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MATHS Assertion (A) & Reason (B) MCQ

DETERMINANTS · Rajasthan Board (RBSE) STD 12 Science (Rajasthan - English Medium). 17 questions.

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Assertion (A) & Reason (B) MCQ

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17 questions · 5 auto-graded MCQ + 12 self-marked written.

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: For a matrix $\begin{bmatrix}2&-1\\-3&4\end{bmatrix},$ A. adj $\text{A}=\begin{bmatrix}4&0\\0&4\end{bmatrix}.$
Reason: For a square matrix A, $\text{A}(\text{adj}\text{A})=(\text{adj}\text{A})\text{A}=\mid\text{A}\mid.$
  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: If $\text{A}=\begin{bmatrix}1&0&1\\0&1&2\\0&0&4\end{bmatrix}$ then $\mid3\text{A}\mid=9\mid\text{A}\mid.$
Reason: If A is a square matrix of order n then $\mid\text{k}\text{A}\mid=\text{k}^{\text{n}}\mid\text{A}\mid.$
  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 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: The value of x for which $\begin{vmatrix}\text{x}&2\\18&\text{x}\end{vmatrix}=\begin{vmatrix}6&2\\18&6\end{vmatrix}$ is $\pm\ 6.$
Reason: The determinant of a matrix A order 2x2, $\text{A}\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$ is = ab - dc.
  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 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: For two matrices A and B of order 3, $\mid\text{A}\mid=2\mid\text{B}\mid=-3$ then if $\mid2\text{AB}\mid$ is -48.
Reason: For a square matrix A, $\text{A}(\text{adj}\ \text{A})=(\text{adj}\ \text{A})\text{A}=\mid\text{A}\mid.$
  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 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: The value of x for which $\begin{vmatrix}3&\text{x}\\\text{x}&1\end{vmatrix}=\begin{vmatrix}3&2\\4&1\end{vmatrix}$ is $\pm2\sqrt{2}.$
Reason: The determinant of a matrix A order 2x2, $\text{A}\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$ is = ad - bc.
  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 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: Inverse of the matrix $\begin{bmatrix}1&-1&2\\0&2&-3\\3&-2&4\end{bmatrix}$ is the matrix $\begin{bmatrix}-2&0&1\\9&2&-3\\6&1&-2\end{bmatrix}.$
Reason: Inverse of a square matrix A, if it exits is given by $\text{A}^{-1}=\frac{1}{\text{IAI}}$ adj A.
  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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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: The points $A(a, b + c), B(b, c +a )$ and $C(c, a + b)$ are collinear.
Reason: Three points $A (x_1, y_1) , B(x_2, y_2)$ and $C(x_3, y_3)$ are collinear if area of a triangle $\text{ABC}$ is zero.
  • ✓
    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 $A.$
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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: Value of x for which the matrix $\begin{bmatrix}1&2&0\\0&1&2\\-1&2&\text{x}\end{bmatrix}$ is singular is 5.
Reason: A square matrix is singular if $\mid\text{A}\mid=0.$
  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 false but R is true.
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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: Values of $k$ for which area of the triangle with vertices $(2, -6), (5, 4)$ and $(k, 4)$ is $35$ sq units are $12, 2.$
Reason: Area of a triangle with vertices $A (x_1, y_1), B(x_2, y_2)$ and $C(x_3, y_3)$ is $\frac{1}{2}\begin{vmatrix}\text{x}1&\text{y}1&1\\\text{x}2&\text{y}2&1\\\text{x}3&\text{y}3&1\end{vmatrix}.$
  • 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.
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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: The equation of the line joining (1, 2) and (3, 6) using determinants is y = 3x.
Reason: The area of $\triangle\text{PAB}$ is zero if P(x, y) is a point on the line joining a A and B.
  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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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: The minor of the element $3$ in the matrix $\begin{bmatrix}2&3&1\\0&-2&4\\2&1&5\end{bmatrix}$ is $8$.
Reason: Minor of an element $a_{ij}$ of a matrix is the determinant obtained by deleting its $j^{th}$ row and $i^{th}$ column.
  • 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.
  • ✓
    Both $A$ and $R$ are false.
Answer
Correct option: D.
Both $A$ and $R$ are false.
Both $A$ and $R$ are false.
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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: Value of x for which the matrix $\begin{bmatrix}1&2&0\\0&1&2\\-1&2&\text{x}\end{bmatrix}$ is singular is 5.
Reason: A square matrix is singular if $\mid\text{A}\mid=0.$
  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 false but R is true.
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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: In a square matrix of order $3$ the minor of an element $a_{22}$ is $6$ then cofactor of $a_{22}$ is $-6.$
Reason: Cofactor an element $\text{aij } = A_{IJ} = (-1)^{i+j} M_{ij}.$
  • 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.
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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: If $A$ is an invertible matrix of order $2, $and det $A = 3$ then det$( A ^{-1})$ is equal to $\frac{1}{3}.$
Reason: If $A$ is an invertible matrix of order $2$ then det $(A ^{-1}) = det\ A.$
  • 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.
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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: Inverse of a matrix $\text{A}=\begin{bmatrix}2&3\\1&2\end{bmatrix}$is the matrix $\text{A}^{-1}=\begin{bmatrix}2&-3\\-1&2\end{bmatrix}.$
Reason: Inverse of a square matrix $\begin{pmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{pmatrix}$ is $\begin{pmatrix}\text{d}&-\text{b}\\-\text{c}&\text{a}\end{pmatrix}.$
  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 161 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 $\text{A}^{-1}=\begin{bmatrix}5&-7\\-2&3\end{bmatrix}$ and $\text{B}^{-1}=\begin{bmatrix}7&6\\8&7\end{bmatrix}$ then $(\text{AB})^{-1}=\begin{bmatrix}23&31\\26&35\end{bmatrix}.$
Reason: $(\text{AB})^{-1}=\text{A}^{-1}\text{B}^{-1}.$
  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 false.
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Question 171 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 non singular square matrix of order 3x3 and $\mid\text{A}\mid=5$ then $\mid\text{adj}\text{A}\mid$ is equal to 125.
Reason: $\mid\text{adj}\text{A}\mid=(\mid\text{A}\mid)^{\text{n}-1}$ where n is order of A.
  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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Assertion (A) & Reason (B) MCQ - MATHS STD 12 Science Questions - Vidyadip