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)
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: यदि है , तो
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)
Show Answer
![Rendered by QuickLaTeX.com (x +\frac 1x)^3 = 27](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-4ef3193267dbdcf75e677cb8e59db222_l3.png)
![Rendered by QuickLaTeX.com x +\frac 1x = (27)^{1/3} = 3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-a403dc6c0fbacf021a91d84f88e6d5c9_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac {1}{x^2} + 2 = 9](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-be66c5a66b9b5d72631ba06351c30b6e_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac {1}{x^2} = 9 - 2 = 7](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-a151d2d0977e8d94190c58692304e9cb_l3.png)
Q.3: यदि है , तो
का मान ज्ञात करें I
(A) 18
(B) 8
(C) 12
(D) 20
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com ({x -\frac 2x)^2} = 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0cbd347f2ce8e19ff07eb765dcda9f07_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac {4}{x^2} - 2\times2 = 16](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-85309cb5e5f62fb31e83f5bb27d6f340_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac {4}{x^2} = 16 + 4 = 20](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-4b729ecf750913a75056bc3f4d029972_l3.png)
Q.4: यदि है , तो
का मान ज्ञात करें I
(A) 2712
(B) 2502
(C) 2270
(D) 2702
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com \sqrt{x} + \frac {1} {\sqrt x} = \sqrt6](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-ade21a7f4ef49b04bbf64f356cebc1bc_l3.png)
![Rendered by QuickLaTeX.com (\sqrt{x} + \frac {1} {\sqrt x})^2 = (\sqrt6)^2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b9ae4a4c3244a74775ab74905445a6d6_l3.png)
![Rendered by QuickLaTeX.com x +\frac 1x +2 = 6](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-45a875a153903ad62d1bffd3fa5f2635_l3.png)
![Rendered by QuickLaTeX.com x +\frac 1x = 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c0fa7caefe440c1f4044811440ad765f_l3.png)
![Rendered by QuickLaTeX.com (x +\frac 1 x)^2 = (4)^2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-9dba321512282b7288ee7b9fe27980e1_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac {1}{x^2} = 16 - 2 = 14](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e4e6e89c0913ea3af7773e8b6ee2078b_l3.png)
![Rendered by QuickLaTeX.com (x^2 +\frac {1}{x^2})^3 = (14)^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-286769b86c4f5bcb8504b04da5d95e1f_l3.png)
![Rendered by QuickLaTeX.com x^6 +\frac {1}{x^6} + 3x^2\times\frac {1}{x^2}\times (x^2 + (\frac {1}{x^2}) = 2744](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-eb7e530ee476406c5e3817a8aef2997a_l3.png)
![Rendered by QuickLaTeX.com x^6 +\frac {1}{x^6} = 2744 - 42 = 2702](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-84e989011cb26a11b9f5decb19b07f95_l3.png)
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)
(SSC CHSL Aug 2021)
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: यदि है , तो
का मान ज्ञात करें I
(A)
(B)
(C)
(D)
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com 45\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-7014742980f3cd2772ff4e31b8c7893a_l3.png)
![Rendered by QuickLaTeX.com x^2 - 3\sqrt2x + 1 = 0](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-81ef7c20ba02290b42e76c89a769077e_l3.png)
![Rendered by QuickLaTeX.com x - 3\sqrt2 +\frac1x = 0](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-694229391681c2fef6ff181646c019dd_l3.png)
![Rendered by QuickLaTeX.com x +\frac 1x =3\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-33d25c4c7b4be9717d2fbf0a31a0eb42_l3.png)
![Rendered by QuickLaTeX.com (x +\frac 1x)^3 = (3\sqrt2)^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-dea3ac649ce6ea8e55605adf907a1c62_l3.png)
