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UPSC Exam  >  UPSC Test  >  CSAT Preparation  >  Test: Cubes And Cube Roots- 2 - UPSC MCQ

Cubes And Cube Roots- 2 - Free MCQ Practice Test with solutions, UPSC


MCQ Practice Test & Solutions: Test: Cubes And Cube Roots- 2 (30 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- 2". These 30 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: 30 minutes
  • - Number of Questions: 30

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Test: Cubes And Cube Roots- 2 - Question 1
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If 73 = 343, then ∛343 = _________.

Detailed Solution: Question 1

Test: Cubes And Cube Roots- 2 - Question 2
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What will be the unit digit of the cube of a number ending with 6 ?

Detailed Solution: Question 2

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Test: Cubes And Cube Roots- 2 - Question 3
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Each prime factor appears _________ times in its cube.

Detailed Solution: Question 3

True
If a3 is the cube and m is one of the prime factors of a. Then, m appears three times in a3.

Test: Cubes And Cube Roots- 2 - Question 4
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What will be the unit digit of the cube of a number ending with 2 ?

Detailed Solution: Question 4

- To find the unit digit of a number ending in 2 when cubed, we can simply cube the unit digit 2.
- The calculation is: 2 x 2 x 2 = 8.
- Therefore, the unit digit of the cube of any number ending with 2 is 8.
- This means if you take a number like 12, 22, or 52, their cubes will all have a unit digit of 8.

Test: Cubes And Cube Roots- 2 - Question 5
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The number of digits in the cube root of a 6-digit number is _______.

Detailed Solution: Question 5

As 1003 = 1000000 which is the smallest 3 digit number. So it’s only 2 digit number which is the cube root of a 6 digit number

Test: Cubes And Cube Roots- 2 - Question 6
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The expansion of a3 is ___________.

Detailed Solution: Question 6

Test: Cubes And Cube Roots- 2 - Question 7
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What will be the unit digit of the cube root of a number ends with 3?

Detailed Solution: Question 7

  • A cube’s unit digit comes solely from its root’s last digit.
  • Check 0–9: 1³=1, 2³=8, 3³=27 (7), 4³=64 (4), 5³=125 (5), 6³=216 (6), 7³=343 (3), 8³=512 (2), 9³=729 (9), 0³=0.
  • Only 7³ ends with 3.
  • Hence any number ending in 3 has a cube root ending in 7.
  • For more tips, visit EduRev.

Test: Cubes And Cube Roots- 2 - Question 8
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The smallest natural number by which 135 must be divided to obtain a perfect cube is

Detailed Solution: Question 8

 we have 135 =  3 x 3 x 3 x 5

Grouping the prime factors of 135 into triples, we are left over with 5.
∴  135 is not a perfect cube
Now, [135]divided by5 = [ 3 x 3 x 3 x 5] divided by5
or  27 = 3 x 3 x 3
i.e. 27 is a perfect cube.
Thus, the required smallest number is 5

Test: Cubes And Cube Roots- 2 - Question 9
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What will be the unit digit of ∛216

Detailed Solution: Question 9

We can find it by Prime Factorization method 
³√216 = 2×2×2×3×3×3 
= 2 and 3 are making triplets i.e. 2 and 3 
= 2×3 = 6 Thus, we can say that 6 i.e option 'B' is correct.

Test: Cubes And Cube Roots- 2 - Question 10
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The value of ∛343 is-

Detailed Solution: Question 10

To determine the value of ∛343, we need to find a number that, when multiplied by itself three times, equals 343. Calculating 73 gives us 7 * 7 * 7 = 343. Therefore, the cube root of 343 is 7.

Test: Cubes And Cube Roots- 2 - Question 11
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What is the volume of a cube whose edge is 2cm ?

Detailed Solution: Question 11

The volume of a cube is calculated by cubing its edge length. For an edge length of 2 cm, the volume is:

  • Volume = edge length × edge length × edge length
  • Volume = 2 cm × 2 cm × 2 cm
  • Volume = 8 cubic centimetres (cm3)

Test: Cubes And Cube Roots- 2 - Question 12
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Which of the following is Hardy-Ramanujan Number ?

Detailed Solution: Question 12

This story is very famous among mathematicians. 1729 is sometimes called the “Hardy-Ramanujan number”.
There are two ways to say that 1729 is the sum of two cubes. 1x1x1=1; 12x12x12=1728. So 1+1728=1729 But also: 9x9x9=729; 10x10x10=1000. So 729+1000=1729 There are other numbers that can be shown to be the sum of two cubes in more than one way, but 1729 is the smallest of them.
Ramanujan did not actually discover this fact. It was known in 1657 by a Frenchmathematician Bernard Franicle de Bessy.

