Algebra Questions in Hindi for SSC Exams

Algebra Questions in Hindi, selected from recently conducted SSC CGL, CHSL Exams. Important and repeated बीजगणित Maths questions for upcoming Competitive Exams.

Algebra Questions with solutions in Hindi for SSC Exams

Q.1: यदि a + b = p, ab = q है , तो (a4 + b4 ) का मान ज्ञात कीजिए I
(A) p4 – 4p2q + q2
(B) p4 – 4p2q2 + 2q2
(C) p4 – 2p2q2 + q2
(D) p4 – 4p2q + 2q2
(SSC CHSL Aug 2021)

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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: यदि (x +\frac 1x)^3 = 27 है , तो (x^2 +\frac {1}{x^2}) का मान क्या होगा ? दिया गया है कि जहां x वास्तविक है I
(A) 9
(B) 25
(C) 7
(D) 11
(SSC CHSL Aug 2021)

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Ans : (C) 7
(x +\frac 1x)^3 = 27
x +\frac 1x = (27)^{1/3} = 3
x^2 +\frac {1}{x^2} + 2 = 9
x^2 +\frac {1}{x^2} = 9 - 2 = 7

Q.3: यदि x -\frac 2x = 4 है , तो x^2 + \frac {4}{x^2} का मान ज्ञात करें I
(A) 18
(B) 8
(C) 12
(D) 20
(SSC CHSL Aug 2021)

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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: यदि \sqrt{x} + \frac {1} {\sqrt x} = \sqrt 6 है , तो x^6 + \frac {1}{x^6} का मान ज्ञात करें I
(A) 2712
(B) 2502
(C) 2270
(D) 2702
(SSC CHSL Aug 2021)

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Ans : (D) 2702
\sqrt{x} + \frac {1} {\sqrt x} = \sqrt6
(\sqrt{x} + \frac {1} {\sqrt x})^2 = (\sqrt6)^2
x +\frac 1x +2 = 6
x +\frac 1x = 4
(x +\frac 1 x)^2 = (4)^2
x^2 +\frac {1}{x^2} = 16 - 2 = 14
(x^2 +\frac {1}{x^2})^3 = (14)^3
x^6 +\frac {1}{x^6} + 3x^2\times\frac {1}{x^2}\times (x^2 + (\frac {1}{x^2}) = 2744
x^6 +\frac {1}{x^6} = 2744 - 42 = 2702

Q.5: यदि x2 + 1 – 2x = 0, x > 0 है, तो x2(x2 – 2) का मान ज्ञात करें I
(A) 0
(B) -1
(C) 1
(D) \sqrt2
(SSC CHSL Aug 2021)

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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: यदि x^2 -3\sqrt2x + 1 =0 है , तो x^3 + (\frac {1}{x^3}) का मान ज्ञात करें I
(A) 15\sqrt6
(B) 30\sqrt6
(C) 45\sqrt2
(D) 30\sqrt2
(SSC CHSL Aug 2021)

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Ans : (C) 45\sqrt2
x^2 - 3\sqrt2x + 1 = 0
x - 3\sqrt2 +\frac1x = 0
x +\frac 1x =3\sqrt2
(x +\frac 1x)^3 = (3\sqrt2)^3
x^3 +\frac {1}{x^3} + 3x\times\frac1x\times (x +\frac1x) = 54\sqrt2
x^3 +\frac{1}{x^3} = 54\sqrt2 - 9\sqrt2
= 45\sqrt2

Q.7: यदि x – y = 4 और xy = 3 है , तो x3 – y3 का मान ज्ञात करें I
(A) 88
(B) 100
(C) 64
(D) 28
(SSC CHSL Aug 2021)

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Ans : (B) 100
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: यदि x -\frac 1x = 2\sqrt2 है , तो x^3 -\frac {1}{x^3} का मान ज्ञात करें I
(A) 12\sqrt2
(B) 10\sqrt2
(C) 20\sqrt2
(D) 22\sqrt2
(SSC CHSL Aug 2021)

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Ans : (D) 22\sqrt2
x -\frac 1x =2\sqrt2
(x -\frac 1x)^3 = (2\sqrt2)^3
x^3 -\frac {1}{x^3} - 3\times x\times\frac 1x (x -\frac1x) = 16\sqrt2
x^3 -\frac {1}{x^3} - 3\times 2\sqrt2 = 16\sqrt2
x^3 -\frac {1}{x^3} = 16\sqrt2 + 6\sqrt2
= 22\sqrt2

