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 : 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 $2\times 2,$ $\text{A}\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$ is $= ab - dc.$
- 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 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 : 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 $A, \text{A}(\text{adj}\ \text{A})=(\text{adj}\ \text{A})\text{A}=\mid\text{A}\mid.$
- 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 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 $\begin{vmatrix}3&\text{x}\\\text{x}&1\end{vmatrix}=\begin{vmatrix}3&2\\4&1\end{vmatrix}$ is $\pm2\sqrt{2}.$
Reason: The determinant of a matrix $A$ order $2 \times 2, \text{A}\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$ is $= ad - bc.$
- ✓
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 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 : 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.
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 : For a matrix $\begin{bmatrix}2&-1\\-3&4\end{bmatrix}, A. \text{adj}$ $\text{A}=\begin{bmatrix}4&0\\0&4\end{bmatrix}.$
Reason : For a square matrix $A, \text{A}(\text{adj}\text{A})=(\text{adj}\text{A})\text{A}=\mid\text{A}\mid.$
- 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 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 : 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 $\mid\text{A}\mid=0.$
- 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 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 $\text{A}=\begin{bmatrix}1&0&1\\0&1&2\\0&0&4\end{bmatrix}$ then $\mid3\text{A}\mid=9\mid\text{A}\mid.$
Reason: If $A$ is a square matrix of order $n$ then $\mid\text{k}\text{A}\mid=\text{k}^{\text{n}}\mid\text{A}\mid.$
- 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 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: Values of $k$ for which area of the triangle with vertices $(2, -6), (5, 4)$ and $(k, 4)$ is $\text{35 sq units}$ 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.
AnswerCorrect option: D. $A$ is false but $R$ is true.
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: 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: $(\text{AB})^{-1}=\text{A}^{-1}\text{B}^{-1}.$
- 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.
- ✓
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: The equation of the line joining $(1, 2)$ and $(3, 6)$ using deter`minants 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 $B.$
- 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 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: 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 $\text{A}^{-1}=\frac{1}{\text{IAI}}\text
{ adj A}.$
- ✓
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.
- 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: 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 aij 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.
- ✓
Answerd. Both A and R are false.
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: 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 $\mid\text{A}\mid=0.$
- 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 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 a non singular square matrix of order $3 \times 3$ 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 $A.$
- 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 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: 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 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.
AnswerCorrect option: D. $A$ is false but $R$ is true.
View full question & answer→MCQ 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: 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.
AnswerCorrect option: C. $A$ is true but $R$ is false.
View full question & answer→MCQ 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: 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 $\begin{pmatrix}\text{d}&-\text{b}\\-\text{c}&\text{a}\end{pmatrix}.$
- 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→