Download App

MATHS Assertion (A) & Reason (B) MCQ

MATRICES · Rajasthan Board (RBSE) STD 12 Science (Rajasthan - English Medium). 15 questions.

Questions

Assertion (A) & Reason (B) MCQ

Take a timed test

15 questions · 9 auto-graded MCQ + 6 self-marked written.

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: 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.
Answer
Correct option: D.
$A$ is false but $R$ is true.
$A$ is false but $R$ is true.
View full question & answer→
Question 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: 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: $\text{A}_{\theta}\cdot\text{A}_{\phi}=\text{A}_{\theta+\phi}.$
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. 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 $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ 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.
Answer
Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→
Question 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: $(\text{A}+\text{B})^{2}\neq\text{A}^{2}+2\text{AB}+\text{B}^{2}.$
Reason: Generally AB = BA.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. A is true but R is false.
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 $A$ 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.
Answer
Correct option: D.
$A$ is false but $R$ is true.
$A$ is false but $R$ is true.
View full question & answer→
Question 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: 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.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true and R is the correct explanation of A.
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 $\text{A}=\begin{pmatrix}1 & 2 & -1\\ 2 & 0 & 3 \\ -1& 3 & 4 \end{pmatrix},$ 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.
Answer
Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
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 $\text{A}=\begin{pmatrix}0&-2&3\\ 2&0&6\\-3&-6&0 \end{pmatrix},$ 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.
Answer
Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
View full question & answer→
Question 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: 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.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true but R is not 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 $\text{A}=\begin{pmatrix}1 \pi 0 1\end{pmatrix},$ then $\text{A}^{100}=\begin{pmatrix}1 100\pi 0 1\end{pmatrix}.$
Reason: If $B$ is matrix of order $2X2$ 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.
Answer
Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→
Question 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: Suppose $\text{X}=\begin{pmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{pmatrix}$ satisfies X2 - 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 X2 - 4X + 3I = O.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true but R is not 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 $\text{A}=\begin{pmatrix}-3 & 2 \\ -5 & 4 \end{pmatrix}$ 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.
Answer
Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
View full question & answer→
Question 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: 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.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
  5. Both A and R are false.
Answer
  1. Both A and R are true and R is 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 : 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.
Answer
Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
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 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.
Answer
Correct option: C.
$A$ is true but $R$ is false.
$A$ is true but $R$ is false.
View full question & answer→
Generate Paper FreeAll MATRICES topics
Assertion (A) & Reason (B) MCQ - MATHS STD 12 Science Questions - Vidyadip