![Rendered by QuickLaTeX.com x^3 +\frac {1}{x^3} + 3x\times\frac1x\times (x +\frac1x) = 54\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-28dc2cc53b86329ca61bc3023faf180d_l3.png)
![Rendered by QuickLaTeX.com x^3 +\frac{1}{x^3} = 54\sqrt2 - 9\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-38696f656175ab2e75733528fbdad988_l3.png)
![Rendered by QuickLaTeX.com = 45\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3b882f6bf8851edb1444bb6e80174a52_l3.png)
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)
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: यदि है , तो
का मान ज्ञात करें I
(A)
(B)
(C)
(D)
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com 22\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3c1b79029bbddcc7d5dd75a0d94b60af_l3.png)
![Rendered by QuickLaTeX.com x -\frac 1x =2\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-521ea0302da965c65a95f4336f3a09a6_l3.png)
![Rendered by QuickLaTeX.com (x -\frac 1x)^3 = (2\sqrt2)^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-08a1a44f9765083e85b9db21d4348224_l3.png)
![Rendered by QuickLaTeX.com x^3 -\frac {1}{x^3} - 3\times x\times\frac 1x (x -\frac1x) = 16\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-904879292e6bf048a268d920b71c8c0c_l3.png)
![Rendered by QuickLaTeX.com x^3 -\frac {1}{x^3} - 3\times 2\sqrt2 = 16\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-36d0c239fb48237e7ed61b506fa343ed_l3.png)
![Rendered by QuickLaTeX.com x^3 -\frac {1}{x^3} = 16\sqrt2 + 6\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-23991c2c2a154016a540942d3fdf1ecf_l3.png)
![Rendered by QuickLaTeX.com = 22\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-daa07488888bebba48e93953d440a567_l3.png)
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)
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 =
![Rendered by QuickLaTeX.com \frac {6498}{19\times6}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-4344d63b9d7b6fe84b7df88225c52e1d_l3.png)
xy = 57
Q.10: यदि है , तो
का मान क्या होगा ?
(A) 4
(B)
(C)
(D) 7
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com \pm 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-87a3a70948d2ef478449f0da3286b697_l3.png)
![Rendered by QuickLaTeX.com (x^2 + \frac{1}{49x^2}) = 15\frac57](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-6bcf837d1c096ae0abc8bd29ca740fcb_l3.png)
![Rendered by QuickLaTeX.com (x^2 + \frac{1}{7x})^2 + 2\times x\times \frac {1}{7x} =\frac{110}{7} + \frac27](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c88d1372a466a8638590f982954349f6_l3.png)
![Rendered by QuickLaTeX.com (x + \frac{1}{7x})^2 = \frac{112}{7} = 16](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-f3a32328a092c86fa11129ebf55ad832_l3.png)
![Rendered by QuickLaTeX.com x + \frac{1}{7x} =\pm 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e379194b5c70c605bfc52202704465ea_l3.png)
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)
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: 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)
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: 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)
(C)
(D) -26
(SSC CHSL Aug 2021)
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 =
![Rendered by QuickLaTeX.com \pm 26](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c5d2056efaab4f79d08a6fb19147605d_l3.png)
a + b + c < 0
so a+b+c = -26
Q.14: यदि है , तो
का मान ज्ञात करें I
(A) 3024
(B) 3420
(C) 3042
(D) 3240
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com x +\frac{1}{3x} = 5](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-599cd47d5aecd6a756eb19a8b69dc66f_l3.png)
![Rendered by QuickLaTeX.com 3x +\frac{1}{x} = 15](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-57f99c56c320c77b9e7e31cf8312f559_l3.png)
![Rendered by QuickLaTeX.com (3x +\frac{1}{x})^3 = 15^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c171e06878368153bb97c90fe49a651e_l3.png)
![Rendered by QuickLaTeX.com 27x^3 +\frac{1}{x^3} + 135 = 3375](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-70e45471bf5652f2f9906cd5b5c62274_l3.png)
