Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Let $f(x)=2 x^3-15 x^2+36 x+1$
Assertion (A): $f$ is strictly decreasing in [2,3]
Reason (R): $f$ is strictly increasing in $(-\infty, 2] \cup[3,(0)$.

A
Both A and R are true and R is the correct explanation of A .
✓
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

Correct option: B.

Both A and R are true but R is not the correct explanation of A.

(b) Both A and R are true but R is not the correct explanation of A .

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MCQ 21 Mark

Assertion (A): Scalar matrix $A =\left[a_{i j}\right]=\left\{\begin{array}{ll}k, & i=j \\ 0, & i \neq j\end{array}\right.$, where k is a scalar, is an identity matrix when $k =1$.
Reason (R): Every identity matrix is not a scalar matrix.

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.
✓
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: C.

A is true but R is false.

(c) A is true but R is false.
Explanation: A scalar matrix $A =\left[a_{i j}\right]=\left\{\begin{array}{ll}k ; & i=j \\ 0 ; & i \neq j\end{array}\right.$ is an identity matrix when $k =1$. But every identity matrix is clearly a scalar matrix.

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

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