Assertion (A) : If [ ll x & 1 ] [ cc 1 & 0 -2 & 3 ] [ c x -5 ]=0,… - Vidyadip

MCQ

Assertion $(A)$ : If $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 3\end{array}\right]\left[\begin{array}{c}x \\ -5\end{array}\right]=0$, then value of $x$ is either $-3 $ or $ 5 $.
Reason $(R)$ : Two matrices $\left(\begin{array}{ll}x & y \\ u & v\end{array}\right)$ and $\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$ are equal if and only if their corresponding entries are equal.

✓
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 $(A)$.

Given $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 3\end{array}\right]\left[\begin{array}{c}x \\ -5\end{array}\right]=0$
$\Rightarrow [(x-2) 3]\left[\begin{array}{c} x \\ -5 \end{array}\right]=O $
$\Rightarrow x(x-2)-15=0$
$ \Rightarrow x^2-2 x-15=0 $
$\Rightarrow x=-3,5$
$\therefore$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.

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 Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

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: $\text{I}=\int_{0}^{1}\frac{\text{dx}}{3\sqrt{1+\text{x}^3}}=\int_{0}^{{2}^\frac{-1}{3}}\frac{\text{dt}}{1-\text{t}^3}$
Reason: The integrand of the integral i becomes rational by the substitution $\text{t}=\frac{\text{x}}{3\sqrt{1+\text{x}^3}}$

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: $\int_{0}^{2\pi}\sin^3\text{x}\text{ dx}=0$
Reason: $\sin^3\text{x}$ an odd function.

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 $(A) :$ The function $f(x) = x^3 - 3x^2 + 6x - 100$ is strictly increasing on $R$
Reason $(R) :$ A strictly increasing functions is an injective function.

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 $x_2 - 2x + 5I = 0,$ then $A$ is invertible.
Reason: If a square matrix satisfies the equation $a_nX^n + a_{n-1}X^{n-1} + .... + a_1X + a_nI^z = 0$ and $\text{a}_\text{n}\neq0,$ Then $A$ is invertible.

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 $(A):\ \text{f(x)}=\sin\text{x}$ is continuous for all $\text{x }\in\text{ R}$
Reason $(R):\ \sin\text{x}$ and $\text{x}$ are continuous at on $R.$

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 curve $x^3 + y^3 = 6xy$, the slope of the tangent at $(3, 3)$ is $2$.
Reason $(R):$ The $\Big(\frac{\text{dy}}{\text{dx}}\Big)_{(\text{at }\text{x}_1,\text{y}_1)}$ gives slope of tangent of $\text{y}=\text{f(x)} $ at $(\text{x}_1,\text{y}_1)$

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 $(A) : f(x) = [x]$ greatest integer function is not differentiable at $x = 2$
Reason $(R) :$ The greatest integer function is not continuous at any integer

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 $(A) :$ At $\text{x}=\frac{\pi}{6},$ the curve $\text{y}=2\cos^2(3\text{x})$ has a vertical tangent.
Reason $(R) :$ The slope of tangent to the curve $\text{y}=2\cos^2(3\text{x})$ at $\text{x}=\frac{\pi}{6}$ is zero.

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 : Consider, the graph of constraints stated as linear inequalities as below: $5\text{x}+\text{y}\leq100,\text{x}+\text{y}\leq60,\text{x},\text{y}\geq0.$

Assertion $(A) : (25, 40) $ is an infeasible solution of the problem.
Reason $(R)$ : Any point inside the feasible region is called an infeasible solution.

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 $(A):$ If $\text{f(x)}=\log(\cos\text{x)},\text{x}>0$ is strictly decreasing in $\Big(0,\frac{\pi}{2}\Big).$
Reason $(R):$ if $\text{f'(x)}\geq0,$ then $\text{f(x)}$ is strictlyincreasing function.