Q.9: यदि x + 2y = 19 और x3 + 8y3 = 361 है , तो xy का मान क्या होगा ?
(A) 58
(B) 56
(C) 55
(D) 57
(SSC CHSL Aug 2021)

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Ans : (D) 57
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 =\frac {6498}{19\times6}
xy = 57

Q.10: यदि (x^2 + \frac{1}{49x^2}) = 15\frac 57 है , तो (x +\frac{1}{7x}) का मान क्या होगा ?
(A) 4
(B) \pm 7
(C) \pm 4
(D) 7
(SSC CHSL Aug 2021)

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Ans : (C) \pm 4
(x^2 + \frac{1}{49x^2}) = 15\frac57
(x^2 + \frac{1}{7x})^2 + 2\times x\times \frac {1}{7x} =\frac{110}{7} + \frac27
(x + \frac{1}{7x})^2 = \frac{112}{7} = 16
x + \frac{1}{7x} =\pm 4
Algebra Questions with solutions in Hindi for SSC Exams

Q.11: यदि x + y = 27 और x2 + y2 = 425 है , तो (x – y)2 का मान ज्ञात करें
(A) 121
(B) 225
(C) 169
(D) 144
(SSC CHSL Aug 2021)

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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: यदि 3x + y = 12 और xy = 9 है, तो (3x – y) का मान क्या होगा ?
(A) 6
(B) 5
(C) 3
(D) 4
(SSC CHSL Aug 2021)

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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: यदि a2 + b2 + c2 = 576 और (ab + bc + ca) = 50 है, तो (a + b + c) का मान क्या होगा, यदि a+b+c < 0 है ?
(A) -24
(B) \pm 24
(C) \pm 26
(D) -26
(SSC CHSL Aug 2021)

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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: यदि x +\frac{1}{3x} = 5 है , तो 27x^3 +\frac{1}{x^3} का मान ज्ञात करें I
(A) 3024
(B) 3420
(C) 3042
(D) 3240
(SSC CHSL Aug 2021)

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Ans : (D) 3240
x +\frac{1}{3x} = 5
3x +\frac{1}{x} = 15 [ Multiply by 3]
(3x +\frac{1}{x})^3 = 15^3
27x^3 +\frac{1}{x^3} + 135 = 3375
27x^3 +\frac{1}{x^3} = 3375 - 135
=3240

Q.15: यदि 3x + 5y = 14 और xy = 6 है, तो 9x2 + 25y2का मान कितना होगा ?
(A) 182
(B) 16
(C) 14
(D) 20
(SSC CHSL Aug 2021)

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Ans : (B) 16
(3x + 5y)2 = (14)2
9x2 + 25y2 + 30xy = 196
9x2 + 25y2 + 30 x 6 = 196
9x2 + 25y2 = 196 – 180
9x2 + 25y2 = 16

Q.16: यदि a – b = 7 और a2 + b2 = 169 है, जहाँ a,b >0 है , तो 3a + b का मान ज्ञात करें
(A) 41
(B) 46
(C) 38
(D) 44
(SSC CHSL Aug 2021)

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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: यदि a + 5b = 25 और ab = 20 है, तो (a – 5b) का एक मान _________ होगा
(A) 16
(B) 15
(C) 13
(D) 14
(SSC CHSL Aug 2021)

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Ans : (B) 15
a + 5b = 25, ab = 20
Put a = 20
b = 1
so a – 5b
= 20 – 5 x 1 = 15

Q.18: यदि \sqrt {x} + \frac{1}{x} =2\sqrt{3} है, तो x^4 +\frac{1}{x^4} का मान ज्ञात करें
(A) 10406
(B) 10402
(C) 9602
(D) 9606
(SSC CHSL Aug 2021)

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Ans : (C) 9602
\sqrt {x} +\frac{1}{x} = 2\sqrt3
(\sqrt {x} +\frac{1}{x})^2 = (2\sqrt3)^2
x +\frac{1}{x} + 2 = 12
x +\frac{1}{x} = 10
x^2 + \frac{1}{x^2} = 100 - 2 = 98
x^4 + \frac{1}{x^4} = 98^2 - 2
= 9604 – 2
x^4 +\frac{1}{x^4} = 9602

