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Test: Cubes And Cube Roots- 2 - UPSC MCQ


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30 Questions MCQ Test CSAT Preparation - Test: Cubes And Cube Roots- 2

Test: Cubes And Cube Roots- 2 for UPSC 2024 is part of CSAT Preparation preparation. The Test: Cubes And Cube Roots- 2 questions and answers have been prepared according to the UPSC exam syllabus.The Test: Cubes And Cube Roots- 2 MCQs are made for UPSC 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Cubes And Cube Roots- 2 below.
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Test: Cubes And Cube Roots- 2 - Question 1
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Which of the following is not a perfect cube ?

Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 1

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 2
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The cube of 4 is _______________.

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Test: Cubes And Cube Roots- 2 - Question 3
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The value of 53 is __________.

Test: Cubes And Cube Roots- 2 - Question 4
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The cube of an even number is always ____________.
Test: Cubes And Cube Roots- 2 - Question 5
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The cube of an odd number is always __________.
Test: Cubes And Cube Roots- 2 - Question 6
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Each prime factor appears _________ times in its cube.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 6

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 7
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Which of the following is Hardy-Ramanujan Number ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 7
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 8
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By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 8


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 9
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The smallest natural number by which 243 must be multiplied to make the product a perfect cube  is __________. 
Test: Cubes And Cube Roots- 2 - Question 10
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The smallest natural number by which 704 must be divided to obtain a perfect cube is
Test: Cubes And Cube Roots- 2 - Question 11
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The smallest natural number by which 135 must be divided to obtain a perfect cube is
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 11

 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 12
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Which of the following is not a perfect cube ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 12

Test: Cubes And Cube Roots- 2 - Question 13
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The expansion of a3 is ___________.
Test: Cubes And Cube Roots- 2 - Question 14
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What will be the unit digit of the cube of a number ending with 2 ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 14
- 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 15
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What will be the unit digit of the cube of a number ending with 4 ?
Test: Cubes And Cube Roots- 2 - Question 16
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What will be the unit digit of the cube of a number ending with 6 ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 16

Test: Cubes And Cube Roots- 2 - Question 17
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A cuboid has dimensions 5cm, 2cm, 5cm. How many such cuboid will be needed to form a cube ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 17

Given, sides of a cuboid are 5cm, 2cm and 5cm
Volume of cuboid =5*2*5 = 50 cm3
Let the side of the cube formed with
minimum number of cuboids = x
Hence volume of the cube = x3
Number of cuboids required = n
Hence n*50 = x3
Now, n*50 must be perfect cube
n*50 = n*2*5*5
So, minimum value of n = 2*2*5 = 20
Hence, the number of cuboid will be
needed to form a cube is 20

Test: Cubes And Cube Roots- 2 - Question 18
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How many cuboids of dimensions 15cm, 30cm,15cm will be needed to form a cube ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 18
Given cuboids of dimensions 15cm, 30cm ,15cm

LCM(15, 30, 15) = 30

Since 15*2 = 30

        30*1 = 30

and  15*2  = 30  {since a cube has all the dimensions are same}

So, the number of cuboids required to form a cube = 2*1*2 = 4

So, by using 4 cuboids, we can form a cube having side 30 cm each.
Test: Cubes And Cube Roots- 2 - Question 19
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729 is the value of  _______________.
Test: Cubes And Cube Roots- 2 - Question 20
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Which of the following is a perfect cube ?
Test: Cubes And Cube Roots- 2 - Question 21
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What is the volume of a cube whose edge is 2cm ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 21
Volume of cube=2×2×2=8
Test: Cubes And Cube Roots- 2 - Question 22
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The symbol for cube root is __________.
Test: Cubes And Cube Roots- 2 - Question 23
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The cube root of 512 is ________.
Test: Cubes And Cube Roots- 2 - Question 24
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The value of ∛343 is-
Test: Cubes And Cube Roots- 2 - Question 25
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Which of the following is true for any natural number n? for n>1
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 25

Take any natural number(except 1). This identity would hold for any natural number.
Natural numbers are 1,2,3,4,5____ upto infinity with all positive terms.

Test: Cubes And Cube Roots- 2 - Question 26
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If the volume of a cube is 125 cm3 then what would be the length of its side?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 26

Test: Cubes And Cube Roots- 2 - Question 27
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What will be the unit digit of the cube root of a number ends with 8?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 27

To determine the unit digit of the cube root of a number that ends in 8, consider the following:

  • When you cube a number with a unit digit of 2, the resulting cube ends with 8. For example, 23=82^3 = 823=8.

Therefore, if a number ends with 8, the unit digit of its cube root will be 2.

So, the correct answer is:

1. 2

Test: Cubes And Cube Roots- 2 - Question 28
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What will be the unit digit of the cube root of a number ends with 2?
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 3?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 29

for example like 343 so its cube root will be 7
because 73 will always have 3 as unit digit

Test: Cubes And Cube Roots- 2 - Question 30
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For a number ending with 7, the unit digit of its cube is equal to:
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 30

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

So, the unit digit will be 3.

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