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UPSC Exam  >  UPSC Test  >  CSAT Preparation  >  Test: Quadratic Equations- 2 - UPSC MCQ

Quadratic Equations- 2 - Free MCQ Practice Test with solutions, UPSC


MCQ Practice Test & Solutions: Test: Quadratic Equations- 2 (10 Questions)

You can prepare effectively for UPSC CSAT Preparation with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Quadratic Equations- 2". These 10 questions have been designed by the experts with the latest curriculum of UPSC 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Test: Quadratic Equations- 2 - Question 1
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Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?

Detailed Solution: Question 1

- To find a/b + b/a, we start with the roots a and b of the equation x^2 + 8x + 4 = 0.
- Using Vieta's formulas, we know:
- a + b = -8
- ab = 4
- We can express a/b + b/a as (a^2 + b^2) / ab.
- a^2 + b^2 can be rewritten using the identity: (a + b)^2 - 2ab.
- This gives us: ((-8)^2 - 2*4) / 4 = (64 - 8) / 4 = 56 / 4 = 14.
- Thus, the answer is 14.

Test: Quadratic Equations- 2 - Question 2
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Detailed Solution: Question 2

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Test: Quadratic Equations- 2 - Question 3
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Find the quadratic equations whose roots are the reciprocals of the roots of 2x2 + 5x + 3 = 0?

Detailed Solution: Question 3

Explanation:

The quadratic equation whose roots are reciprocal of 2x2 + 5x + 3 = 0 can be obtained by replacing x by 1/x.
Hence, 2(1/x)2 + 5(1/x) + 3 = 0
=> 3x2 + 5x + 2 = 0

Test: Quadratic Equations- 2 - Question 4
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A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?

Detailed Solution: Question 4

Explanation:

Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x 
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x2 + 5x = 0
multiplying both sides by -1/10x
=> x2 + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.

Test: Quadratic Equations- 2 - Question 5
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I. a2 - 7a + 12 = 0,
II. b2 - 3b + 2 = 0 to solve both the equations to find the values of a and b?

Detailed Solution: Question 5

Explanation:

I.(a - 3)(a - 4) = 0
=> a = 3, 4


II. (b - 2)(b - 1) = 0
=> b = 1, 2
=> a > b

Test: Quadratic Equations- 2 - Question 6
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I. a2 - 9a + 20 = 0,
II. 2b2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?

Detailed Solution: Question 6

Explanation:

I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b

Test: Quadratic Equations- 2 - Question 7
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 I. a2 + 11a + 30 = 0,
II. b2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?

Detailed Solution: Question 7

Explanation:

I. (a + 6)(a + 5) = 0
=> a = -6, -5
II. (b + 5)(b + 1) = 0
=> b = -5, -1 => a ≤ b

Test: Quadratic Equations- 2 - Question 8
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I. a2 + 8a + 16 = 0,
II. b2 - 4b + 3 = 0 to solve both the equations to find the values of a and b?

Detailed Solution: Question 8

Explanation:

I. (a + 4)2 = 0 => a = -4
II.(b - 3)(b - 1) = 0
=> b = 1, 3 => a < b

Test: Quadratic Equations- 2 - Question 9
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I. a2 - 2a - 8 = 0,
II. b2 = 9 to solve both the equations to find the values of a and b?

Detailed Solution: Question 9

Explanation:

I. (a - 4)(a + 2) = 0
=> a = 4, -2
II. b2 = 9
=> b = ± 3
-2 < 3, -2 > -3, 4 > 3, 4 > -3,
No relation can be established between a and b.

Test: Quadratic Equations- 2 - Question 10
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I. x2 + 5x + 6 = 0,
II. y2 + 9y +14 = 0 to solve both the equations to find the values of x and y?

Detailed Solution: Question 10

I. x2 + 3x + 2x + 6 = 0
=> (x + 3)(x + 2) = 0 => x = -3 or -2
II. y2 + 7y + 2y + 14 = 0
=> (y + 7)(y + 2) = 0 => y = -7 or -2
No relationship can be established between x and y.

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About this UPSC Practice Test

This test contains 10 MCQs on Quadratic Equations- 2 with detailed solutions for each question. It is part of the CSAT Preparation course on EduRev, designed to align with the current UPSC syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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