![Rendered by QuickLaTeX.com 27x^3 +\frac{1}{x^3} = 3375 - 135](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c9cfcfc4d9b4b0ae359d4ecc0ef4fc6b_l3.png)
=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)
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: 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)
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: 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)
Show Answer
a + 5b = 25, ab = 20
Put a = 20
b = 1
so a – 5b
= 20 – 5 x 1 = 15
Q.18: यदि है, तो
का मान ज्ञात करें
(A) 10406
(B) 10402
(C) 9602
(D) 9606
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com \sqrt {x} +\frac{1}{x} = 2\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-944d6fe10de65f86febf4b77e8060c3a_l3.png)
![Rendered by QuickLaTeX.com (\sqrt {x} +\frac{1}{x})^2 = (2\sqrt3)^2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-463f8e1069a32b8932c31bf3d06edb4f_l3.png)
![Rendered by QuickLaTeX.com x +\frac{1}{x} + 2 = 12](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-f3d840c5a9c765f0a6a7d6e78a5b385f_l3.png)
![Rendered by QuickLaTeX.com x +\frac{1}{x} = 10](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-5ac784e6d44fc44ebda67c4d78a1ee7d_l3.png)
![Rendered by QuickLaTeX.com x^2 + \frac{1}{x^2} = 100 - 2 = 98](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-1527665e19e8404f4918f5efd17cb10a_l3.png)
![Rendered by QuickLaTeX.com x^4 + \frac{1}{x^4} = 98^2 - 2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-d2c897b88b68a79ff7e8ef0476d35979_l3.png)
= 9604 – 2
![Rendered by QuickLaTeX.com x^4 +\frac{1}{x^4} = 9602](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3819187339be8c1d14c5cfff266ab5da_l3.png)
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)
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: यदि है, तो
का मान ज्ञात करें
(A)
(B)
(C)
(D)
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com 21- 8\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-9580b41ef7e5b95c9d83f3199627fbf9_l3.png)
![Rendered by QuickLaTeX.com x^2 +(4 -\sqrt3)x - 1 = 0](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-8f2e5f6e17770f7f132e4041e8225da7_l3.png)
![Rendered by QuickLaTeX.com \div x](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-dd348d357844c65e76ce3aa835cbc60b_l3.png)
![Rendered by QuickLaTeX.com x +(4 -\sqrt{3}) - \frac1x = 0](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3f039a49176b6675fb6708b58a27866b_l3.png)
![Rendered by QuickLaTeX.com x -\frac1x = \sqrt3 - 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-2472522236e5b7d2bf0af0bcfe9be604_l3.png)
square Both side
![Rendered by QuickLaTeX.com (x -\frac1x)^2 = (\sqrt 3 - 4)^2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0b1e93900186f7f5f144ca55b06396c3_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} - 2 = 3 + 16 - 8\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-45c8c7c50358e96504c2c004d379edbe_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} = 21 - 8\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-2cc9ccf2b11b9ac89d21e44f2c51263e_l3.png)
Algebra Questions with solutions in Hindi for SSC Exams
Q.21: यदि , x > 0 है, तो
का मान ज्ञात करें
(A) 675
(B) 756
(C) 746
(D) 576
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} = 83](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-01b641e48b75e842443efe9abd2470b0_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} - 2 = 83 - 2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-79558af30cf670f606e81ddfbffc42d6_l3.png)
![Rendered by QuickLaTeX.com (x -\frac{1}{x})^2 = 81](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c393013b323380c5e21ea927cfc2ef56_l3.png)
![Rendered by QuickLaTeX.com x -\frac{1}{x} = 9](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-33fdfbc8d560f2877e16cb68ab7d75c1_l3.png)
![Rendered by QuickLaTeX.com (x -\frac{1}{x})^3 = 9^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b28970742c5d798bb944b757aadb664d_l3.png)
