# Algebraic Expressions Questions

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

#### List of algebraic expressions Questions

Question NoQuestionsClass
1Write each of the following as decimals
( mathbf{2 0 0}+mathbf{6 0}+mathbf{5}+mathbf{1} / mathbf{1 0} )
7
2Simplify 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
4The 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
5The 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
6If ( x^{2}+frac{1}{x^{2}}=51, ) find the value of ( x^{3}- )
1
( overline{x^{3}} )
7
7f ( x^{2}+y^{2}=2 ) and ( y^{11}+A . y^{-3}=0 ) then
( A ) is
7
8A 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
9If 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
10f ( a=2, b=-2, ) find the value of:
( a^{2}+a b+b^{2} )
7
11Simplify the expression and find the
value if ( x ) is equal to 2
( 3(x+2)+5 x-7 )
7
12Divide
( frac{x^{2}-36}{x^{2}-49} div frac{x+6}{x+7} )
7
13ff ( 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
14The value of ( x=sqrt{2}+sqrt{2+sqrt{2+ldots}} ) is7
15Draw a graph between ( y=p(x), ) where
polynomial having three zeros.
7
16Find ( x ) for which ( f(x)=0 ) when ( f(x)= )
( x^{2}-64 )
7
17Solve: ( left(x^{2}+1right)^{5} sin 4 x )7
18Solve: ( (x+y)^{2}+(x-y)^{2} )
A ( cdot 2 x^{2} )
B.
c. ( 2 x^{2}+2 y^{2} )
D. ( 2 y^{2} )
7
19Simplify:
( boldsymbol{p}^{2} boldsymbol{q}-boldsymbol{p} boldsymbol{q}^{2}-boldsymbol{p} boldsymbol{q}+boldsymbol{r}^{2} )
7
20If ( 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
21Find the value of :
( 36 x^{2}+49 y^{2}+84 x y, ) when ( x=3, y=6 )
7
22If ( 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
23Simplify ( 3 x(4 x-5)+3 ) and find its
value for ( (mathrm{i}) x=3 )
(ii) ( x=frac{1}{2} )
7
24The 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
25Verify:
( boldsymbol{x}^{3}+boldsymbol{y}^{3}=(boldsymbol{x}+boldsymbol{y})left(boldsymbol{x}^{2}-boldsymbol{x} boldsymbol{y}+boldsymbol{y}^{2}right) )
7
26If ( x^{y}=y^{x} ) and ( x=2 y, ) then find the
value of ( x+y . ) (Assume that ( y neq 0 ) )
7
27Solve: ( 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
291x + 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
30f ( 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
31Evaluate:
( left(frac{a}{2 b}+frac{2 b}{a}right)^{2}-left(frac{a}{2 b}-frac{2 b}{a}right)^{2}-4 )
7
32Consider 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
33If ( f(x)=x^{3}-3 x^{2}+5 )
Find ( f(0)+f(3) )
7
34If one roots of the polynomial ( k x^{2}- )
( 15 x+18=0 ) is 2 then ( k= )
7
35Solve ( left(x^{2}+3 xright)(2 x+3)-16 frac{2 x+3}{x^{2}+3 x} )7
36f ( x=-3, ) find the value of:
( 2 x-3 )
7
3769. 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
38If ( x^{2}+x-12 ) divides ( P(x)=x^{3}+ ) ( a x^{2}+b x-84 ) exactly, find ( a ) and ( b ).7
39Find the value of the polynomial ( 5 x- )
( 4 x^{2}+3 ) at ( x=-1,2,-2 )
7
4070. The simplified value of
T2 + 53 – 75
(1) 1
12-13 – Tois
(2) O
7
41Find 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
42Prove 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
4365. Find the value
V1x2 + y2 + 2)(x + y -3z) +
wyz2 when x= + 1, y =-3. z
=-1.
(1) 1
(2) 0
(3) -1
7
44Solve : ( (a+b)(a-b) )7
45Simplify:
( frac{m^{2}-n^{2}}{(m+n)^{2}} times frac{m^{2}+m n+n^{2}}{m^{3}-n^{3}} )
7
46f ( 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
47Simplify the following algebraic
expression.
( 14 c-13 c-17+8 )
