750+ Algebra Question with Solution PDF
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Algebra Question with Solution PDF
Q : If a+b=2c, find
(A) 2
(B) -1
(C) 0
(D) 1
Correct Answer : D
Q : If a, b are rational number and (a-1)√2+3=b√2+a, the value of (a+b) is :
(A) -3
(B) 5
(C) -5
(D) 3
Correct Answer : B
Q : If a-6b = 3 then the value of a3-216b3-54ab is :
(A) 27
(B) 64
(C) 9
(D) 1
Correct Answer : A
Q : if a3b = abc = 180, a, b, c are positive integers, then the value of c is
(A) 4
(B) 25
(C) 110
(D) 1
Correct Answer : D
Q : If then the value of is
(A)
(B) 5
(C) 6
(D) 7
Correct Answer : A
Q : If for two real constants a and b the expression ax3+3×2-8x+b is exactly divisible by (x+2) and (x-2), then
(A) a = 2, b = -12
(B) a = -2, b = 12
(C) a = 2, b = 12
(D) a = 12, b = 12
Correct Answer : A
Q : Find the minimum value of x which the expression
x3-7×2+11x – 5 ≥ 0.
(A) 1
(B) – 3
(C) 0
(D) 5
Correct Answer : A
Q : If x = b+c -2a, y=c+a-2b, z=a+b-2c, then the value of x2+y2-z2+2xy is :
(A) a-b+c
(B) a+b-c
(C) 0
(D) a+b+c
Correct Answer : C
Q : Find the value of a and b if (x-1) and (x+1) are factors of x4+ax3-3×2+2x+b
(A) -2, 2
(B) 1, -1
(C) 2, -1
(D) -2, 1
Correct Answer : A
Q : If x2+y2-4x-4y+8=0, then the value of x-y is:
(A) 0
(B) 8
(C) 4
(D) -4
Correct Answer : A
Important Algebra Questions and Answers
Q :Sum of the factors of 4b2c2-(b2+c2-a2)2 is :
(A) 0
(B) 1
(C) a+b+c
(D) 2(a+b+c)
Correct Answer : D
Algebra Question with Solution PDF
Q : If a+b+c=15 and a2+b2+c2=83 then the value of a3+b3+c3-3abc
(A) 190
(B) 210
(C) 200
(D) 180
Correct Answer : D
Q : If a-b=1 and a3-b3=61, then the value of ab will be
(A) 30
(B) 60
(C) -20
(D) 20
Correct Answer : D
Q : If x = a – b, y = b – c, z = c – a, then the numerical value of the algebraic expression x3 +y3 + z3 -3xyz will be
(A) 4 (a+b+c)
(B) 3 abc
(C) a + b + c
(D) 0
Correct Answer : D
Q : If p=99, then the value of p(p2+3p+3) will be
(A) 1000001
(B) 999998
(C) 999999
(D) 1000000
Correct Answer : C
Algebra Question
Q : If a=34, b=c=33, then the value of a3+b3+c3-3abc is
(A) 50
(B) 100
(C) 0
(D) 111
Correct Answer : B
Q : If a\b + b\a =1, then the value of a3+b3 will be
(A) -1
(B) 2
(C) 1
(D) 0
Correct Answer : D
Q : If a+b = 1 and a3+b3+3ab=k, then the value of k is :
(A) 5
(B) 7
(C) 1
(D) 3
Correct Answer : C
Q : What will be the value of x3+y3+z3-3xyz when x+y+z=9 and x2+y2+z2=31?
(A) 54
(B) 9
(C) 27
(D) 3
Correct Answer : A
Q : If then the value of x
(A)
(B) 2
(C) 1
(D) 0
Correct Answer : D
Important Algebra Questions and Answers
Q :If a ≠ b, then which of the following statement is true ?
