Collegedunia Team Content Curator
Content Curator | Updated On - Jul 23, 2025
Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols are ranged from 0-9 and are termed as digits. The Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box. Number Systems consist of multiple types based on the base value for its digits.
MCQs
Question 1. Is it possible to write 0 as p/q?
- No
- Can’t explain
- Yes
- None of the Above
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Question 2. Which of the following is the same as the number x3?
- x6/x3
- (x6)3
- X6-x3
- x6.x3
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Ans: (A)
Explanation: x6/x3 = x6-3 = x3
Question 3. 3√6 + 5√6 is equal to:
- 5√6
- 7√12
- 8√6
- 4√12
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Ans: (C)
Explanation: 3√6 + 5√6 = (3+5) √6 = 8√6
Question 4. √4 is a __________ number.
- Neither rational or irrational
- Rational
- Irrational
- None of the above
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Ans: (B)
Explanation: √4 = 2. Hence, 2 is a rational number.
Question 5. Which of the following is an irrational number?
- √15
- √100
- √16
- √(12/3)
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Ans: (A)
Explanation: √15 cannot be simplified, It is an irrational number.
Question 6. √6 x √27 is equal to:
- 9√3
- 2√2
- 3√3
- 9√2
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Ans: (D)
Explanation: √6 x √27 = √(6 x 27) = √(2x3x3x3x3) = 3×3√2 =9√2
Question 7. Which of the following are irrational numbers?
- √29
- √225
- 7.478478
- 0.3796
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Ans: (A)
Explanation: √29 = 5.38516480713
Since it is not a perfect square, √29 is an irrational number.
Question 8. 4√6 + 7√6 is equal to:
- 11√6
- 10√6
- 4√12
- 8√12
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Ans: (A)
Explanation: 4√6 + 7√6 = (4 + 7) √6 = 11√6.
Question 9. The three rational numbers between 3 and 4 are:
- 12/7,13/7,14/7
- 11/4,12/4,13/4
- 5/2,6/2,7/2
- 13/4,14/4,15/4
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Ans: (D)
Explanation:
There are many rational numbers in between 3 and 4
To find 3 rational numbers, we need to multiply and divide both the numbers by 3+1 = 4. Hence, 3 x (4/4) = 12/4 and 4 x (4/4) = 16/4.
Therefore, three rational numbers between 12/4 and 16/4 are 13/4, 14/4 and 15/4.
Question 10. If √3=1.732, then \(\sqrt { \frac{\sqrt{3}-1}{\sqrt{3}+1}}\) is equal to:
a) 2.732
b) 0.2679
c) 0.732
d) 0.517
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Ans: (d)
Explanation: √((√3-1)/(√3+1)) = √((√3-1)(√3-1)/(√3+1)(√3-1) )
= √((√3-1)2/((√3)^2-12 )) = √((√3-1)2/(3-1))
= ((√3-1))/√2 = (√2 (√3-1))/(√2 √(×&2))
= (1⋅414(1.732-1))/2
= (1⋅414×0.732)/2 = (1.035)/2 = 0.517
Question 11. Value of 256x0.16(256)0.09 is:
- 256.25
- 64
- 4
- 16
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Ans: (c)
Explanation: (256)x0.16(256)0.09 = (256)0.16+0.09
2560.16+0.09= 2560.25
2560.25 = ((2)8)1/4
((2)8)1/4 = (2)2
(2)2 = 4
Question 12. The value of \(\sqrt [4]{16^{-2}}\) is:
- 1/2
- 4
- 1/4
- 1/16
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Ans: (a)
Explanation: \(\sqrt [4]{16^{-2}}\) = 4\(\sqrt{\frac{1}{(16)^2}}\)
Question 13. √12 X √15 is equal to:
- √25
- 10√5
- 5√6
- 6√5
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Ans: (d)
Explanation: 12 ×15 = 180
√180 = 6√5
Question 14. 4√5 + 5√5 is equal to:
- 9√10
- 9√5
- 7√5
- 5√10
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Ans: (b)
Explanation: 4√5 + 5√5 = 9√5
Question 15. A rational number between √2 and √3:
- (√2. √3)/2
- 1.5
- 1.8
- 1.9
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Ans: (b)
Explanation: √2 = 1.4142…
√3 = 1.732
Hence, the rational number between √2 and √3 is 1.5
Question 16. The product of \(\sqrt[3]{2} . (2)^ {-\frac{1}{3}} . \sqrt[12]{32}\) equals:
- \(\sqrt[12]{2}\)
- \(\sqrt{2}\)
- \(\sqrt[12]{32}\)
- 2
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Ans: (c)
Explanation: (16)^(-1/4) × \(\sqrt[4]{16}\) = (16)^(-1/4) × (16)^(1/4) [\(\because\)xm. xn = xm+n]
= (16)^(-1/4+1/4) = (16)^0 [\(\because\)x0=1]
= 1
(16)^(-1/4) × √(4&16) = 1
Question 17. The product of a rational and an irrational number is:
- Sometimes rational and sometimes irrational
- Always an integer
- Always a rational number
- Always an irrational number
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Ans: (d)
Explanation: Rational and Irrational numbers both are real numbers but different with respect to their properties. Rational numbers are the numbers that can be expressed in the form of a ratio (P/Q & Q≠0) and irrational numbers cannot be expressed as a fraction. But both the numbers are real numbers and can be represented in a number line.
