Algebra Hand Written Notes in Hindi PDF

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Important Algebra Hand Written Notes PDF

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Today, we are sharing Algebra Hand Written Notes in Hindi PDF It can prove very useful for upcoming competitive exams like SSC CGL, BANK, RAILWAYS, RRB NTPC, LIC AAO, and many more. So English Grammer Book PDF is very important for any competitive exam. This PDF is being provided to you for free which you have given below DOWNLOAD button You can do DOWNLOAD by clicking on it, you can also go to the related notes and DOWNLOAD some new PDF related to this PDF. You can learn about all the new updates on govtjobpdf.com by clicking on the Allow button on the screen.

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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

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 Math Questions and Answers in Hindi for Competitive Exams

1.420 का 36% – 350 का 56% = ? – 94

  • (A) 48.2
  • (B) 49.2
  • (C) 138.8
  • (D) 158.8

उत्तर: B. 

2.आधे घण्टे का 1 मिनट 10 सैकण्ड कौन सा प्रतिशत है ?

  • (A) 2.5%
  • (B) 3.89%
  • (C) 3.5%
  • (D) 4%

उत्तर: B. 

3.6.8 किग्रा का कितने प्रतिशत 17 ग्राम है ?

  • (A) 2.5%
  • (B) 25%
  • (C) 0.25
  • (D) 0.025

उत्तर: C. 

4 7/128 × ? + 595 = 883

  • (A) 4480
  • (B) 4352
  • (C) 4608
  • (D) 4690

उत्तर: B. 

5.किसी संख्या को 195 से भाग देने पर 47 शेष बचते हैं, इस संख्या को 15 से भाग देने पर शेष क्या बचेगा ?

  • (A) 5
  • (B) 4
  • (C) 3
  • (D) 2

उत्तर: D. 

6.यदि a/3 = b/4 = c/7 हो, तो a+b+c/c = ?
(A) 2
(B) 7
(C) 1/7
(D) 1/2

उत्तर: A. 

7.√64009 = ?
(A) 803
(B) 423
(C) 253
(D) 323

उत्तर: C. 

8.2432 ÷ ? = √23104
(A) 12
(B) 14
(C) 16
(D) 18

उत्तर: C. 

9.यदि ab = 64 हो, तो निम्न में से कौन-सा कथन सत्य है
(A) 32 : a = b : 2
(B) a : 8 = b : 8
(C) a : 16 = b : 4
(D) 8 : a = 8 : b

उत्तर: A. 

10.2.4,0.36 तथा 7.2 का महत्तम समापवर्तक क्या होगा ?
(A) 12
(B) 1.2
(C) 0.12
(D) 120

उत्तर: D. 

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