TGT PGT Algebra Previous Year Questions with Shortcut Solutions

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Solve important TGT PGT Algebra previous year questions with shortcut methods. Each question includes multiple choice options and step-by-step solutions, perfect for quick exam preparation.

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TGT/PGT Algebra — Previous Year Questions (Slides)

TGT/PGT Algebra — Previous Year Questions

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Q1

यदि \(a+b=7\) और \(ab=10\), तो \(a^2 + b^2 =\) ?

Topic: Algebra — Identities
  • A) 29
  • B) 39
  • C) 49
  • D) 59
Shortcut: \(a^2+b^2=(a+b)^2-2ab\).
\(=7^2-2\times10=49-20=29\).
Answer: 29.
Q2

यदि \(x+\dfrac{1}{x}=4\), तो \(x^2+\dfrac{1}{x^2} =\) ?

Topic: Reciprocal identities
  • A) 12
  • B) 14
  • C) 15
  • D) 17
Shortcut: \((x+\tfrac{1}{x})^2 = x^2+\tfrac{1}{x^2}+2\).
\(4^2 = x^2+\tfrac{1}{x^2}+2 \Rightarrow x^2+\tfrac{1}{x^2}=16-2=14\).
Answer: 14.
Q3

यदि \(x-\dfrac{1}{x}=5\), तो \(x^2+\dfrac{1}{x^2} =\) ?

Topic: Reciprocal identities
  • A) 21
  • B) 23
  • C) 25
  • D) 27
Shortcut: \((x-\tfrac{1}{x})^2 = x^2+\tfrac{1}{x^2}-2\).
\(5^2 = x^2+\tfrac{1}{x^2}-2 \Rightarrow x^2+\tfrac{1}{x^2}=25+2=27\).
Answer: 27.
Q4

यदि \(x+y=10\) और \(xy=21\), तो \(x^3+y^3=\) ?

Topic: Sum of cubes
  • A) 370
  • B) 730
  • C) 748
  • D) 784
Shortcut: \(x^3+y^3=(x+y)^3-3xy(x+y)\).
\(=10^3-3\cdot21\cdot10=1000-630=370\).
Answer: 370.
Q5

यदि \(a+b=12\) और \(ab=35\), तो \(a^3+b^3=\) ?

Topic: Sum of cubes
  • A) 468
  • B) 1228
  • C) 1234
  • D) 1248
Shortcut: \(a^3+b^3=(a+b)^3-3ab(a+b)\).
\(=12^3-3\cdot35\cdot12=1728-1260=468\).
Answer: 468.
Q6

यदि \(x^2+y^2=13\) और \(xy=6\), तो \(x+y=\) ?

Topic: Sum from squares
  • A) 3
  • B) 5
  • C) 7
  • D) 9
Shortcut: \((x+y)^2 = x^2+y^2+2xy = 13 + 12 = 25\).
\(x+y = \sqrt{25}=5\) (positive root assumed).
Answer: 5.
Q7

यदि \(x+\dfrac{1}{x}=3\), तो \(x^3+\dfrac{1}{x^3}=\) ?

Topic: Cubes with reciprocals
  • A) 18
  • B) 20
  • C) 24
  • D) 27
Shortcut: \(x^3+\tfrac{1}{x^3}=(x+\tfrac{1}{x})^3-3(x+\tfrac{1}{x})\).
\(=3^3-3\cdot3=27-9=18\).
Answer: 18.
Q8

यदि \(x^2-y^2=28\) और \(x-y=4\), तो \(x+y=\) ?

Topic: Difference of squares
  • A) 5
  • B) 6
  • C) 7
  • D) 8
Shortcut: \(x^2-y^2=(x-y)(x+y)\).
\(28 = 4(x+y) \Rightarrow x+y = 7\).
Answer: 7.
Q9

यदि \(a+b=8\) और \(a^2+b^2=34\), तो \(ab=\) ?

Topic: Using square identity
  • A) 15
  • B) 17
  • C) 18
  • D) 20
Shortcut: \(a^2+b^2=(a+b)^2-2ab\).
\(34 = 8^2 – 2ab = 64 – 2ab \Rightarrow 2ab = 30 \Rightarrow ab = 15\).
Answer: 15.
Q10

यदि \(\alpha, \beta\) समीकरण \(t^2-5t+6=0\) के मूल हों, तो \(\alpha^2+\beta^2=\) ?

Topic: Roots of quadratic
  • A) 11
  • B) 12
  • C) 13
  • D) 14
Shortcut: \(\alpha+\beta=5\), \(\alpha\beta=6\).
\(\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta=5^2-2\cdot6=25-12=13\).
Answer: 13.

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