Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A) : If $2 \tan \theta=4 \sin \theta$, then $\sin \theta=\cos \theta$.
Reason (R) : For any acute angle $\theta, \sin ^2 \theta \cdot \operatorname{cosec}^2 \theta=1$.

A
A is true, R is false.
✓
A is false, R is true.
C
Both A and R are true, and R is the correct reason for A .
D
Both A and R are true, and R is incorrect reason for A .

Answer

Correct option: B.

A is false, R is true.

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MCQ 21 Mark

Assertion (A) : $\left(1-\operatorname{cosec}^2 \theta\right)\left(1-\sec ^2 \theta\right)=1$.
Reason (R) : $1+\tan ^2 \theta=\sec ^2 \theta$ and $1+\cot ^2 \theta=\operatorname{cosec}^2 \theta$.

A
A is true, R is false.
B
A is false, R is true.
✓
Both A and R are true, and R is the correct reason for A .
D
Both A and R are true, and R is incorrect reason for A .

Answer

Correct option: C.

Both A and R are true, and R is the correct reason for A .

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MCQ 31 Mark

Assertion (A) : $\sin \theta$ can be expressed in terms of $\sec \theta$ as : $\sin \theta=\frac{\sqrt{\sec ^2 \theta-1}}{\sec \theta}$
Reason (R) : For an acute angle $\theta, 1+\tan ^2 \theta=\sec ^2 \theta$.

A
A is true, R is false.
B
A is false, R is true.
✓
Both A and R are true, and R is the correct reason for A .
D
Both A and R are true, and R is incorrect reason for A .

Answer

Correct option: C.

Both A and R are true, and R is the correct reason for A .

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MCQ 41 Mark

Assertion (A) : If $x=2 \sin ^2 \mathrm{~A}, y=2 \cos ^2 \mathrm{~A}+1$, then the value of $x+y$ is 3 .
Reason (R) : For an acute angle, $\theta, \sin ^2 \theta+\cos ^2 \theta=1$.

A
A is true, R is false.
B
A is false, R is true.
✓
Both A and R are true, and R is the correct reason for A .
D
Both A and R are true, and R is incorrect reason for A .

Answer

Correct option: C.

Both A and R are true, and R is the correct reason for A .

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Mathematics Assertion (A) & Reason (B) MCQ

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