Algebra Handwritten Notes in Hindi PDF for SSC CGL Exams

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Most Important Algebra Question Answer

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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
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)

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)

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)

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

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Algebra Questions with solutions in Hindi for SSC Exams

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)

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 9×2 + 25y2का मान कितना होगा ?
(A) 182
(B) 16
(C) 14
(D) 20
(SSC CHSL Aug 2021)

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: 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)

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)

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)

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 49×2 + 100y2 का मान क्या होगा ?
(A) 632
(B) 623
(C) 746
(D) 764
(SSC CHSL Aug 2021)

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: 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)

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

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)

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)

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)

Ans : (C) -175
(x – 2y) x (5x + y)3
(x – 2y) x [ 125×3 + y3 + 15xy (5x + y)
(x – 2y) x [ 125×3 + y3 + 75x2y + 15xy2 ]
coefficient of x3y
= 75×3 – 250x3y
= -175x3y
so coefficient of x3y
= -175

Q.24: यदि 9×2 – 6x + 1 = 0 है, तो 27×3 + (27×3)-1 का मान ज्ञात करें
(A) 1
(B) 4
(C) 2
(D) 8
(SSC CHSL Aug 2021)

Ans : (C) 2
9×2 – 6x + 1 = 0
27×3 + (27×3)-1
9×2 – 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)

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

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