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Maths Assertion (A) & Reason (B) MCQ

MATRICES · Gujarat Board (GSEB) STD 12 Science (GSEB - English Medium). 15 questions.

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Assertion (A) & Reason (B) MCQ

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15 questions · timed · auto-graded

Question 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 = A2 + 2AB + B2.
Reason: $\text{AB}\neq\text{BA}.$
  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 false but R is true.
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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.
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Question 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.
  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.
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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.
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Question 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 A2 = I, then (I + A)2 - 3A = I.
Reason: Al = IA = A, where I is Idetity matrix.
  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 false but R is true.
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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.
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Question 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.
  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.
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Question 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.
  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.
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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.
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Question 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 B2 = O, then (I + B)n = I + nB, for all $\text{n}\in\text{N}.$
  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.
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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.
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Question 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 A100B = BA100.
Reason: If AB = BA 
⇒ AnB = BAn for all positive integers n.
  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.
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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.
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Question 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 anXn + an-1Xn-1 + .... + a1X + anIz = 0 and $\text{a}_\text{n}\neq0,$ Then A is invertible.

  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.
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Question 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 2x2 matrices. AB = I2

⇒ A = B-1.

Reason: AB = 0

⇒ A = 0 or B = 0.

  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.
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Assertion (A) & Reason (B) MCQ - Maths STD 12 Science Questions - Vidyadip