![Rendered by QuickLaTeX.com x^3 -\frac{1}{x^3} -3x \frac1x (x -\frac1x) = 729](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b178292c19b0d6f277f7fd71b8a40112_l3.png)
![Rendered by QuickLaTeX.com x^3 -\frac{1}{x^3} = 729 + 27](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e0eea85a2b0bd44e3fe71af71361a2b5_l3.png)
= 756
Q.22: यदि है, तो
का एक मान ज्ञात करें I
(A) 36
(B) 32
(C)
(D)
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com x +\frac1x = \sqrt{13}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-845c25fc52bcd5a5ca852a06e81b4a19_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} + 2 = 13](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-d49d11fb6804d63088ac8a25baf90ee0_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} = 11](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-d3133dbbf323351f1c9b004fbc3ce7c4_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} - 2 = 11 - 2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c19712675574429d8276af321324f4cb_l3.png)
![Rendered by QuickLaTeX.com x^2 +\frac{1}{x^2} - 2 = 9](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-09a6468f6a8a640abe3d0cedbc55aabb_l3.png)
![Rendered by QuickLaTeX.com (x -\frac{1}{x})^2 = 9](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-295761615f7c94d4cb12a02e45e58e64_l3.png)
![Rendered by QuickLaTeX.com x -\frac1x = 3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3d33df0e3d50d802f7202abcc01ff107_l3.png)
![Rendered by QuickLaTeX.com x^3 +\frac{1}{x^3} - 3\times3 = 27](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-4e1fb845ad35923521bc4b1cb090ccef_l3.png)
![Rendered by QuickLaTeX.com x^3 -\frac{1}{x^3} = 27 + 9](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-00cb535c6a616900703eb1c6549b1000_l3.png)
= 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)
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: 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)
Show Answer
9x2 – 6x + 1 = 0
27x3 + (27x3)-1
9x2 – 6x + 1 = 0
(3x – 1)2 = 0
3x – 1 = 0
3x = 1
![Rendered by QuickLaTeX.com x =\frac13](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e99bc9f5d31ca68568d9af176069fa1b_l3.png)
put
![Rendered by QuickLaTeX.com x =\frac13](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e99bc9f5d31ca68568d9af176069fa1b_l3.png)
![Rendered by QuickLaTeX.com 27x^3 +\frac{1}{27^3}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-f8bd41306e8779c0722a14845425b1ae_l3.png)
![Rendered by QuickLaTeX.com 27\times\frac{1}{27} +\frac{{1}\times{27}}{{27}\times{1}}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0a4d7c66e297bd49f6caac14693e0547_l3.png)
= 1 + 1 = 2
Q.25: व्यंजक के विस्तार
(A)
(B)
(C)
(D)
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com 225\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b88e93faad6678cef8ef717046a75e6e_l3.png)
![Rendered by QuickLaTeX.com (\sqrt2y^2 - 5\sqrt3)^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-9db091a5b62a282b06906c7d68671ea9_l3.png)
(a – b)3 = a3 – b3 – 3ab(a – b)
![Rendered by QuickLaTeX.com (\sqrt2y^2)^3 - (5\sqrt3)^3 - 3\sqrt2y^2\times5\sqrt3 (\sqrt2y^2 - 5\sqrt3)](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-f17529961204b9c9d0ba52ea371b7b83_l3.png)
केवल y2 का गुणांक लेने पर
![Rendered by QuickLaTeX.com = -3\sqrt2y^2 \times 5\sqrt3\times - 5\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-bdfdae282ec5b7354cab13e8d79c4c88_l3.png)
![Rendered by QuickLaTeX.com = +225\sqrt2y^2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-8e4146e1de2b7723b76bb9ffda5a89d7_l3.png)
y2 का गुणांक
![Rendered by QuickLaTeX.com = 225\sqrt2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-49a29bab7b3f6659e1cf5d165bc37ec9_l3.png)
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)
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: यदि है तो
का मान ज्ञात करें
(A) 237.6
(B) 273.6
(C) 367.2
(D) 376.2
