Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): The ratio of the circumference and the diameter of a circle is always constant.
Reason (R): The circumference of a circle having radius r is given by C = $2 \pi r$.

✓
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): The circumference of a circle having radius r is given by $C=2 \pi r$.
Now, $C=2 \pi r \Rightarrow \frac{C}{2 r}=\pi \Rightarrow \frac{\text { circumference }}{\text { diameter }}=\pi$ (constant $)$.
$\therefore A$ and R are both true and R is the correct explanation of A .

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MCQ 21 Mark

Assertion (A): Area of a triangle $=\frac{1}{2} \times$ base $\times$ height.
Reason (R): Area of a triangle having sides $a, b, c=\sqrt{s(s-a)(s-b)(s-c)}$, where s = semi-perimeter of the triangle.

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): Area of a triangle $=\frac{1}{2} \times$ base $\times$ height.
Also, area of a triangle having sides $a, b, c=\sqrt{s(s-a)(s-b)(s-c)}$, where s = semi-perimeter of the triangle,
$\therefore A$ is true but $R$ is false.

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MCQ 31 Mark

Assertion (A): Area of a parallelogram $=\frac{1}{2} \times$ product of two adjacent sides.
Reason (R): Area of a parallelogram = base x height.

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): Area of a parallelogram $=\frac{1}{2} \times$ product of diagonals.
And, area of a parallelogram = base x height.
$\therefore A$ is false but R is true.

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MCQ 41 Mark

Assertion (A): The area of the square formed by joining the midpoints of the sides of a square having area $64 cm^2$ is $16 cm^2$.
Reason (R): The diagonal of the square formed by joining the midpoints of the sides of a square is equal to the side of the outer 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).
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): When a square is formed by joining the midpoints of the sides of another square, then:
(i) The area of inner square is half of the area of outer square.
If the area of outer square is $64 cm^2$ then the area of the inner square is $32 cm^2$.
(ii) The diagonal of the inner square is equal to the side of the outer square.
$\therefore A$ is false but $R$ is true.

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MATHS Assertion (A) & Reason (B) MCQ

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