But it got famous after the ramanujans above conversation.

So it's famously known as Ramanujan Number.

Test: Cubes And Cube Roots- 2 - Question 13
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The value of 53 is __________.

Detailed Solution: Question 13

Raising 5 to the power of 3 is 

Test: Cubes And Cube Roots- 2 - Question 14
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How many zeros will be there in the cube root of 800?

Detailed Solution: Question 14

First find the cube root of 800
800 = 8 × 100

Now, 100 is not a perfect cube, so its cube root is not a whole number.
Hence, the cube root of 800 is a decimal number, not a whole number
Therefore, we can say the cube root does not exist as a whole number.
So, Correct Option: B

Test: Cubes And Cube Roots- 2 - Question 15
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By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?

Detailed Solution: Question 15


392 = 2 × 2 × 2 × 7 × 7
Hence the number should be multiplied by 7 to make it a perfect cube.

Test: Cubes And Cube Roots- 2 - Question 16
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The cube of an even number is always ____________.

Detailed Solution: Question 16

The cube of an even number is always an even number. Here's why:

Test: Cubes And Cube Roots- 2 - Question 17
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729 is the value of  _______________.

Detailed Solution: Question 17

To find the value of 729729729, we check cube powers:

Test: Cubes And Cube Roots- 2 - Question 18
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The cube of an odd number is always __________.

Detailed Solution: Question 18

The cube of an odd number is always an odd number because:

Test: Cubes And Cube Roots- 2 - Question 19
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The smallest natural number by which 243 must be multiplied to make the product a perfect cube  is __________. 

Detailed Solution: Question 19

Test: Cubes And Cube Roots- 2 - Question 20
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How many zeros will be there in the cube root of 27000?

Detailed Solution: Question 20

Test: Cubes And Cube Roots- 2 - Question 21
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Which of the following is a perfect cube ?

Detailed Solution: Question 21

Test: Cubes And Cube Roots- 2 - Question 22
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What will be the unit digit of the cube of a number ending with 4 ?

Detailed Solution: Question 22

Test: Cubes And Cube Roots- 2 - Question 23
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For a number ending with 7, the unit digit of its cube is equal to:

Detailed Solution: Question 23

If the unit digit is 7, the cube will have unit digit as 7×7×7 = 343

So, the unit digit will be 3.

Test: Cubes And Cube Roots- 2 - Question 24
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Which of the following is not a perfect cube ?

Detailed Solution: Question 24

To determine which of the following numbers is not a perfect cube, we need to check whether the number can be expressed as the cube of an integer.

  • a) 1 is a perfect cube because 1=13.
  • b) 9 is not a perfect cube. The cube root of 9 is not an integer.
  • c) 8 is a perfect cube because 8 = 23.
  • d) 27 is a perfect cube because 27 = 33.

Thus, the number that is not a perfect cube is:

b) 9.

Test: Cubes And Cube Roots- 2 - Question 25
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The cube root of 512 is ________.

Detailed Solution: Question 25

Test: Cubes And Cube Roots- 2 - Question 26
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9 is the cube root of  __________.

Detailed Solution: Question 26

  • A cube root of a number is the value that when multiplied by itself twice equals the original number.
  • Calculating 9×9×9 gives 729.
  • This shows 9 is the cube root of 729.
  • Thus, option B is correct.

Test: Cubes And Cube Roots- 2 - Question 27
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If 43 = 64, then ∛64 = ​

Detailed Solution: Question 27

The cube root of a number is a value which, when raised to the power 3, gives the number.
We are given that 43 = 64.
Therefore the cube root of 64 is 4, because 43 = 64.

Test: Cubes And Cube Roots- 2 - Question 28
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The smallest natural number by which 704 must be divided to obtain a perfect cube is

Detailed Solution: Question 28

Test: Cubes And Cube Roots- 2 - Question 29
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What will be the unit digit of the cube root of a number ends with 2?

Detailed Solution: Question 29

Test: Cubes And Cube Roots- 2 - Question 30
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The cube of 4 is _______________.

Detailed Solution: Question 30

The cube of 4 is:

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About this UPSC Practice Test

This test contains 30 MCQs on Cubes And Cube Roots- 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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