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This mock test of Test: Cubes for UPSC helps you for every UPSC entrance exam.
This contains 10 Multiple Choice Questions for UPSC Test: Cubes (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The cube root of .000216 is:

Solution:

QUESTION: 2

Cube root of 0.064 is

Solution:

0.064 = 64/1000= 4^3 / 10^3 =(4/10)^3= (2/5)^3

taking cube root of 0.064= 2/5=0.4

QUESTION: 3

The cube of any multiple of 2 is always divisible by

Solution:

Cube of multiple of 2 is divisible by 8

eg:

QUESTION: 4

What is the smallest number by which 3600 be divided to make it a perfect cube?

Solution:

Prime factorise 3600.

You will get 3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5

Now group the numbers into groups of 3.

You will get 1 group of 2 and remaining numbers i.e. 2,3,3,5,5

Now multiply these extra numbers

You will get 2 x 3 x 3 x 5 x 5 = 450

So, 3600 divided by 450 = perfect cube (8)

QUESTION: 5

Cube of all odd natural numbers is

Solution:

Odd, Any odd number to power 3 will have unit digit odd

Ex. 7^3=3. 49^3=9.

QUESTION: 6

(8.01)^{2} + ? = (8.97)^{2} What will approximately come in place of question mark?

Solution:

QUESTION: 7

The smallest number by which 5400 must be multiplied so that it become a perfect cube, is

Solution:

Find prime factors of 5400

5400=2×3×3×3×2×2×5×5

If we group them in the group of 3

5400=(2×2×2)×(3×3×3)×5×5

Here to make group of 3 for 5

We have to multiply 5400 by 5.

QUESTION: 8

Cube of all even natural numbers is

Solution:

QUESTION: 9

Cube of a natural number will never end with the digit

Solution:

There'd no such digit which can't end in a cube of a natural number. Hence a cube of a natural number can end with any digit.

1³= 1 (ends with 1)

2³= 8 (ends with 8)

3³= 27 (ends with 7)

4³= 64 (ends with 4)

5³= 125 (ends with 5)

6³= 216 (ends with 6)

7³= 343 (ends with 3)

8³= 512 (ends with 2)

9³= 729 (ends with 9)

0³= 0 (ends with 0)

Hence the last digits are 0,1,8,7,4,5,6,3,2,9

Therefore we see every digits are last digits of these cubes. Hence a cube of a natural number can end with any digit.

QUESTION: 10

Cube of 0.2 is

Solution:

0.2×0.2×0.2=0.008

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