Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion (A): The rate of change of area of a circle with respect to its radius r when $\mathrm{r}=6 \mathrm{~cm}$ is $12 \pi \mathrm{~cm}^{2} / \mathrm{cm}$.
Reason (R): Rate of change of area of a circle with respect to its radius r is $\frac{d A}{d r}$, where A is the area of the circle.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of A.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of A.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

(A) Both A and R are true and R is the correct explanation of A.
Explanation: Both A and R are true and R is the correct explanation of A.

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MCQ 21 Mark

Assertion (A): If $\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$, then $\mathrm{A}+\mathrm{B}=\left[\begin{array}{ll}3 & 7 \\ 1 & 7\end{array}\right]$.
Reason (R): Two different matrices can be added only if they are of same order.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of A.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of A.
C
$A$ is true but $R$ is false.
D
A is false but $R$ is true.

Answer

(A) Both A and R are true and R is the correct explanation of A.
Explanation: The given matrices are $A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$
Then, $\mathrm{A}+\mathrm{B}=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]+\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$
$=\left[\begin{array}{ll}2+1 & 4+3 \\ 3-2 & 2+5\end{array}\right]=\left[\begin{array}{ll}3 & 7 \\ 1 & 7\end{array}\right]$

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Applied Maths Assertion (A) & Reason (B) MCQ

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