Q.19: यदि (7x – 10y) = 8 और xy = 5 है, तो 49x2 + 100y2 का मान क्या होगा ?
(A) 632
(B) 623
(C) 746
(D) 764
(SSC CHSL Aug 2021)

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Ans : (D) 764
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: यदि x^2 +(4 - \sqrt {3})x - 1 = 0 है, तो x^2 +\frac{1}{x^2} का मान ज्ञात करें
(A) 21- 8\sqrt3
(B) 17- 8\sqrt3
(C) 9- 8\sqrt3
(D) 21- 12\sqrt3
(SSC CHSL Aug 2021)

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Ans : (A) 21- 8\sqrt3
x^2 +(4 -\sqrt3)x - 1 = 0
\div x Both side
x +(4 -\sqrt{3}) - \frac1x = 0
x -\frac1x = \sqrt3 - 4
square Both side
(x -\frac1x)^2 = (\sqrt 3 - 4)^2
x^2 +\frac{1}{x^2}  - 2 = 3 + 16 - 8\sqrt3
x^2 +\frac{1}{x^2} = 21 - 8\sqrt3
Algebra Questions with solutions in Hindi for SSC Exams

Q.21: यदि x^2 +\frac{1}{x^2} = 83, x > 0 है, तो x^3 +\frac{1}{x^3} का मान ज्ञात करें
(A) 675
(B) 756
(C) 746
(D) 576
(SSC CHSL Aug 2021)

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Ans : (B) 756
x^2 +\frac{1}{x^2} = 83
x^2 +\frac{1}{x^2} - 2 = 83 - 2
(x -\frac{1}{x})^2 = 81
x -\frac{1}{x} = 9
(x -\frac{1}{x})^3 = 9^3
x^3 -\frac{1}{x^3} -3x \frac1x (x -\frac1x) = 729
x^3 -\frac{1}{x^3} = 729 + 27
= 756

Q.22: यदि x +\frac1x = \sqrt{13} है, तो x^3 -\frac{1}{x^3} का एक मान ज्ञात करें I
(A) 36
(B) 32
(C) 4\sqrt{13}
(D) 4\sqrt{11}
(SSC CHSL Aug 2021)

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Ans : (A) 36
x +\frac1x = \sqrt{13}
x^2 +\frac{1}{x^2} + 2 = 13
x^2 +\frac{1}{x^2} = 11
x^2 +\frac{1}{x^2} - 2 = 11 - 2
x^2 +\frac{1}{x^2} - 2 = 9
(x -\frac{1}{x})^2 = 9
x -\frac1x = 3
x^3 +\frac{1}{x^3} - 3\times3 = 27
x^3 -\frac{1}{x^3} = 27 + 9
= 36

Q.23: (x – 2y) x (5x + y)3 में x3y का गुणांक (coefficient) ज्ञात करें
(A) -150
(B) 75
(C) -175
(D) 250
(SSC CHSL Aug 2021)

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Ans : (C) -175
(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: यदि 9x2 – 6x + 1 = 0 है, तो 27x3 + (27x3)-1 का मान ज्ञात करें
(A) 1
(B) 4
(C) 2
(D) 8
(SSC CHSL Aug 2021)

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Ans : (C) 2
9x2 – 6x + 1 = 0
27x3 + (27x3)-1
9x2 – 6x + 1 = 0
(3x – 1)2 = 0
3x – 1 = 0
3x = 1
x =\frac13
put x =\frac13
27x^3 +\frac{1}{27^3}
27\times\frac{1}{27} +\frac{{1}\times{27}}{{27}\times{1}}
= 1 + 1 = 2

Q.25: व्यंजक (\sqrt2y^2 - 5\sqrt3)^3 के विस्तार
(A) 30\sqrt3
(B) -225\sqrt2
(C) -30\sqrt3
(D) 225\sqrt2
(SSC CHSL Aug 2021)

