Algebraic Expressions Questions

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List of algebraic expressions Questions

Question No Questions Class
1 Write each of the following as decimals
( mathbf{2 0 0}+mathbf{6 0}+mathbf{5}+mathbf{1} / mathbf{1 0} )
7
2 Simplify these expression and find their values if ( boldsymbol{x}=mathbf{3}, boldsymbol{a}=-mathbf{1}, boldsymbol{b}=-mathbf{2} )
( 2-8 x+4 x+4 )
7
3 ( (1+x)^{m}(1-x)^{n} x^{2}-6 )
Find absolute value at ( boldsymbol{x}=mathbf{0} )
( A cdot 6 )
B. -6
c. 12
D. 24
7
4 The value of the following polynomial at the indicate value of variables:
( boldsymbol{q}(boldsymbol{y})=boldsymbol{3} boldsymbol{y}^{2}-boldsymbol{4} boldsymbol{y}+sqrt{11} ) at ( boldsymbol{y}=boldsymbol{2} ) is
equal to ( 4+sqrt{11} )
A. True
B. False
7
5 The number of real solutions of the
equation ( left(frac{mathbf{9}}{mathbf{1 0}}right)^{boldsymbol{x}}=-mathbf{3}+boldsymbol{x}-boldsymbol{x}^{2} ) is
A .2
B.
( c cdot 0 )
D. None of these
7
6 If ( x^{2}+frac{1}{x^{2}}=51, ) find the value of ( x^{3}- )
1
( overline{x^{3}} )
7
7 f ( x^{2}+y^{2}=2 ) and ( y^{11}+A . y^{-3}=0 ) then
( A ) is
7
8 A value of ( x ) satisfying the equation ( x^{2}+b^{2}=(a-x)^{2} ) is:
A ( cdot frac{b^{2}+a^{2}}{2 a} )
в. ( frac{b^{2}-a^{2}}{2 a} )
c. ( frac{a^{2}-b^{2}}{2 a} )
D. ( frac{a-b}{2} )
7
9 If a monomial ( frac{2}{5} x^{2} y^{2}, ) binomial ( 2 x+3 y ) and a trinomial ( 2 x+3 y+4 z ) are
added, then the resultant expression is
( a )
A. Monomial
B. Binomial
c. Multinomial
D. Trinomial
7
10 f ( a=2, b=-2, ) find the value of:
( a^{2}+a b+b^{2} )
7
11 Simplify the expression and find the
value if ( x ) is equal to 2
( 3(x+2)+5 x-7 )
7
12 Divide
( frac{x^{2}-36}{x^{2}-49} div frac{x+6}{x+7} )
7
13 ff ( boldsymbol{x}=mathbf{3}+mathbf{3}^{mathbf{1} / mathbf{3}}+mathbf{3}^{mathbf{2} / 3} ) then ( boldsymbol{x}^{mathbf{3}}-mathbf{9} boldsymbol{x}^{mathbf{2}}+ )
( 18 x-12= )
A . 2
B. 3
c. 0
D. 5
7
14 The value of ( x=sqrt{2}+sqrt{2+sqrt{2+ldots}} ) is 7
15 Draw a graph between ( y=p(x), ) where
polynomial having three zeros.
7
16 Find ( x ) for which ( f(x)=0 ) when ( f(x)= )
( x^{2}-64 )
7
17 Solve: ( left(x^{2}+1right)^{5} sin 4 x ) 7
18 Solve: ( (x+y)^{2}+(x-y)^{2} )
A ( cdot 2 x^{2} )
B.
c. ( 2 x^{2}+2 y^{2} )
D. ( 2 y^{2} )
7
19 Simplify:
( boldsymbol{p}^{2} boldsymbol{q}-boldsymbol{p} boldsymbol{q}^{2}-boldsymbol{p} boldsymbol{q}+boldsymbol{r}^{2} )
7
20 If ( a^{2}+b^{2}+c^{2}=14, ) then ( a b+b c+c a )
is always greater than or equal to?
( mathbf{A} cdot mathbf{0} )
B. 14
c. -1
D. –
7
21 Find the value of :
( 36 x^{2}+49 y^{2}+84 x y, ) when ( x=3, y=6 )
7
22 If ( boldsymbol{x}=mathbf{7}+mathbf{4} sqrt{mathbf{3}}, boldsymbol{y}=mathbf{7}-mathbf{4} sqrt{mathbf{3}}, ) then ( frac{mathbf{1}}{boldsymbol{x}}+ )
( frac{1}{y}= )
A . 11
B. 14
c. 8
D. 6
7
23 Simplify ( 3 x(4 x-5)+3 ) and find its
value for ( (mathrm{i}) x=3 )
(ii) ( x=frac{1}{2} )
7
24 The area enclosed by the polynomial function of least degree satisfying ( lim _{x rightarrow 0}left[1+frac{f(x)}{x^{3}}right]^{frac{1}{x}}=e ) and the circle
( x^{2}+y^{2}=2 ) above the ( X ) -axis is
in square units.
