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 $\begin{bmatrix}2&-1\\-3&4\end{bmatrix}, A. adj$ $\text{A}=\begin{bmatrix}4&0\\0&4\end{bmatrix}.$
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 $35$ 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.
$A$ 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.
- ✓
Both $A$ and $R$ are false.
AnswerCorrect option: D. Both $A$ and $R$ are 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 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 $B.$
- 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.
- ✓
Both $A$ and $R$ are false.
AnswerCorrect option: D. Both $A$ and $R$ are false.
d. 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: 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 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: 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.
$A$ 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: 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 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: 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→MCQ 171 Mark
Assertion (A) : The inverse of a matrix $A=\left(\begin{array}{lll}43 & 1 & 6 \\ 35 & 7 & 4 \\ 17 & 3 & 2\end{array}\right)$ does not exist.
Reason (R) : The inverse of singular matrix is not possible.
- ✓
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).
(a) : $|A|=\left|\begin{array}{lll}43 & 1 & 6 \\ 35 & 7 & 4 \\ 17 & 3 & 2\end{array}\right|$
Applying $C_1 \rightarrow C_1-7 C_3$, we get
$
|A|=\left|\begin{array}{lll}
1 & 1 & 6 \\
7 & 7 & 4 \\
3 & 3 & 2
\end{array}\right|=0 \quad\left(\because C_1 \sim C_2\right)
$
$\therefore \quad A$ is singular matrix
$\because \quad A$ is singular matrix $\therefore A^{-1}$ does not exist.
$\therefore \quad$ Assertion and reason both are true and reason is the correct explanation of assertion.
View full question & answer→MCQ 181 Mark
Assertion (A) : The inverse of the matrix $A=\left(\begin{array}{ccc}4 & 2 & 3 \\ 8 & 5 & 2 \\ 12 & -4 & 5\end{array}\right)$ certainly exists.
Reason (R) : The matrix $A$ is non-singular and every non-singular matrix possesses its inverse.
- ✓
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).
(a) : We have $A=\left(\begin{array}{ccc}4 & 2 & 3 \\ 8 & 5 & 2 \\ 12 & -4 & 5\end{array}\right)$
$
\begin{aligned}
\therefore \quad|A| & =4(25+8)-2(40-24)+3(-32-60) \\
& =-176 \neq 0
\end{aligned}
$
$\Rightarrow A$ is non-singular $\Rightarrow A^{-1}$ exists.
$\therefore$ Assertion and reason both are correct and reason is the correct explanation of assertion.
View full question & answer→MCQ 191 Mark
Assertion (A) : The inverse of $A=\left(\begin{array}{ll}3 & 4 \\ 3 & 5\end{array}\right)$ does not exist.
Reason (R) : The matrix $A$ is non-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).
(a) : $\because|A|=\left|\begin{array}{ll}3 & 4 \\ 3 & 5\end{array}\right|=15-12=3 \neq 0$
$\therefore \quad A$ is non-singular.
$\therefore \quad A^{-1}$ exists.
View full question & answer→MCQ 201 Mark
Assertion (A) : If $A=\left(\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right)$, then $\operatorname{adj}(\operatorname{adj} A)=A$.
Reason (R) : $|\operatorname{adj}(\operatorname{adj} A)|=|A|^{(n-1)^2}, A$ be $n$ rowed non singular matrix.
- 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).
(b): $\operatorname{adj}(\operatorname{adj} A)=|A|^{n-2} A$
Here, $n=3$
$\therefore \quad \operatorname{adj}(\operatorname{adj} A)=|A| A$ ....(i)
Now, $|A|=\left|\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right|=3(-3+4)+3(2)+4(-2)=1$
From Eq. (i), adj $(\operatorname{adj} A)=A$
View full question & answer→MCQ 211 Mark
Assertion (A) : The inverse of the matrix $\left[\begin{array}{ccc}1 & 3 & 5 \\ 2 & 6 & 10 \\ 9 & 8 & 7\end{array}\right]$ does not exist.
Reason (R) : The matrix $\left[\begin{array}{ccc}1 & 3 & 5 \\ 2 & 6 & 10 \\ 9 & 8 & 7\end{array}\right]$ 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).
(a) : $\because\left[\begin{array}{ccc}1 & 3 & 5 \\ 2 & 6 & 10 \\ 9 & 8 & 7\end{array}\right]$ is singular therefore inverse does not exist.
$
\left[\because\left|\begin{array}{ccc}
1 & 3 & 5 \\
2 & 6 & 10 \\
9 & 8 & 7
\end{array}\right|=0 \text {, since } R_2=2 R_1\right]
$
$\therefore \quad$ Assertion and reason are both true but reason is the correct explanation of assertion.
