Let A= [ ccc 1 & 0 & a 2 & 3 & b -3 & 1 & c ], B= [ ccc 1 & 0 & x… - Vidyadip

Question

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) : $A+B=C$.

✓

Answer

(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.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Assertion (A) & Reason (B) MCQ" from Determinants→Determinants — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Assertion (A): For any symmetric matrix A, B'AB is a skew-symmetric matrix.
Reason (R): A square matrix P is skew-symmetric if P'$P^{\prime}=-P$.

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): For the LPP Z= 3x + 2y, subject to the constraints $\text{x}+2\text{y}\leq2;\text{x}\geq;\text{y}\geq0$ both maximum value of Z and Minimum value of Z can be obtained.
Reason (R): If the feasible region is bounded then both maximum and minimum values of Z exists.

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
A is true but R is false.
A is false but R is true.

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.

Assertion (A): The principal value of $\cot ^{-1}(\sqrt{3})$ is $\frac{\pi}{6}$.
Reason $( R )$ : Domain of $\cot ^{-1} x$ is $R -\{-1,1\}$.

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: A relation R = {(1, 1), (1, 2), (2, 2), (2, 3), (3, 3)} defined on the set A = {1, 2, 3} is symmetri.
Reason: A relation R on the set A is symmetric $(\text{a},\text{b})\in\text{R}$
$\Rightarrow(\text{b},\text{a})\in\text{R}.$

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.
A is true but R is false.
A is false but R is true.
Both A and R are fals.

Assertion $(A) :$ Quadrilateral formed by vertices $A(0,0,0), B(3,4,5), C(8,8,8)$ and $D(5,4,3)$ is a rhombus. Reason $(R): A B C D$ is a rhombus if $A B=B C=C D=D A$, $A C \neq B D$.

Assertion (A) : If $f^{\prime}(x)=(x-1)^3(x-2)^8$, then $f(x)$ has neither maximum nor minimum at $x=2$.
Reason $( R ): f^{\prime}(x)$ changes sign from negative to positive at $x=2$.

Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: The area of the region bounded by the curve $y^2 = 4x$ and the line $x = 3$ is $8\sqrt{3} \text{ sq.units}$
Reason: The area of the region bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$ is $\frac{9}{8}\text{ sq.units}$

Assertion (A) : $\int_0^{2 \pi} \sin ^3 x d x=0$
Reason (R) : $\sin ^3 x$ is an odd function.

Directions: In these questions, a statement of Assertion is followed by a statement of Reason is given.Choose the correct answer out of the following choices:
Assertion: If $\frac{\text{dy}}{\text{dy}}+\text{xy}=\text{x}^3\text{y}^3,\text{x}>0,\text{y}\geq0$ and $\text{y}(0)=1,$ then $\text{y}(1)=\frac{1}{\sqrt{2}}$
Reason: The differential equation is linear with integrating factor $e^x$