( A )
[
frac{3}{5}+frac{pi}{2}
]
B.
[
frac{2}{5}-frac{pi}{2}
]
c. ( frac{2}{5}+frac{pi}{2} )
D.
[
frac{1}{5}+frac{pi}{2}
]
7
25 Verify:
( boldsymbol{x}^{3}+boldsymbol{y}^{3}=(boldsymbol{x}+boldsymbol{y})left(boldsymbol{x}^{2}-boldsymbol{x} boldsymbol{y}+boldsymbol{y}^{2}right) )
7
26 If ( x^{y}=y^{x} ) and ( x=2 y, ) then find the
value of ( x+y . ) (Assume that ( y neq 0 ) )
7
27 Solve: ( 5-frac{2 d+7}{9}=0 )
A . 19
B. 14
( c .9 )
D.
7
28 ( boldsymbol{f}(boldsymbol{x})=boldsymbol{x}^{2}+mathbf{3} boldsymbol{x}+mathbf{5} ) find ( boldsymbol{f}(boldsymbol{4}) ) 7
29 1x + 2 + VX-2
59. If a =
Tx+2-x-2
then
2-VX-2
the value of (a? – and is
(1) 1
(2) 2
(3) -1
(4) O
toi
7
30 f ( a+b+c=8 ), then the value of
( (a-4)^{3}+(b-3)^{3}+(c-1)^{3}-3(a- )
4) ( (b-3)(c-1) ) is:
( A cdot 2 )
B. 4
( c cdot 1 )
( D )
7
31 Evaluate:
( left(frac{a}{2 b}+frac{2 b}{a}right)^{2}-left(frac{a}{2 b}-frac{2 b}{a}right)^{2}-4 )
7
32 Consider the algebraic equation:
( 3 x^{3} y-4 x^{2} y^{2}+frac{1}{2} x y^{2}-5 x ) How many
terms are there in the equation? List all the terms.What is the numerical coefficient of the term ( frac{1}{2} x y^{2} ? )
7
33 If ( f(x)=x^{3}-3 x^{2}+5 )
Find ( f(0)+f(3) )
7
34 If one roots of the polynomial ( k x^{2}- )
( 15 x+18=0 ) is 2 then ( k= )
7
35 Solve ( left(x^{2}+3 xright)(2 x+3)-16 frac{2 x+3}{x^{2}+3 x} ) 7
36 f ( x=-3, ) find the value of:
( 2 x-3 )
7
37 69. If x2 = y + z, y2 = 2 + x,
z = x + y, then the value of
1 1 1
x+1+ y +1 ++1 is
(1)-1 (2) 1
(3) 2
(4) 4.
7
38 If ( x^{2}+x-12 ) divides ( P(x)=x^{3}+ ) ( a x^{2}+b x-84 ) exactly, find ( a ) and ( b ). 7
39 Find the value of the polynomial ( 5 x- )
( 4 x^{2}+3 ) at ( x=-1,2,-2 )
7
40 70. The simplified value of
T2 + 53 – 75
(1) 1
12-13 – Tois
(2) O
7
41 Find the value of the polynomial ( y^{3}- )
( 5 y-2 y^{2}+3 ) when, ( y=-b )
A. ( -b^{3}-2 b^{2}+5 b+3 )
3
В. ( b^{2}-2 b^{3}+b+1 )
C. ( -b^{3}-2 b^{2}-b+3 )
D. ( b^{3}-2 b^{2}+b-3 )
7
42 Prove that ( boldsymbol{x}^{4}+boldsymbol{4}=(boldsymbol{x}+mathbf{1}+boldsymbol{i})(boldsymbol{x}+ )
( mathbf{1}-boldsymbol{i})(boldsymbol{x}-mathbf{1}+boldsymbol{i})(boldsymbol{x}-mathbf{1}-boldsymbol{i}) )
7
43 65. Find the value
V1x2 + y2 + 2)(x + y -3z) +
wyz2 when x= + 1, y =-3. z
=-1.
(1) 1
(2) 0
(3) -1
7
44 Solve : ( (a+b)(a-b) ) 7
45 Simplify:
( frac{m^{2}-n^{2}}{(m+n)^{2}} times frac{m^{2}+m n+n^{2}}{m^{3}-n^{3}} )
7
46 f ( boldsymbol{m}=-mathbf{1} mathbf{9} ) and ( boldsymbol{n}=mathbf{2 3}, ) the value of
( 25 m^{2}+40 m n+16 n^{2} ) is
( A cdot 9 )
в. -9
( c .1 )
D. 3
7
47 Simplify the following algebraic
expression.