View full question & answer→MCQ 221 Mark
Assertion (A) : The determinant of $A=\left(\begin{array}{lll}1 & 2 & 3 \\ 5 & 6 & 7 \\ 2 & 4 & 6\end{array}\right)$ is zero.
Reason (R) : The determinant of a matrix vanishes if any two rows or columns are proportional.
- ✓
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).
(a) : $|A|=\left|\begin{array}{lll}1 & 2 & 3 \\ 5 & 6 & 7 \\ 2 & 4 & 6\end{array}\right|=\left|\begin{array}{ccc}4 & 2 & 3 \\ 12 & 6 & 7 \\ 8 & 4 & 6\end{array}\right|$
$
\text { (using } C_1 \rightarrow C_1+C_3 \text { ) }
$
$\therefore \quad|A|=0\left(\because C_1 \sim C_2\right)$
$\therefore \quad$ Assertion and reason are both correct and reason is the correct explanation of assertion.
View full question & answer→MCQ 231 Mark
Assertion (A) : If $A=\left(\begin{array}{ccc}l & 0 & 0 \\ 0 & m & 0 \\ 0 & 0 & n\end{array}\right)$, then
$
A^{-1}=\left(\begin{array}{ccc}
1 / l & 0 & 0 \\
0 & 1 / m & 0 \\
0 & 0 & 1 / n
\end{array}\right)
$
Reason $( R )$ : The inverse of a diagonal matrix is a diagonal matrix.
- 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).
(b) : $\because A=\left(\begin{array}{ccc}l & 0 & 0 \\ 0 & m & 0 \\ 0 & 0 & n\end{array}\right)$
$\therefore \quad|A|=l m n$ and $\operatorname{adj}(A)=\left(\begin{array}{ccc}m n & 0 & 0 \\ 0 & l n & 0 \\ 0 & 0 & l m\end{array}\right)$
$
\therefore \quad A^{-1}=\frac{\operatorname{adj} A}{|A|}=\left(\begin{array}{ccc}
1 / l & 0 & 0 \\
0 & 1 / m & 0 \\
0 & 0 & 1 / n
\end{array}\right)=\operatorname{diag}\left(\frac{1}{l}, \frac{1}{m}, \frac{1}{n}\right)
$
$\therefore \quad$ Assertion and reason are both correct but reason is not the correct explanation of assertion.
View full question & answer→MCQ 241 Mark
Let $A$ be a $2 \times 2$ matrix.
Assertion $( A ): \operatorname{adj}(\operatorname{adj} A)=A$.
Reason (R): $|\operatorname{adj} A|=|A|$.
- 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).
(b) : Let $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, adj $A=\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right]$
$\Rightarrow \operatorname{adj}(\operatorname{adj} A)=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=A$
$\operatorname{adj} A=\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right] \Rightarrow|\operatorname{adj} A|=a d-b c=|A|$.
View full question & answer→MCQ 251 Mark
Assertion (A) : If $A$ is skew-symmetric of order 3, then its determinant should be zero.
Reason (R) : If $A$ is square matrix, then $\operatorname{det} A=\operatorname{det} A^{\prime}=\operatorname{det}\left(-A^{\prime}\right)$.
- 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).
(b) : Reason is false since
$\operatorname{det} A^{\prime}=\operatorname{det}\left(-A^{\prime}\right)$ is not true.
Indeed, $\operatorname{det}\left(-A^{\prime}\right)=(-1)^3 \operatorname{det} A^{\prime}$
Now as $A=-A^{\prime} \quad(\because A$ is skew-symmetric $)$
$\therefore \quad \operatorname{det} A=\operatorname{det}\left(-A^{\prime}\right)=-\operatorname{det}\left(A^{\prime}\right)=-\operatorname{det} A$
$\Rightarrow \operatorname{det} A=0$.
Thus assertion is correct.
$\therefore \quad$ Assertion and reason are both correct but reason is not the correct explanation of assertion.
View full question & answer→MCQ 261 Mark
Let $A=\left[\begin{array}{ccc}1 & 0 & a \\ 2 & 3 & b \\ -3 & 1 & c\end{array}\right], B=\left[\begin{array}{ccc}1 & 0 & x \\ 2 & 3 & y \\ -3 & 1 & z\end{array}\right]$
and $C=\left[\begin{array}{ccc}1 & 0 & a+x \\ 2 & 3 & b+y \\ -3 & 1 & c+z\end{array}\right]$.
Assertion (A) : $\operatorname{det} A+\operatorname{det} B=\operatorname{det} C$.
Reason (R) : $A+B=C$.
- 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.
(c) : Clearly $A+B \neq C$. Hence, reason is wrong.
However, by a property of determinants, $\operatorname{det} C=\operatorname{det} A+\operatorname{det} B$.
$\therefore \quad$ Assertion is correct statement but reason is wrong statement.
View full question & answer→