(A)
(B)
(C)
(D) All of the above
Correct Answer : B
Q : If, the value of 8 × 2 is :
(A) 14
(B) 16
(C) 6
(D) 10
Correct Answer : A
Q : If then the value of n is :
(A) 44
(B) 46
(C) 40
(D) 42
Correct Answer : D
Q : Two numbers x and y (x>y) such that their sum is equal to three times their difference. Then value of
will be
(A)
(B)
(C)
(D) 1
Correct Answer : D
Q : If 5√x + 12√x = 13√x, then x is equal to:
(A) 9
(B) 16
(C)
(D) 4
Correct Answer : D
Q : If a = 7, b = 5 and c = 3, then the value of is
(A) 0
(B) 8
(C) 12
(D) -12
Correct Answer : C
Algebra Question with Solution PDF
Q : If, then the value of a is :
(A)
(B)
(C)
(D)
Correct Answer : D
Q : If x, y are two positive real number and , then which of the following relations is true?
(A)
(B)
(C)
(D)
Correct Answer : B
Q : If x is real then the minimum value of (x2-x-1) is :
(A) 1
(B)
(C)
(D) 0
Correct Answer : B
Q : If a2x+2=1, where a is a positive real number other than 1, then x is equal to
(A) 0
(B) 1
(C) – 2
(D) – 1
Correct Answer : D
SSC CHSL ALGEBRA QUESTIONS
Q.1: If a + b = p, ab = q, then (a4 + b4 ) is equal to:
(A) p4 – 4p2q + q2
(B) p4 – 4p2q2 + 2q2
(C) p4 – 2p2q2 + q2
(D) p4 – 4p2q + 2q2
Ans : (D) p4 – 4p2q + 2q2
a + b = p , ab = q
(a + b)2 = p2
a2 + 2ab + b2 = p2
a2 + b2 = p2 – 2q
(a2 + b2)2 = (p2 – 2q)2
a4 + b4 + 2a2b2 = p4 – 4p2q + 4q2 [ab = q, a2 b2 = q2]
a4 + b4 = p4 – 4p2q + 2q2
Q.2: If (x +\frac 1x)^3 = 27 , then what is the value of (x^2 +\frac {1}{x^2}) ? Given the x is real.
(A) 9
(B) 25
(C) 7
(D) 11
Ans : (C) 7
Q.3: If x -\frac 2x = 4 , then what will be the value of x^2 + \frac {4}{x^2} ?
(A) 18
(B) 8
(C) 12
(D) 20
Ans : (D) 20
({x -\frac 2x)^2} = 4
x^2 +\frac {4}{x^2} – 2\times2 = 16
x^2 +\frac {4}{x^2} = 16 + 4 = 20
Q.4: If \sqrt{x} + \frac {1} {\sqrt x} = \sqrt 6 , then the value of x^6 + \frac {1}{x^6} will be:
(A) 2712
(B) 2502
(C) 2270
(D) 2702
Ans : (D) 2702
Q.5: If x2 + 1 – 2x = 0, x > 0 , then x2(x2 – 2) =_______.
(A) 0
(B) -1
(C) 1
(D) \sqrt2
Ans : (B) -1
x2 + 1 – 2x = 0
x > 0
x = 1, so 1 + 1 – 2 = 0
Put x = 1 in x2(x2 – 2)
1 (1 – 2)
= -1
Q.6: If x^2 -3\sqrt2x + 1 =0 , then what is the value of x^3 + (\frac {1}{x^3}) ?
(A) 15\sqrt6
(B) 30\sqrt6
(C) 45\sqrt2
(D) 30\sqrt2
Ans : (C) 45\sqrt2
Q.7: If x – y = 4 and xy = 3 , then what is the value of x3 – y3 ?
(A) 88
(B) 100
(C) 64
(D) 28
Ans : (B) 100
Q.9: If x + 2y = 19 and x3 + 8y3 = 361 , then xy is equal to:
(A) 58
(B) 56
(C) 55
(D) 57
Ans : (D) 57
Q.10: If (x^2 + \frac{1}{49x^2}) = 15\frac 57 , then what is the value of (x +\frac{1}{7x}) ?