( 14 c-13 c-17+8 )
A ( . c=-9 )
B ( . c=9 )
c. ( c=-25 )
D. ( c=25 )
7
48 If ( x^{4}+frac{1}{x^{4}}=194, ) then ( x^{3}+frac{1}{x^{3}} ) is equal
to
A . 76
B. 52
c. 64
D. None of these
7
49 The coefficient of middle term in the
expansion of ( (1+x)^{10} ) is
A . ( 10 ! / 5 ! 6 ! )
B . ( 10 ! / 5 !^{2} )
c. ( 10 ! ) 5! 7
D. None of these
7
50 If ( boldsymbol{x}=frac{sqrt{mathbf{3}}+sqrt{mathbf{2}}}{sqrt{mathbf{3}}-sqrt{mathbf{2}}} ) find ( boldsymbol{x}^{2}+frac{mathbf{1}}{boldsymbol{x}^{2}} ) 7
51 Write the expressions ( 5 x^{2}-4-3 x^{2}+ )
( 6 x+8+5 x-3 ) in its simplified form
Find its value when ( boldsymbol{x}=-mathbf{2} )
7
52 Find the value of following polynomial
by taking ( boldsymbol{x}=mathbf{1}, boldsymbol{y}=mathbf{3} )
( boldsymbol{y}^{2}-boldsymbol{x} boldsymbol{y}+boldsymbol{y} )
( A cdot 7 )
B. 8
( c .9 )
D. 11
7
53 If ( x=2 ) and ( x=3 ) are the roots of the
equation ( 3 x^{2}-2 m x+2 n=0, ) find the
values of ( m ) and ( n )
7
54 If ( z=3-4 i, ) then ( z^{4}-3 z^{3}+3 z^{2}+ )
( 99 z-95 ) is equal to
A . 5
B. 6
( c .-5 )
D. – 4
7
55 Solve the following equations:
( boldsymbol{x}+boldsymbol{y}+boldsymbol{z}=frac{mathbf{1}}{boldsymbol{x}}+frac{mathbf{1}}{boldsymbol{y}}+frac{mathbf{1}}{boldsymbol{z}}=frac{mathbf{7}}{mathbf{2}}, boldsymbol{x} boldsymbol{y} boldsymbol{z}=mathbf{1} )
7
56 If ( a+b=5 ) and ( a b=6 ) then find the
value of ( a^{3}+b^{3} )
7
57 Find ( 6 y^{5}-y^{4}+4 y^{3}-5 y^{2}-y-15 ) if
( y=3 )
7
58 59. Which of the following will sat-
(1) 2
(3) 4
these
(2) 3
(4) None of
7
59 Find the value of ( sqrt{a sqrt{a sqrt{a ldots . . infty}}} )
( A )
B ( cdot a^{2} )
( mathbf{c} cdot a^{3} )
D. ( sqrt{a} )
7
60 Find the value of following if ( x=-1 ) ( x(x)^{2}-(3 x)^{2} ) 7
61 If ( (x-1),(x+1) ) and ( (x-2) ) are
factors of ( boldsymbol{x}^{4}+(boldsymbol{p}-boldsymbol{3}) boldsymbol{x}^{3}-(boldsymbol{3} boldsymbol{p}- )
5)( x^{2}+(2 p-9) x+6, ) what is the value
of p?
( mathbf{A} cdot mathbf{1} )
B . 2
( c cdot 3 )
D.
7
62 Find ( boldsymbol{y} ) when ( boldsymbol{x}=frac{mathbf{3}}{mathbf{2}} ) when ( mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{1 2} ) 7
63 ff ( P(x)=2 x^{3}-3 x^{2}+4 x-2, ) then ( P(-1) )
is:
( A cdot-2 )
B. -11
( c cdot 0 )
D.
7
64 ( f(x)=x^{2}-2 sqrt{2} x+1 . ) Then find the
value of ( boldsymbol{p}(boldsymbol{2} sqrt{boldsymbol{2}}) )
7
65 Find the value of the following
expressions, when ( x=-1 )
( 2 x^{2}-x-2 )
7
66 f ( boldsymbol{x}=mathbf{1} ; boldsymbol{y}=mathbf{2} ) find the values:
( boldsymbol{x}^{2}+boldsymbol{y}^{2} )
7
67 ff ( P(x) ) is a polynomial of degree 3 such that ( P(i)=frac{1}{i+1} forall i={1,2,3,4} ) then find ( P(5) ) 7
68 Find the zero of the polynomial in each of the following: ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}+mathbf{2} )
A . -2
B. –
c. 0
D. 2
7
69 If ( boldsymbol{x}=frac{1}{2}, boldsymbol{y}=1, boldsymbol{z}=2 operatorname{then} boldsymbol{x}^{100} boldsymbol{y}^{99} boldsymbol{z}^{99}+ )
( boldsymbol{x}^{99} boldsymbol{y}^{100} boldsymbol{z}^{99}+boldsymbol{x}^{99} boldsymbol{y}^{99} boldsymbol{z}^{100}= )
( A cdot frac{5}{2} )
B. ( frac{7}{2} )
( c cdot frac{3}{2} )
D.
