find the remainder when ( 4 x^{3}-3 x^{2}+ )
( 4 x-2 ) divided by ( (text { i) } x-1 )
(ii) ( x-2 )
10
595If ( x+frac{1}{x}=7 ) the value of ( x^{4}+frac{1}{x^{4}} ) is
A .2401
в. 2023
c. 2209
D. 2207
9
596If 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
597Is ( x^{8}+a^{8} ) divisible by ( x+a ? )10
598Using 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
599The 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
600ff ( 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
601Degree of the polynomial ( left(x^{3}-2right)left(x^{2}+right. )
11) is
( mathbf{A} cdot mathbf{0} )
B. 5
( c .3 )
D.
10
602If ( 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
603Divide the polynomial ( 39 y^{3}left(50 y^{2}-98right) )
by ( 36 y^{2}(5 y+7) )
10
604Expand using suitable identities
( (2 a-3 b)^{3} )
9
605Divide ( (24 x-42) ) by ( (4 x-7) )
A ( .4 x-7 )
B. 3
( c cdot 6 )
D. 7
10
606If ( 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
607Which type of polynomial, the given
expression ( 5 x^{2}+x-7 ) is?
9
608Find a quadratic polynomial each with the give numbers as the sum and
product of its zeros respectively.
4,1
10
609State 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
610Write the degree of each polynomial
given below:
( boldsymbol{x} boldsymbol{y}+boldsymbol{y} boldsymbol{z}-boldsymbol{z} boldsymbol{x}^{3} )
10
611Perform the division: ( x^{3}-5 x^{2}+8 x-4 )
by ( boldsymbol{x}-mathbf{2} )
10
612Simplify: ( frac{mathbf{6 x}^{2}+mathbf{9 x}}{mathbf{3 x}^{2}-mathbf{1 2 x}} )10
613Factorize:
( 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
614Which 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
615Write 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
61666. 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
617Solve: ( x^{3}-(x+1)^{2}=2001 )
( A cdot 13 )
B. 16
c. 10
D. 21
10
618Carry out the following divisions ( 11 x y^{2} z^{3} ) by ( 55 x y z )10
619Evaluate the following using suitable identity:
( (10 x-1)^{2} )
( (x-8 y)^{2} )
9
620Simplify : ( 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
621Write the degree of the following polynomial:
( 5 y+sqrt{2} )
9
622Degree 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
623Solution:
( 10 a^{2}(0.1 a-0.5 b) )
9
624( (2 x+3 y)^{2}-16 z^{2} )9
625The 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
626Simplify:
i) ( left(a^{2}-b^{2}right)^{2} )
ii) ( (2 x+5)^{2}-(2 x-5)^{2} )
9
62759. 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
628Use the identity and expand the following ( (2 x+y)^{2} )9
629What is meant by division algorithm
give example?
10
630If ( x+frac{1}{x}=sqrt{3}, ) find the value of ( x^{3}+ )
( frac{1}{x^{3}} )
9
631The 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
632Solve:
( left(y^{2}+10 y+24right) div(y+4) )
10
633Find 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
634Factorise 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
635What 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
63665. If x2 + y2 – 4x – 4y + 8 = 0, then
the value of x-y is
(1) 4
(2) 4
(3) O
(4) 8
9
637Find the quotient and remainder when
( p(x)=x^{3}-3 x^{2}+5 x-3 ) is divided by
( g(x)=x^{2}-2 )
10
638Find 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
639Using 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
640Find ( 302 times 308 )9
641Divide 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
642Find the remainder if ( x-1 ) is divided by
( 5 x^{3}-2 x^{2}+3 x-22 )
9
643The 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
644Find the value of ( (2-sqrt{1-x})^{6}+(2+ )
( sqrt{1-x})^{6} )
9
645Work 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
646Using the Remainder and Factor Theorem, factorise the following polynomial: ( x^{3}+10 x^{2}-37 x+26 )10
647If ( 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
648Divide 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
649If 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
650Using 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
651Divide ( 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
652If ( 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
653Factorise the expression and divide them as directed.
( 5 p qleft(p^{2}-q^{2}right) div 2 p(p+q) )
10
654If ( 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
655Solve
( left(15 y^{4}+10 y^{3}-3 y^{2}right) div 5 y^{2} )
10
656Evaluate ( 8.5 times 9.5 ) using suitable
standard identity.