(A) 4
(B) \pm 7
(C) \pm 4
(D) 7
Ans : (C) \pm 4
Q.11: If x + y = 27 and x2 + y2 = 425 , then the value of (x – y)2 will be:
(A) 121
(B) 225
(C) 169
(D) 144
Ans : (A) 121
x + y = 27
x2 + y2 = 425
(x + y)2 = (27)2
x2 + y2 + 2xy = 729
2xy = 729 – 425
2xy = 304
(x – y)2 = x2 + y2 – 2xy
= 425 – 304
(x – y)2 = 121
Q.12: If 3x + y = 12 and xy = 9 , then the value of (3x – y) is:
(A) 6
(B) 5
(C) 3
(D) 4
Ans : (A) 6
3x + y = 12
xy = 9
put x = 3, y = 3 Both Equation
So its satify
3x – y = 3 x 3 – 3
= 9 – 3 = 6
Q.13: If a2 + b2 + c2 = 576 and (ab + bc + ca) = 50 , then what is the value of (a + b + c), if (a+b+c) < 0 ?
(A) -24
(B) \pm 24
(C) \pm 26
(D) -26
Ans : (D) -26
(a + b + c)2 = a2 + b2 +c2 + 2 (ab + bc + ca)
576 + 2 x 50
(a + b + c)2 = 676
a + b + c = \pm 26
a + b + c < 0
so a+b+c = -26
Q.14: If x +\frac{1}{3x} = 5 , then the value of 27x^3 +\frac{1}{x^3} will be:
(A) 3024
(B) 3420
(C) 3042
(D) 3240
Ans : (D) 3240
=3240
Q.15:If 3x + 5y = 14 and xy = 6 , then what is the value of 9×2 + 25y2 ?
(A) 182
(B) 16
(C) 14
(D) 20
Ans : (B) 16
(3x + 5y)2 = (14)2
9×2 + 25y2 + 30xy = 196
9×2 + 25y2 + 30 x 6 = 196
9×2 + 25y2 = 196 – 180
9×2 + 25y2 = 16
Q.16: If a – b = 7 and a2 + b2 = 169 where a,b >0 , then the value of 3 a+b is:
(A) 41
(B) 46
(C) 38
(D) 44
Ans : (A) 41
a – b = 7
(a – b)2 = 72
a2 + b2 – 2ab = 49
169 – 2ab = 49
2ab = 169 – 49
2ab = 120
ab = 60 [12 x 5]
a = 12, b = 5
3a + b
= 3 x 12 + 5
= 41
Q.17: If a + 5b = 25 and ab = 20 , then one of the values of (a-5 b) is:
(A) 16
(B) 15
(C) 13
(D) 14
Ans : (B) 15
a + 5b = 25, ab = 20
Put a = 20
b = 1
so a – 5b
= 20 – 5 x 1 = 15
Q.18: If \sqrt {x} + \frac{1}{x} =2\sqrt{3} , then what will be the value of x^4 +\frac{1}{x^4} ?
(A) 10406
(B) 10402
(C) 9602
(D) 9606
Ans : (C) 9602
Q.19: If (7x – 10y) = 8 and xy = 5 , then what is the value of 49×2 + 100y2 ?
(A) 632
(B) 623
(C) 746
(D) 764
Ans : (D) 764
7x – 10y = 8
(7x – 10y)2 = (8)2
49×2 + 100y2 – 140xy = 64
49×2 + 100y2 = 64 + 140xy
= 64 + 140xy
= 64 + 140 x 5
= 764
Q.20: If x^2 +(4 – \sqrt {3})x – 1 = 0 , then what is the value of x^2 +\frac{1}{x^2} ?
(A) 21- 8\sqrt3
(B) 17- 8\sqrt3
(C) 9- 8\sqrt3
(D) 21- 12\sqrt3
Ans : (A) 21- 8\sqrt3
SSC CHSL Algebra Questions with solutions for Competitive Exams
Q.21: If x^2 +\frac{1}{x^2} = 83, x > 0 , then the value of x^3 +\frac{1}{x^3} is:
(A) 675
(B) 756
(C) 746
(D) 576
Ans : (B) 756
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