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Ans : (D) 225\sqrt2
(\sqrt2y^2 - 5\sqrt3)^3
(a – b)3 = a3 – b3 – 3ab(a – b)
(\sqrt2y^2)^3 - (5\sqrt3)^3 - 3\sqrt2y^2\times5\sqrt3 (\sqrt2y^2 - 5\sqrt3)
केवल y2 का गुणांक लेने पर
= -3\sqrt2y^2 \times 5\sqrt3\times - 5\sqrt3
= +225\sqrt2y^2
y2 का गुणांक = 225\sqrt2

Q.26: यदि a + b + c = 2 और ab + bc + ca = -1 है तो a3 + b3 + c3 – 3abc का मान ज्ञात कीजिए
(A) 5
(B) 10
(C) 2
(D) 14
(SSC CHSL Aug 2021)

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Ans : (D) 14
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: यदि x +\frac{1}{15x} =3 है तो 9x^3 +\frac{1}{375x^3} का मान ज्ञात करें
(A) 237.6
(B) 273.6
(C) 367.2
(D) 376.2
(SSC CHSL Aug 2021)

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Ans : (A) 237.6
x +\frac{1}{15x} =3
(x +\frac{1}{15x})^3 =(3)^3
x^3 +\frac{1}{3375x^3} +3x\times\frac{1}{15x} \times3 = 27
x^3 +\frac{1}{3375x^3} +\frac35 = 27
x^3 +\frac{1}{3375x^3} = 27 -\frac35 =\frac{132}{5}
9 से गुणा Both side
9x^3 +\frac{1}{375x^3} =\frac{132}{5}\times 9
9x^3 +\frac{1}{375x^3} =\frac{1188}{2} = 237.6

Q.28: यदि a+b+c = 11 और ab+bc+ca = 15 है, तो a3+b3+c3 – 3abc का मान ज्ञात करें
(A) 386
(B) 836
(C) 368
(D) 638
(SSC CHSL Aug 2021)

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Ans : (B) 836
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: यदि a+b+c = 5, a2+b2+c2 = 27, और a3+b3+c3 = 125 है, तो \frac{abc}{5} का मान ज्ञात करें
(A) -5
(B) -1
(C) 5
(D) 1
(SSC CHSL Aug 2021)

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Ans : (B) -1
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
\frac{abc}{5} = -1

Q.30: यदि x4 + x-4 = 47, x>0 है, तो (2x – 3)2 का मान ज्ञात करें
(A) 9
(B) 5
(C) 3
(D) 7
(SSC CHSL Aug 2021)

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Ans : (B) 5
x^4 + \frac{1}{x^4} = 47
x^4 + \frac{1}{x^4} + 2 = 47+ 2
(x^2 + \frac{1}{x^2})^2 = 49
x^2 + \frac{1}{x^2} = 7
x^2 + \frac{1}{x^2} + 2 = 7+2
(x + \frac{1}{x})^2 = 9
x +\frac1x = 3
x2 + 1 = 3x
4x2 – 12x = -4
(2x – 3)2
= 4x2 + 9 – 12x
4x2 – 12x + 9
-4 + 9 = 5
Algebra Questions in Hindi for SSC Exams

Q.31: यदि a-\frac{24}{a} = 5 है, जहाँ a > 0, है, तो a^2 +\frac{64}{a^2} का मान ज्ञात करें
(A) 45
(B) 60
(C) 65
(D) 56
(SSC CHSL Aug 2021)

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Ans : (C) 65
a-\frac{24}{a} = 5
Put x = 8 its satisfy this equation
So a^2-\frac{64}{a^2}
64 +\frac{64}{64}
64 + 1 = 65

Q.32: यदि x = 555, y = 556 और z = 557 है, तो x3+y3+z3 – 3xyz का मान क्या होगा ?
(A) 5002
(B) 5008
(C) 5006
(D) 5004
(SSC CHSL Aug 2021)

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Ans : (D) 5004
x3+y3+z3 – 3xyz = \frac12 (x+y+z)[(x – y)2 +(y – z)2 +(z – x)2 ]
\frac12\times 1668\times[1+1+4]
= 3 x 1668
= 5004

Q.33: यदि 3x-2y+3=0 है, तो 27x3+54xy+30-8y3 का मान ज्ञात करें
(A) 57
(B) -57
(C) -27
(D) 3
(SSC CHSL Aug 2021)

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Ans : (D) 3
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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