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com x +\frac{1}{15x} =3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b155ef92524fbac0a7e203df00119cdc_l3.png)
![Rendered by QuickLaTeX.com (x +\frac{1}{15x})^3 =(3)^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b383b94875084640a152a3cb8e81655d_l3.png)
![Rendered by QuickLaTeX.com x^3 +\frac{1}{3375x^3} +3x\times\frac{1}{15x} \times3 = 27](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b0f0ab9330227a5388e1650e837c8048_l3.png)
![Rendered by QuickLaTeX.com x^3 +\frac{1}{3375x^3} +\frac35 = 27](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e8cfdd3a224d39807c2547e26e4c88e6_l3.png)
![Rendered by QuickLaTeX.com x^3 +\frac{1}{3375x^3} = 27 -\frac35 =\frac{132}{5}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-fe510d914556e55262f0cd3cca9a3260_l3.png)
9 से गुणा Both side
![Rendered by QuickLaTeX.com 9x^3 +\frac{1}{375x^3} =\frac{132}{5}\times 9](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-efce3d76decb093b812ed95c3a411849_l3.png)
![Rendered by QuickLaTeX.com 9x^3 +\frac{1}{375x^3} =\frac{1188}{2} = 237.6](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c18bb81e6cdd2a1a40281e45a357500b_l3.png)
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)
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: यदि a+b+c = 5, a2+b2+c2 = 27, और a3+b3+c3 = 125 है, तो का मान ज्ञात करें
(A) -5
(B) -1
(C) 5
(D) 1
(SSC CHSL Aug 2021)
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
![Rendered by QuickLaTeX.com \frac{abc}{5} = -1](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-729d5b26c4e8038e29bce192442f074e_l3.png)
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)
Show Answer
![Rendered by QuickLaTeX.com x^4 + \frac{1}{x^4} = 47](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-2466b8550e7a352dff0ecc847d5ba228_l3.png)
![Rendered by QuickLaTeX.com x^4 + \frac{1}{x^4} + 2 = 47+ 2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-2d79001223f349eefc34487b5d0f5546_l3.png)
![Rendered by QuickLaTeX.com (x^2 + \frac{1}{x^2})^2 = 49](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-f8a91d2009a0ce214dee8e9f98948b57_l3.png)
![Rendered by QuickLaTeX.com x^2 + \frac{1}{x^2} = 7](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-d198fc5bc9f9eed74585a795f0ff44aa_l3.png)
![Rendered by QuickLaTeX.com x^2 + \frac{1}{x^2} + 2 = 7+2](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-8820276d532a9e7a718a325a36160dc5_l3.png)
![Rendered by QuickLaTeX.com (x + \frac{1}{x})^2 = 9](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-bc636678e3ef9083f5924cd3d7cf6df2_l3.png)
![Rendered by QuickLaTeX.com x +\frac1x = 3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-b3ad177508155eaa950b36318dcdda61_l3.png)
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 है, जहाँ a > 0, है, तो
का मान ज्ञात करें
(A) 45
(B) 60
(C) 65
(D) 56
(SSC CHSL Aug 2021)
Show Answer
![Rendered by QuickLaTeX.com a-\frac{24}{a} = 5](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-bfeb57ed356a60206eddc93bd927cf07_l3.png)
Put x = 8 its satisfy this equation
So
![Rendered by QuickLaTeX.com a^2-\frac{64}{a^2}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-5a5f759819427400022104d85cc56efb_l3.png)
![Rendered by QuickLaTeX.com 64 +\frac{64}{64}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-6511a21330af7820ebbf7e0c6df79b34_l3.png)
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)
Show Answer
x3+y3+z3 – 3xyz =
![Rendered by QuickLaTeX.com \frac12](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3cbfcd118f8ec308948439a1927a4782_l3.png)
![Rendered by QuickLaTeX.com \frac12\times 1668\times[1+1+4]](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-d3ff5a603e0fdc79a32dfb318d03a4af_l3.png)
= 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)
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
Thanks for study the Algebra Questions with solutions in Hindi for SSC Exams
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