SSC CHSL Algebra Questions with solutions from all shifts of August 2021. Solved Algebra question answer with short tricks are very useful for upcoming SSC CGL, CHSL and other Competitive Exams.
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
Show Answer
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 , then what is the value of
? Given the x is real.
(A) 9
(B) 25
(C) 7
(D) 11
Show Answer
Q.3: If , then what will be the value of
?
(A) 18
(B) 8
(C) 12
(D) 20
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Q.4: If , then the value of
will be:
(A) 2712
(B) 2502
(C) 2270
(D) 2702
Show Answer
Q.5: If x2 + 1 – 2x = 0, x > 0 , then x2(x2 – 2) =_______.
(A) 0
(B) -1
(C) 1
(D)
Show Answer
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 , then what is the value of
?
(A)
(B)
(C)
(D)
Show Answer
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
Show Answer
x – y = 4
(x – y)3 = 43
x3 – y3 – 3xy (x – y) = 64 [Put xy = 3, x – y =4]
x3 – y3 – 3 x 3 x 4 = 64
x3 – y3 = 64 + 36 = 100
Q.8: If , then what will be the value of
?
(A)
(B)
(C)
(D)
Show Answer
Q.9: If x + 2y = 19 and x3 + 8y3 = 361 , then xy is equal to:
(A) 58
(B) 56
(C) 55
(D) 57
Show Answer
x + 2y = 19
(x + 2y)3 = (19)3
x3 + 8y3 + 6xy (x + 2y) = 6859
x3 + 8y3 + 6xy x 19 = 6859
6xy x 19 = 6859 – 361 = 6498
xy =
xy = 57
Q.10: If , then what is the value of
?
(A) 4
(B)
(C)
(D) 7
Show Answer
SSC CHSL Algebra Questions with solutions for Competitive Exams
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
Show Answer
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
Show Answer
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)
(C)
(D) -26
Show Answer
(a + b + c)2 = a2 + b2 +c2 + 2 (ab + bc + ca)
576 + 2 x 50
(a + b + c)2 = 676
a + b + c =
a + b + c < 0
so a+b+c = -26
Q.14: If , then the value of
will be:
(A) 3024
(B) 3420
(C) 3042
(D) 3240
Show Answer
=3240
Q.15:If 3x + 5y = 14 and xy = 6 , then what is the value of 9x2 + 25y2 ?
(A) 182
(B) 16
(C) 14
(D) 20
Show Answer
(3x + 5y)2 = (14)2
9x2 + 25y2 + 30xy = 196
9x2 + 25y2 + 30 x 6 = 196
9x2 + 25y2 = 196 – 180
9x2 + 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
Show Answer
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
Show Answer
a + 5b = 25, ab = 20
Put a = 20
b = 1
so a – 5b
= 20 – 5 x 1 = 15
Q.18: If , then what will be the value of
?
(A) 10406
(B) 10402
(C) 9602
(D) 9606
Show Answer
= 9604 – 2
Q.19: If (7x – 10y) = 8 and xy = 5 , then what is the value of 49x2 + 100y2 ?
(A) 632
(B) 623
(C) 746
(D) 764
Show Answer
7x – 10y = 8
(7x – 10y)2 = (8)2
49x2 + 100y2 – 140xy = 64
49x2 + 100y2 = 64 + 140xy
= 64 + 140xy
= 64 + 140 x 5
= 764
Q.20: If , then what is the value of
?
(A)
(B)
(C)
(D)
Show Answer
square Both side
SSC CHSL Algebra Questions with solutions for Competitive Exams
Q.21: If , x > 0 , then the value of
is:
(A) 675
(B) 756
(C) 746
(D) 576
Show Answer
= 756
Q.22: If , then one of the values of
is:
(A) 36
(B) 32
(C)
(D)
Show Answer
= 36
Q.23: The coefficient of x3 y in (x – 2y) x (5x + y)3 is:
(A) -150
(B) 75
(C) -175
(D) 250
Show Answer
(x – 2y) x (5x + y)3
(x – 2y) x [ 125x3 + y3 + 15xy (5x + y)
(x – 2y) x [ 125x3 + y3 + 75x2y + 15xy2 ]
coefficient of x3y
= 75x3 – 250x3y
= -175x3y
so coefficient of x3y
= -175
Q.24: If 9x2 – 6x + 1 = 0 , then the value of 27x3 + (27x3)-1 will be:
(A) 1
(B) 4
(C) 2
(D) 8
Show Answer
9x2 – 6x + 1 = 0
27x3 + (27x3)-1
9x2 – 6x + 1 = 0
(3x – 1)2 = 0
3x – 1 = 0
3x = 1
put
= 1 + 1 = 2
Q.25: What is the coefficient of y2 in the expansion of ?
