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UPSC Exam  >  UPSC Test  >  CSAT Preparation  >  Test: Cubes And Cube Roots- 1 - UPSC MCQ

Cubes And Cube Roots- 1 - Free MCQ Practice Test with solutions, UPSC


MCQ Practice Test & Solutions: Test: Cubes And Cube Roots- 1 (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: Cubes And Cube Roots- 1". 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: Cubes And Cube Roots- 1 - Question 1
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What is the smallest number by which 72 must be multiplied to make it a perfect cube?

Detailed Solution: Question 1

Prime factorising 72, we get, 72 = 2 × 2 × 2 × 3 × 3. We know, a perfect cube has multiples of 3 as powers of prime factors. Here, number of 2's is 3 and number of 3's is 2. So we need to multiply another 3 in the factorization to make 72 a perfect cube.

Test: Cubes And Cube Roots- 1 - Question 2
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What is the cube of double of ‘a’?

Detailed Solution: Question 2

To find the cube of double 'a', first determine the double of 'a', which is 2a. Then, cube this value:

(2a)3 = 8a3. Therefore, the correct answer is 8a3.

Step-by-step explanation:

  • Double of 'a' is calculated as 2 × a = 2a.
  • Cubing 2a gives (2a)3 = 23 × a3 = 8a3.

Hence, the cube of double 'a' is 8a3.

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Test: Cubes And Cube Roots- 1 - Question 3
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Which of the following is the cube root of 27000?

Detailed Solution: Question 3


Prime factorisation of 27000,
is:
27000 = (2 x 2 x 2) x (3 x 3 x 3) x (5 x 5 x 5)
= 23 x 33 x 53
∴ ∛27000
= 2 x 3 x 5
= 30
Thus, the cube root of 27000
= 300.

Test: Cubes And Cube Roots- 1 - Question 4
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A natural number is said to be a perfect cube, if it is the cube of some ________.

Detailed Solution: Question 4

A natural number is said to be a perfect cube if it is the cube of some natural number.
Example
8 = 2 x 2 x 2
8 = 2 3
8 is the perfect cube because it is a cube of 2 which is a natural number.
But 12 is not a perfect cube because it is not a cube of any natural numbers.

Test: Cubes And Cube Roots- 1 - Question 5
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36 x K is a perfect cube number, then K = ______

Detailed Solution: Question 5

To determine K such that 36 × K is a perfect cube, follow these steps:

  • Factorise 36 into prime factors: 36 = 22 × 32.
  • For the product to be a perfect cube, each prime's exponent must be a multiple of three.
  • Multiplying by 6 (which is 2 × 3) adds one to each exponent, making them:
    • 22 becomes 23
    • 32 becomes 33
  • Thus, 36 × 6 = 216 = 63, confirming that K = 6.

Test: Cubes And Cube Roots- 1 - Question 6
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Express 63 as the sum of odd numbers.

Detailed Solution: Question 6

We know,

⇒ 31 + 33 + 35 + 37 + 39 + 41 = 216

And the cube of 6 is also 216

⇒ 6 × 6 × 6 = 216

Test: Cubes And Cube Roots- 1 - Question 7
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The numbers 1, 8, 27... are ____________.

Detailed Solution: Question 7

1 × 1 × 1 = 1
2 × 2 × 2 = 8
3 × 3 × 3 = 27
4 × 4 × 4 = 64
5 × 5 × 5 = 125
Hence all are cubes

Test: Cubes And Cube Roots- 1 - Question 8
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Ones place digit in the cube of 5832 is ______.

Detailed Solution: Question 8

A number ending with 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 0 then it's cube ends with 1 , 8 , 7 , 4 , 5 , 6 , 3 , 2 , 0 respectively  

⇒ One's digit of 5832= 2
⇒ Cube of 2=23 = 8 

So, the one's digit of cube of 5832=8

Test: Cubes And Cube Roots- 1 - Question 9
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Find the prime factorisation of 175616.

Detailed Solution: Question 9


Hence 175616 = 29×73, which can be written as 23×23×23×73.

Test: Cubes And Cube Roots- 1 - Question 10
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The cube of an odd natural number is:

Detailed Solution: Question 10

Solution:
The cube of an odd natural number is always odd. This is because when you multiply three odd numbers together (odd × odd × odd), the result is always odd.

Correct Answer: (b) odd

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About this UPSC Practice Test

This test contains 10 MCQs on Cubes And Cube Roots- 1 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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