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

Question

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.

✓

Answer

Given $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 3\end{array}\right]\left[\begin{array}{c}x \\ -5\end{array}\right]=0$
$ \begin{array}{l} \Rightarrow [(x-2) 3]\left[\begin{array}{c} x \\ -5 \end{array}\right]\end{array}=0 $
$ \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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Assertion (A) : Let $A=\{-1,1,2,3\}$ and $B=\{1,4,9\}$, where $f: A \rightarrow B$ given by $f(x)=x^2$, then $f$ is not one-one function.
Reason (R): If $x_1 \neq x_2 \Rightarrow f\left(x_1\right) \neq f\left(x_2\right)$, for every $x_1, x_2 \in$ domain, then $f$ is one-one.

Assertion (A) : If $y=\log _{10} x+\log _e x$, then $\frac{d y}{d x}=\frac{\log _{10} e}{x}+\frac{1}{x}$.
Reason (R): $\frac{d}{d x}\left(\log _{10} x\right)=\frac{\log x}{\log 10}$ and
$
\frac{d}{d x}\left(\log _e x\right)=\frac{\log x}{\log e}
$

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.

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 $(A): \text{f(x)}=\tan^2\text{x}$ is continuous at $\text{x}=\frac{\pi}{2}$
Reason $(R):\ ?$ is continuous at $\text{x}=\frac{\pi}{2}$

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: $\tan^{-1}\big(\frac{3}{4}\big)+\tan^{-1}\big(\frac{1}{7}\big)=\frac{\pi}{4}.$
Reason: For x > 0, y > 0, xy < 1, $\tan^{-1}\text{x}+\tan^{-1}\text{y}=\tan^{-1}\Big(\frac{\text{x}+\text{y}}{1-\text{xy}}\Big).$

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 false.

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 $ (\vec{\text{a}}\times\vec{\text{b}})+(\vec{\text{a}}.\vec{\text{b}})=400$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|=9.$
Reason: If $\vec{\text{a}}$ and $\vec{\text{b}}$ are any two vectors, then $(\vec{\text{a}}\times\vec{\text{b}})^2$ is equal to $(\vec{\text{a}})^2(\vec{\text{b}})^2-(\vec{\text{a}}.\vec{\text{b}})^2.$

Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
Assertion is correct statement but Reason is wrong statement.
Assertion is wrong statement but Reason is correct statement.

For any square matrix $A$ with real number entries, consider the following statements.
Assertion (A) : $A+A^{\prime}$ is a symmetric matrix.
Reason (R): $A-A^{\prime}$ is a skew-symmetric matrix.

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: In $\triangle\text{ABC},\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}+\overrightarrow{\text{CA}}=0.$
Reason: If $\overrightarrow{\text{OA}}=\overrightarrow{\text{a}},\overrightarrow{\text{OB}},\overrightarrow{\text{b}},$ then $\overrightarrow{\text{AB}}=\overrightarrow{\text{a}}+\overrightarrow{\text{b}}.$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
Assertion is correct but Reason is incorrect.
Both Assertion and Reason are incorrect.

Assertion $(A)$ : If $y=\frac{1}{4} u^4$ and $u=\frac{2}{3} x^3+5$ then $\frac{d y}{d x}=\frac{2}{27} x^2\left(2 x^3+15\right)^3$.
Reason $(R)$ : If $y$ is a function of $v$ and $v$ is a function of $x$, then $\frac{d y}{d x}=\frac{d y}{d v} \times \frac{d v}{d x}$.

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.