SSC Algebra Questions with Answers

By Rahul Rawat On Aug 1, 2022

SSC Algebra Questions with Answers

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SSC Algebra Questions with Answers

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) $\pm 4$
$(x^2 + \frac{1}{49x^2}) = 15\frac57$
$(x^2 + \frac{1}{7x})^2 + 2\times x\times \frac {1}{7x} =\frac{110}{7} + \frac27$
$(x + \frac{1}{7x})^2 = \frac{112}{7} = 16$
$x + \frac{1}{7x} =\pm 4$
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)

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)

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)

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

SSC Algebra Questions with Answers

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 9x² + 25y²का मान कितना होगा ?
(A) 182
(B) 16
(C) 14
(D) 20
(SSC CHSL Aug 2021)

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)

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 49x² + 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
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)

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)

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 [ 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)

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)

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)

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)

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)

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)

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
$\frac{abc}{5} = -1$

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SSC Algebra Questions with Answers

SSC Algebra Questions with Answers

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