Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): For positive values of a rational number $n, n^2>n$ only if $n>1$.
Reason (R): For $0<n<1$, we have $n^2<n$.

✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: A.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
R is true and correctly explains A.

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MCQ 21 Mark

Assertion (A): Since 9 is a perfect square, so each one of 0.9, 0.09, 0.009, 0.0009 is a perfect square.
Reason (R): $0.9=\frac{9}{10}, 0.09=\frac{9}{100}, 0.009=\frac{9}{1000}, 0.0009=\frac{9}{10000}$.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is true.

(D) Assertion (A) is false but Reason (R) is true.
$\sqrt{0.09}=\sqrt{\frac{9}{100}}=\frac{3}{10}=0.3$
$\sqrt{0.0009}=\sqrt{\frac{9}{10000}}=\frac{3}{100}=0.03$
But 0.9 and 0.009 are not perfect squares. So, A is false.
R is clearly true.

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MCQ 31 Mark

Assertion (A): The square of a prime number may be prime or composite.
Reason (R): The square of a number can never be prime.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
✓
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: D.

Assertion (A) is false but Reason (R) is true.

(D) Assertion (A) is false but Reason (R) is true.
The square of a number has at least 3 factors. So, it can never be prime. Hence, A is false but R is true.

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MCQ 41 Mark

Assertion (A): $\left(\frac{3}{4}\right)^2<\frac{3}{4}$
Reason (R) : The square of a proper fraction is smaller than the fraction.

✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: A.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$\left(\frac{3}{4}\right)^2=\frac{9}{16}<\frac{3}{4} \cdot$ So, A is true.
R is true and correctly explains A.

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MCQ 51 Mark

Assertion (A): A number ending in 2, 3, 7 or 8 is never a perfect square.
Reason (R): None of the numbers from 1 to 9 when squared ends in 2, 3, 7 or 8 .

✓
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: A.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Units digit in x	1	2	3	4	5	6	7	8	9
Units digit in $x^2$	1	4	9	6	5	6	9	4	1

R is true and correctly explains A.

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MCQ 61 Mark

Assertion (A): $\sqrt{1 \frac{11}{25}}=1 \frac{1}{5}$.
Reason (R): 25 is a perfect square, but 11 is not.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
✓
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
C
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: B.

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
$\sqrt{1 \frac{11}{25}}=\sqrt{\frac{36}{25}}=\frac{6}{5}=1 \frac{1}{5} \cdot$ So, A is true.
$\sqrt{25}=5$, but 11 is not a perfect square. So, R is true but R doesn't explain A.

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MCQ 71 Mark

Assertion (A): Each of the numbers 400, 900,1600 and 2500 is a perfect square.
Reason (R): A number ending in an even number of zeros is always a perfect square.

A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
B
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
✓
Assertion (A) is true but Reason (R) is false.
D
Assertion (A) is false but Reason (R) is true.

Answer

Correct option: C.

Assertion (A) is true but Reason (R) is false.

(C) Assertion (A) is true but Reason (R) is false.
$\sqrt{400}=20 ; \sqrt{900}=30 ; \sqrt{1600}=40 ; \sqrt{2500}=50$. So, A is true.
None of the numbers $200,300,500,600,700,. . .$ is a perfect square. So, R is false.

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MATHS Assertion (A) & Reason (B) MCQ

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