A ( . c=-9 )
B ( . c=9 )
c. ( c=-25 )
D. ( c=25 )
7
48If ( 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
49The 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
50If ( 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
51Write 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
52Find 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
53If ( 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
54If ( 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
55Solve 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
56If ( a+b=5 ) and ( a b=6 ) then find the
value of ( a^{3}+b^{3} )
7
57Find ( 6 y^{5}-y^{4}+4 y^{3}-5 y^{2}-y-15 ) if
( y=3 )
7
5859. Which of the following will sat-
(1) 2
(3) 4
these
(2) 3
(4) None of
7
59Find 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
60Find the value of following if ( x=-1 ) ( x(x)^{2}-(3 x)^{2} )7
61If ( (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
62Find ( boldsymbol{y} ) when ( boldsymbol{x}=frac{mathbf{3}}{mathbf{2}} ) when ( mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{1 2} )7
63ff ( 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
65Find the value of the following
expressions, when ( x=-1 )
( 2 x^{2}-x-2 )
7
66f ( boldsymbol{x}=mathbf{1} ; boldsymbol{y}=mathbf{2} ) find the values:
( boldsymbol{x}^{2}+boldsymbol{y}^{2} )
7
67ff ( 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
68Find 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
69If ( 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
70f ( 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
71If ( 3 x+frac{1}{3 x}=3 ) find ( 9 x^{2}+frac{1}{9 x^{2}} )7
72Find the value of the polynomial ( 4 x^{2}- )
( mathbf{5} boldsymbol{x}+mathbf{3}, ) when ( boldsymbol{x}=mathbf{0} )
7
73If ( boldsymbol{m}=mathbf{2} ) and ( boldsymbol{n}=mathbf{1}, ) then find the value
of following polynomials:
( m+3 n )
7
74If ( x=3, ) then find the value of the
expression ( boldsymbol{x}-mathbf{2} )
7
75Solve:
( 2.5 x-6+7.5 x-24=0 )
7
76Find ( 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
77Find the value of the polynomial ( 5 x- )
( 4 x^{4}+3 ) at
( boldsymbol{x}=mathbf{0} )
7
78Find ‘a’, if ( x+1 ) is a factor of ( x^{3}+3 x^{2}- )
( 2 a x )
7
79Find the value of ( 12 x^{3}+x^{3}+x . ) If ( x=3 )7
80If ( 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
81f ( boldsymbol{m}=mathbf{2}, ) find the value of ( boldsymbol{3} boldsymbol{m}-boldsymbol{2} )7
82If ( m=2, ) find the value of ( frac{5 m}{2}-4 )7
83Find 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
84f ( a=1 ) and ( b=-1, ) find the value of
the following:
( left(a^{2}+b^{2}right)left(-a^{2}+b^{2}right) )
7
85If ( 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
86Simplify ( :(a+2 b+3 c)^{2}- )
( (a-2 b+3 c)^{2}-6 b^{2}-9 b c )
7
87Find the value of the polynomial ( 5 x- )
( 4 x^{4}+3 ) at
( boldsymbol{x}=mathbf{2} )
7
8864.
If x = 2+ 13 y = 2-13
then the value of 8xy (x + y ) is
(1) 196 (2) 290
(3) 112 (4) 194
7
89Solve:
( mathbf{3}(boldsymbol{t}-mathbf{5})-mathbf{1 6} boldsymbol{t}=mathbf{1 2}-mathbf{2}(boldsymbol{t}-mathbf{3}) )
7
90If ( frac{a}{b}=frac{2}{3}, ) then find the value of ( frac{4 a+3 b}{3 b} )7
91Give 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
92Solve
( (3 a+4 b) times(4 a+3 b) )
7
93In 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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