9
657ff both ( (x-2) ) and ( left(x-frac{1}{2}right) ) are factors of ( p x^{2}+5 x+r, ) show that ( p=r )9
658Find the cube of 239
659Which 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
660Expand ( 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
661Find the degrees of the following polynomial
( 3-4 a b+5 b^{3}+2 a b^{2} )
9
662Prove 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
663Which 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
664Find the product. ( (3+sqrt{2})(2+sqrt{3})(3-sqrt{2})(2-sqrt{3}) )9
6653+ x + V3 -X=2 then x is
66. V3+r
13 + x – 13-
equal to
9
666Simplify:
( a^{6}-b^{6} )
9
667Divide ( 4 x^{3}+3 x^{2}-2 x+8 ) by ( x-2 )10
668Write the polynomial in standard form
and also write down their degree. ( 4 z^{3}-3 z^{5}+2 z^{4}+z+1 )
10
669Find 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
67067. If a+b= 10 and a + b = 58,
then a + b3 will be equal to
(1) 340 (2) 540
(3) 270 (4) 370
9
671Use 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
672Find the degree of the polynomial:
( mathbf{7} boldsymbol{x}^{mathbf{3}}+mathbf{2} boldsymbol{x}^{mathbf{2}}+boldsymbol{x} )
10
673If ( b ) is zero of the polynomial ( p(x)= )
( a x^{2}-3(a-1) x-1, ) then find the
value of ( boldsymbol{a} )
9
674Divide ( x^{4}-y^{4} ) by ( x-y )10
675Factorize ( 27 m^{3}-216 n^{3} )9
676Check 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
677Find the remainder when ( p(x)=x^{3}- )
( 4 x^{2}+3 x+1 ) is divided by ( (x-1) )
9
678Classify the following polynomial based on their degrees:
( boldsymbol{y}+mathbf{3} )
10
679Two 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
680Divide
( left(2 a^{2}-13 a b+15 b^{2}right) b y(a-5 b) )
10
681Factorise 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
68252.
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
68357. If xy (x + y) = 1, then the val-
ue of –
+3,3-*-y is :
(1) o
(3) 3
(2) 1
(4) -2
9
68466. 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
68570. If x
3 then the value of
x1 + x2 + x + 1 is
(1)
(2) 1
(3) 2
(4) 3
9
68655. 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
687If ( 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
688Convert into factors ( a^{2}+4 a+4-b^{2} )9
689Evaluate ( (10 x-25) div(2 x-5) )
( mathbf{A} cdot mathbf{5} )
B. 4
( c cdot 3 )
D.
10
690Write the constant term of each of the
following algebraic expressions: ( a^{3}- ) ( 3 a^{2}+7 a+5 )
9
691If ( 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
692Find ( 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
693Find 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
694If ( 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
695Divide
( 4 sqrt{2} y^{3} ) by ( 3 sqrt{2} y^{2} ) The answer is ( frac{m y}{3} )
Then ( m= )
10
696If ( 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
697Which type of polynomial is ( 45 y^{2} ? )
A. Linear Polynomial
c. Cubic Polynomial
9
698Find the missing terms such that the given polynomial become a perfect square trinomial:
( 81 x^{2}+dots-1 )
10
699Factorise:
( 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
700If ( (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
701Find the square of:
607
A. 368549
B. 368449
( c .368349 )
D. 368249
9
702Zero of the polynomial ( p(x)=2-5 x ) is10
703Use 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
704Verify ( f(x)=2 x^{3}+11 x^{2}-7 x-6 ) is
the factor of ( (x-1) ) using factor
theorem.
10
705Find 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
706State 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
707Find the value of ( 87^{2}-13^{2} )
A . 7300
B. 7350
( c .7400 )
D. 7450
9
708Divide ( 6 x^{4}+13 x^{3}+39 x^{2}+37 x+45 )
by ( 3 x^{2}+2 x+9 )
10
709Degree of a constant term of a
polynomial is
A .
B. 0
( c cdot 2 )
D. Not defined
9
7106.
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
711Using identity find the value of ( (4.7)^{2} )9
712Divide ( 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
713Find the remainder when ( p(x)=x^{3}+ )
( 3 x^{2}+3 x+1, ) is divided by ( x )
( A )
B.
( c cdot-1 )
D.
9
714State 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
D. constant
10
716State whether True or False.
Divide: ( x^{2}+3 x-54 ) by ( x-6, ) then the
answer is ( x+9 )
A. True
B. False
10
717Expand ( (sqrt{10} x-sqrt{5} y)^{2} ) using
appropriate identity
9
718When ( 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
719Find the degree of each of the polynomials given below ( 5 t-sqrt{3} )10
720Divide and write the quotient and
remainder:
( left(4 x^{4}-5 x^{3}+0 x^{2}-7 x+1right) div(4 x-1) )
10
721Find whether ( x-1 ) is a factor of ( 2 x^{2}- )
( mathbf{5} boldsymbol{x}+mathbf{3} )
10
722What 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
723Find 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
724Degree of which of the following polynomial is zero?
( A cdot x )
B . 15
c. ( y )
D. ( _{x+frac{1}{x}} )
9
725In 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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