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UPSC Exam  >  UPSC Test  >  CSAT Preparation  >  Test: Surds And Indices- 2 - UPSC MCQ

Surds And Indices- 2 - Free MCQ Practice Test with solutions, UPSC


MCQ Practice Test & Solutions: Test: Surds And Indices- 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: Surds And Indices- 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: 18 minutes
  • - Number of Questions: 10

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Test: Surds And Indices- 2 - Question 1
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If m and n are integers such that then m is

Detailed Solution: Question 1

Comparing the powers of same bases we get

19 / 2 + 4 + 3n = 4m + 3 / 2 ...(1)

4 + 2m = n ...(2)

Substitute the value of n from (2) in (1) and solving for m, we get m = −12

*Answer can only contain numeric values
Test: Surds And Indices- 2 - Question 2
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If  for all non-zero real values of a and b, then the value of x + y is


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*Answer can only contain numeric values
Test: Surds And Indices- 2 - Question 3
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If n is a positive integer such that  then the smallest value of n is


Detailed Solution: Question 3


1 + 2 + ... + n = 21
We can see that if n = 6, 1 + 2 + 3 + ... + 6 = 21.

Test: Surds And Indices- 2 - Question 4
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The sum of all real values of k for which  is

Detailed Solution: Question 4

*Answer can only contain numeric values
Test: Surds And Indices- 2 - Question 5
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If then x equals


Detailed Solution: Question 5

Test: Surds And Indices- 2 - Question 6
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(a + b√3)2 = 52 + 30√3, where a and b are natural numbers, then a + b equals

Detailed Solution: Question 6

Test: Surds And Indices- 2 - Question 7
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If  and  x > 0, then the value of  is

Detailed Solution: Question 7



Option A is the correct answer.

*Answer can only contain numeric values
Test: Surds And Indices- 2 - Question 8
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If 1212x × 424x+12 × 52y = 84z × 2012x × 2433x−6, where x , y and z are natural numbers, then x + y + z equals


Detailed Solution: Question 8

On rewriting after prime factorisation, we get,

Since LHS = RHS, the corresponding powers must be equal. We have,

Test: Surds And Indices- 2 - Question 9
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Detailed Solution: Question 9

Test: Surds And Indices- 2 - Question 10
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If m and n are whole numbers and mn = 196, what is the value of (m - 3)(n+1) ?

Detailed Solution: Question 10

mn = 196

We know that 142 = 196

Hence we can take m = 14 and n = 2

(m - 3)(n+1) = (14 - 3)(2+1) = 113 = 1331

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About this UPSC Practice Test

This test contains 10 MCQs on Surds And Indices- 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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