CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Product of Two Numbers = HCF X LCM of the Two Numbers

Assertion A T...

Question

Assertion (A)
The HCF of two number is 9 and their LCM is 2016. If one of the numbers is 54, then the other is 306.
Reason (R)
For any positive integers a and b, we have:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Open in App

Solution

(d) Assertion (A) is false and Reason (R) is true.
It is given that:
HCF = 9 and LCM = 2016
Let the two positive integers be x and y.
It is given that:
x = 54
We know,
Product of two numbers = HCF $\times$ LCM
54 $\times$ y = 9 $\times$ 2016
∴ y = $\frac{18144}{54} = 336$ ≠ 306
Hence, Assertion is false and the Reason (R) is true.

Suggest Corrections

thumbs-up

1

Similar questions

Q. Assertion (A)
If the probability of winning a game is

\frac{8}{15}

, then the probability of losing the game is

\frac{7}{15}

.

Reason (R)
For any event E, we have P(E) + P(not E) = 1.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)

\sqrt{8}

is an irrational number.
Reason (R)
If m is a natural number which is not a perfect square, then

\sqrt{m}

is irrational.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)

\frac{1242}{49}

is a non-terminating, repeating decimal.
Reason (R)
The rational number

\frac{p}{q}

is a terminating decimal if q = (2m × 5n) for some whole numbers m and n.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
If the circumferences of two circles are in the ratio 2 : 3, then the ratio of their areas is 4 : 9.

Reason (R)
The circumference of a circle of radius r is 2πr.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) Reason (R) true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion (A)
The polynomial p(x) = x³ + x has one real zero.

Reason (R)
A polynomial of nth degree has at most n zeros.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

The Fundamental Theorem of Arithmetic

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Product of Two Numbers = HCF X LCM of the Two Numbers

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon