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Real Numbers

7 Board Maths previous year questions on Real Numbers — options free on every question; 1 include the answer & explanation free, the rest unlock with PYQ Pass.

Q1 FREE PREVIEW

If \(HCF = LCM\) for two rational numbers, then numbers always should be

[PYQ 2025]

a

Composite

b

Equal

c

Prime

d

Co-prime

✓ Correct answer: b)

Equal

Explanation

The HCF of two numbers is always less than or equal to the numbers, and the LCM is always greater than or equal to the numbers.

It is given that, HCF(a, b) = LCM(a, b), this holds true only when HCF(a, b) = a = b and LCM(a, b) = a = b.

Therefore, we can say that this condition is true when the two numbers are equal.

Q2

L.C.M. of numbers 6 and 15 is

a

6

b

3

c

15

d

30

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Q3

The Highest Common Factor of two numbers is 27 and their Least Common Multiple is 162. If one number is 54, then the other number is :

a

81

b

27

c

54

d

18

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Q4

Section-A

Multiple choice question ( Q1- Q18)

- 1 mark each

The sum of powers of prime factors of 400 is

a

4

b

9

c

6

d

8

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Q5

The sum of powers of prime factors of 400 is

a

4

b

9

c

6

d

8

🔒
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Q6

The sum of the powers of the prime factors of 196 is-

[PYQ 2023]

a

1

b

2

c

4

d

6

🔒
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Q7

Choose the correct option and write :
HCF of \((6,20)\) is -

a

6

b

20

c

2

d

120

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