MCQ 11 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Let $\text{A}_{\theta}=\begin{pmatrix}\cos\theta+\sin\theta&\sqrt{2}\sin\theta\\-\sqrt{2}\sin\theta&\cos\theta-\sin\theta\end{pmatrix}\Big(\text{A}_{\frac{\pi}{3}}\Big)^{3}=-\text{I}.$
Reason : $\text{A}_{\theta}\cdot\text{A}_{\phi}=\text{A}_{\theta+\phi}.$
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 21 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : If $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason : If $A$ is skew symmetric matrix then $A^{-1}$ is skew symmetric matrix.
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 31 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : If $A$ is a square matrix such that $A^2 = I$, then $(I + A)^2 - 3A = I$.
Reason : $Al = IA = A,$ where $I$ is Idetity 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 $A.$
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
AnswerCorrect option: D. $A$ is false but $R$ is true.
View full question & answer→MCQ 41 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : If $\text{A}=\begin{pmatrix}3&-2&10\\-2&4&5\\10&5&6\end{pmatrix}$ and $\text{x}=\begin{pmatrix}1&5&6\\-2&0&1\\4&3&2\end{pmatrix} X\ 'AX$ is symmetric matrix.
Reason :$ X\ 'AX$ is symmetric or skew symmetric as $A$ is symmetric or skew symmetric.
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 51 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : If $\text{A}=\begin{pmatrix}1 & 2 & -1\\ 2 & 0 & 3 \\ -1& 3 & 4 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason : If $A$ is symmetric matrix then $A^{-1}$ is symmetric matrix.
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 61 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : $(\text{A}+\text{B})^{2}\neq\text{A}^{2}+2\text{AB}+\text{B}^{2}.$
Reason : Generally $AB = BA.$
- 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.
AnswerCorrect option: C. $A$ is true but $R$ is false.
View full question & answer→MCQ 71 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : If $\text{A}=\begin{pmatrix}-3 & 2 \\ -5 & 4 \end{pmatrix}$ and $\text{B}=\begin{pmatrix}4&-2\\5&-3\end{pmatrix}.$ then $A^{100}B = BA^{100}$.
Reason : If $AB = BA\ \Rightarrow A^nB = BA^n$ for all positive integers $n.$
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 81 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If the matrix $\text{P}=\begin{pmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&3\end{pmatrix}$ is a symmetric matrix, then $\text{a}=-\frac{2}{3}$ and $\text{b}=-\frac{2}{3}.$
Reason: If $P$ is a symmetric matrix, then $P\ ' = P.$
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 91 Mark
Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}1&\pi\\0&1\end{pmatrix},$ then $\text{A}^{100}=\begin{pmatrix}1&100\pi\\0&1\end{pmatrix}.$
Reason: If $B$ is matrix of order $2 \times 2$ and $B^2 = O$, then $(I + B)^n = I + nB$, for all $\text{n}\in\text{N}.$
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 101 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as :
Assertion : If $\text{A}=\begin{pmatrix}0&-2&3\\ 2&0&6\\-3&-6&0 \end{pmatrix},$ then $A^{-1}$ does not exist.
Reason : If $A$ is a skew symmetric matrix of odd order, then $A$ is singular.
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 111 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Matrix $\text{A}=\begin{pmatrix}1 & 2 \\ -2 & 1\end{pmatrix},$ satisfies the equation $x2 - 2x + 5I = 0$, then $A$ is invertible.
Reason : If a square matrix satisfies the equation $a_nX^n + a_{n-1}X^{n-1} + .... + a_1X + a_nI^z = 0$ and $\text{a}_\text{n}\neq0,$ Then $A$ is invertible.
- ✓
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.
AnswerCorrect option: A. Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→MCQ 121 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : If $\text{A}=\begin{pmatrix}1 & 2\\ 2& 3 \end{pmatrix}$ and $\text{B}=\begin{pmatrix}-1&4\\0&5\end{pmatrix}. (A + B)^2 = A^2 + 2AB + B^2$.
Reason : $\text{AB}\neq\text{BA}.$
- 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.
- ✓
$A$ is false but $R$ is true.
AnswerCorrect option: D. $A$ is false but $R$ is true.
View full question & answer→MCQ 131 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Suppose $\text{X}=\begin{pmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{pmatrix}$ satisfies $X^2 - 4X + 3I = O.$ If $\text{a}+\text{d}\neq4,$ then there are just two matrices such $X$.
Reason : There are infinitely many matrices $X$ satisfies the equation $X^2 - 4X + 3I = O.$
- 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.
AnswerCorrect option: B. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
View full question & answer→MCQ 141 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Let $A$ and $B$ are $2\times 2$ matrices. $AB = I_2 \ \Rightarrow A = B^{-1}$.
Reason : $AB = 0 \ \Rightarrow A = 0$ or $B = 0$.
- 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.
AnswerCorrect option: C. $A$ is true but $R$ is false.
View full question & answer→MCQ 151 Mark
Directions : In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as :
Assertion : Let $\text{A}=\begin{pmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{pmatrix}$ and $\text{X}=\begin{pmatrix}\text{x}\\\text{y}\end{pmatrix}.$ If $X\ 'AX = O$ for each $X, $ then $A$ must be skew symmetric matrix.
Reason : If $A$ is symmetric matrix and $X\ 'AX = O$ for each $X,$ then $A = O.$
- 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.
AnswerCorrect option: B. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
View full question & answer→