(A)
(B)
(C)
(D)
Show Answer
(a – b)3 = a3 – b3 – 3ab(a – b)
केवल y2 का गुणांक लेने पर
y2 का गुणांक
Q.26: If a + b + c = 2 and ab + bc + ca = -1 , then the value of a3 + b3 + c3 – 3abc is:
(A) 5
(B) 10
(C) 2
(D) 14
Show Answer
a + b + c = 2
(a + b + c)2 = ( 2 )2
a2+b2+c2 + 2(ab + bc + ca) = 4
a2+b2+c2 + 2 x(-1) = 4
a2+b2+c2 = 6
a3+b3+c3 – 3abc = (a+b+c) [(a2+b2+c2) – (ab+bc+ca)]
= 2[6 – (-1)]
= 2 x 7 = 14
Q.27: If , then the value of
will be:
(A) 237.6
(B) 273.6
(C) 367.2
(D) 376.2
Show Answer
9 से गुणा Both side
Q.28: If a+b+c = 11 and ab+bc+ca = 15 , then what is the value of a3+b3+c3 – 3abc ?
(A) 386
(B) 836
(C) 368
(D) 638
Show Answer
a+b+c = 11
(a+b+c)2 = 112
a2+b2+c2 + 2 (ab+bc+ca) = 121
a2+b2+c2 + 2 x 15 = 121
a2+b2+c2 = 121 – 30
a2+b2+c2 = 91
a3+b3+c3-3abc =(a+b+c) [(a2+b2+c2 )-(ab+bc+ca)]
= 11[91 – 15]
= 11 x 76
a3+b3+c3-3abc = 836
Q.29: If a+b+c = 5, a2+b2+c2 = 27, and a3+b3+c3 = 125 , then the value of is:
(A) -5
(B) -1
(C) 5
(D) 1
Show Answer
a+b+c = 5
(a+b+c)2 = (5)2
a2+b2+c2 +2(ab+bc+ca) = 25
27 + 2(ab+bc+ca) = 25
ab+bc+ca = -1
a3+b3+c3 -3abc = (a+b+c) [(a2+b2+c2 -(ab+bc+ca)
125 – 3abc = 5 [27 – (-1)
= 5 x 28
125 – 3abc = 140
3abc = -15
abc = -5
Q.30: If x4 + x-4 = 47, x>0 , then the value of (2x – 3)2 is:
(A) 9
(B) 5
(C) 3
(D) 7
Show Answer
x2 + 1 = 3x
4x2 – 12x = -4
(2x – 3)2
= 4x2 + 9 – 12x
4x2 – 12x + 9
-4 + 9 = 5
SSC CHSL Algebra Questions with solutions for Competitive Exams
Q.31: If , where a > 0, then the value of
is:
(A) 45
(B) 60
(C) 65
(D) 56
Show Answer
Put x = 8 its satisfy this equation
So
64 + 1 = 65
Q.32: If x = 555, y = 556 and z = 557 , then find the value of x3+y3+z3 – 3xyz.
(A) 5002
(B) 5008
(C) 5006
(D) 5004
Show Answer
x3+y3+z3 – 3xyz =
= 3 x 1668
= 5004
Q.33: If 3x-2y+3=0 , then what will be the value of 27x3+54xy+30-8y3 ?
(A) 57
(B) -57
(C) -27
(D) 3
Show Answer
3x-2y+3=0
3x-2y=-3
(3x-2y)3 = (-3)3
27x3 – 8y3+54xy =-27
27x3 – 8y3 =-27 – 54xy
27x3 +54xy+30 -8y3
-27-54xy+54xy+30
= 30-27 = 3
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