Question 18. Every rational number is:
- Real number
- Natural number
- Whole number
- Integer
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Ans: (a)
Explanation: Real numbers include all rational and irrational numbers. It can be expressed in p/q form where q ≠ 0. Therefore, a rational number is a subset of real numbers.
Question 19. What would be the denominator after rationalising \(\frac{7}{(5\sqrt{3}-9\sqrt{2})}\) ?
- 19
- 20
- 25
- None of these
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Ans: (d)
Explanation: 7/((5√3-9√2) ) = 7/((5√3-9√2) ) × (5√3-9√2)/(5√3-9√2)
= 7(5√3-9√2)/((5√3)^2-(5√2)^2 ) = (35√3+35√2)/(75-50)
= (35√3+35√2)/25
The denominator of 7/((5√3-9√2) ) is 25
Question 20. The decimal expansion of an irrational number may be:
- Recurring
- Non-terminating and non-recurring
- Terminating
- Either terminating or non- terminating
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Ans: (b)
Explanation: The decimal expansion of an irrational number is non-terminating non-recurring. Moreover, a number whose decimal expansion is non-terminating non-recurring is irrational.
Question 21. 2√3+√3 is equal to:
- 3√3
- 6
- 4√6
- 2√6
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Ans: (a)
Explanation: 2√3+√3 = (2+1) √3= 3√3
Question 22. The value of √10 times √15 is equal to
- √25
- 10√5
- 5√6
- √5
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Ans: c
Explanation: √10×√15 = (√2. √5) × (√3. √5) = 5√6
Question 23. When 15√15 is divided by 3√3 find the quotient
- 5√5
- 3√5
- 5√3
- 3√3
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Ans: (a)
Question 24. If x = \(\frac{ \sqrt{7}}{5}\) and \(\frac{5}{x}\) = p√7, then the value of p is
- \(\frac{5}{\sqrt{7}}\)
- \(\frac{25}{7}\)
- \(\frac{7}{25}\)
- \(\frac{ \sqrt{7}}{5}\)
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Ans:( b)
Question 25. The rational number between – \(\frac{1}{5}\) and – \(\frac{2}{5}\) is
- 4
- - \(\frac{1}{4}\)
- - \(\frac{3}{10}\)
- - \(\frac{7}{25}\)
Click here for the answer
Ans: c
Explanation: 1/5 + -2/5 / 2
= -3/5 /2
= -3/5 * 1/2
= -3/10
Question 26. The simplified value of 
is
- 9
- 3
- 1
- 0
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Ans: (a) 9
Question 27. If x1/12 = 491/24 then find the value of x.
- 49
- 2
- 12
- 7
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Ans: (d)
Explanation: 49 = 72
The given equation is x1/12 = 72x(1/24)
x1/12 = 71/12
The power on the number 7 is the same as on the variable x. On comparing both the expressions on either side of the equal to sign, x is equal to 7.
Therefore, the value of x is 7.
Question 28. The decimal expansion of √2 is:
- finite decimal
- 1.4121
- non-terminating recurring
- non-terminating non-recurring
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Ans: (d)
Explanation: The value of √2 is 1.414
The rational number’s decimal expansion is either ending or repeating non-terminating. We may therefore confidently assume that the decimal expansion of a rational number can be repeated by terminating or non-terminating.
√2 is a rational number.
∴ Decimal Expansion of √2 is Non-Terminating non- repeating.
Question 29. Find the value of \(\sqrt[3]{\frac{54}{250}}\)
- \(\frac{9}{25}\)
- \(????\frac{3}{5}\)
- \(????\frac{27}{125}\)
- \(????\frac{3}{25}\)
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Ans: (b)
Question 30. Find the value of 464-2 is
- 12
- 18
- 164
- 8
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Ans: (f)
Explanation: \(\sqrt[4]{64^{-2}} = \sqrt[4]\frac{1}{64^2}\) [\(\because\)x−n=xn1]
Question 31. Find the value of \(\sqrt[3]216 - \sqrt[3]125\)
- 1
- -1
- \(\sqrt[3]{91}\)
- \(\frac{6}{5}\)
Click here for the answer
Ans: (i)
Explanation: \(\sqrt[3]216 - \sqrt[3]125\) = \(\sqrt[3]6^3 - \sqrt[3]5^3\)
= 6 – 5
= 1
Hence, the value of \(\sqrt[3]216 - \sqrt[3]125\) = 1
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