7
70 f ( a=2 ) and ( b=3, ) find the value of
(i) ( 2 a-3 b )
(ii) ( 5 a^{2}-2 a b )
(iii) ( a^{3}-b^{3} )
7
71 If ( 3 x+frac{1}{3 x}=3 ) find ( 9 x^{2}+frac{1}{9 x^{2}} ) 7
72 Find the value of the polynomial ( 4 x^{2}- )
( mathbf{5} boldsymbol{x}+mathbf{3}, ) when ( boldsymbol{x}=mathbf{0} )
7
73 If ( boldsymbol{m}=mathbf{2} ) and ( boldsymbol{n}=mathbf{1}, ) then find the value
of following polynomials:
( m+3 n )
7
74 If ( x=3, ) then find the value of the
expression ( boldsymbol{x}-mathbf{2} )
7
75 Solve:
( 2.5 x-6+7.5 x-24=0 )
7
76 Find ( mathbf{S}, ) where ( boldsymbol{S}=frac{[boldsymbol{n}(boldsymbol{n}+mathbf{1})(boldsymbol{2} boldsymbol{n}+mathbf{1})]}{mathbf{6}} )
and ( n=20 )
A . 2780
в. 2870
c. 1460
D. 1870
7
77 Find the value of the polynomial ( 5 x- )
( 4 x^{4}+3 ) at
( boldsymbol{x}=mathbf{0} )
7
78 Find ‘a’, if ( x+1 ) is a factor of ( x^{3}+3 x^{2}- )
( 2 a x )
7
79 Find the value of ( 12 x^{3}+x^{3}+x . ) If ( x=3 ) 7
80 If ( boldsymbol{x}=(-mathbf{3}), ) then find the value of
( left(x^{2}right)^{3} timesleft(frac{1}{x}right)^{4} times x )
A ( cdot(-25) )
B . (-27)
c. (-15)
D. None of these
7
81 f ( boldsymbol{m}=mathbf{2}, ) find the value of ( boldsymbol{3} boldsymbol{m}-boldsymbol{2} ) 7
82 If ( m=2, ) find the value of ( frac{5 m}{2}-4 ) 7
83 Find the value of ( f ) in ( frac{1}{f}=frac{1}{u}+frac{1}{v}, ) when
( boldsymbol{u}=mathbf{1 5} ) and ( boldsymbol{v}=mathbf{1 0} )
A . -6
в. ( frac{1}{6} )
( c cdot 6 )
D. ( -frac{1}{6} )
7
84 f ( a=1 ) and ( b=-1, ) find the value of
the following:
( left(a^{2}+b^{2}right)left(-a^{2}+b^{2}right) )
7
85 If ( x+y=4 ) and ( frac{1}{x}+frac{1}{y}=4, ) then the
value of ( x^{3}+y^{3} ) is
( mathbf{A} cdot 52 )
B. 64
( c cdot 4 )
D. 25
7
86 Simplify ( :(a+2 b+3 c)^{2}- )
( (a-2 b+3 c)^{2}-6 b^{2}-9 b c )
7
87 Find the value of the polynomial ( 5 x- )
( 4 x^{4}+3 ) at
( boldsymbol{x}=mathbf{2} )
7
88 64.
If x = 2+ 13 y = 2-13
then the value of 8xy (x + y ) is
(1) 196 (2) 290
(3) 112 (4) 194
7
89 Solve:
( mathbf{3}(boldsymbol{t}-mathbf{5})-mathbf{1 6} boldsymbol{t}=mathbf{1 2}-mathbf{2}(boldsymbol{t}-mathbf{3}) )
7
90 If ( frac{a}{b}=frac{2}{3}, ) then find the value of ( frac{4 a+3 b}{3 b} ) 7
91 Give possible expressions for the length and breadth of the rectangle whose area is given by
(i) ( 25 a^{2}-35 a+12 )
(ii) ( 24 x^{2}-15 x )
7
92 Solve
( (3 a+4 b) times(4 a+3 b) )
7
93 In the equation ( x+y=4, ) what is the
value of ( x ) if ( y=2 ? )
( A cdot 2 )
B. 4
( c cdot 6 )
D.
7

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