Download App

DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS2 Marks
Question
If $\begin{vmatrix}\text{x}+1&\text{x}-1\\\text{x}-3&\text{x}+2\end{vmatrix}=\begin{vmatrix}4&-1\\1&3\end{vmatrix},$ then write the value of x.
✓

Answer

$\begin{vmatrix}\text{x}+1&\text{x}-1\\\text{x}-3&\text{x}+2\end{vmatrix}=\begin{vmatrix}4&-1\\1&3\end{vmatrix}$
⇒ (x + 1)(x + 2) - (x - 1)(x - 3) = 12 + 1
⇒ x2 + 3x + 2 - x2 + 4x - 3 = 13
⇒ 7x - 1 = 13
⇒ 7x = 14
⇒ x = 2
Hence, the value of x is 2

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 "2 Marks" from DETERMINANTS→DETERMINANTS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the integral: $\int \frac{2-3 \sin x}{\cos ^{2} x} d x$ 
→
Express matrix as the sum of a symmetric and a skew-symmetric matrix:$\left[\begin{array}{ccc} {3} & {3} & {-1} \\ {-2} & {-2} & {1} \\ {-4} & {-5} & {2} \end{array}\right]$
→
A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its cooler is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be,
Blue followed by red.
→
Find $\frac{{dy}}{{dx}}$ if x3 + x2y + xy2 + y3 = 81.
→
Find the domain of

$\sec^{-1}\text{x}-\tan^{-1}\text{x}$

→
If A is a non-singular square matrix such that |A| = 10, find |A-1|.
→
Without expanding, show that the values of the following determinant are zero:
$\begin{vmatrix}8&2&7\\12&3&5\\16&4&3 \end{vmatrix}$
→
If $\text{A}=\begin{bmatrix}4&3\\1&2 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}-4\\3\end{bmatrix},$ write AB.
→
The random variable X has a probability distribution P(X) of the following form, where ‘k’ is some number.
$\text{P}(\text{X}=\text{x})=\begin{cases}\text{k}, & \text{if x}=0\\2\text{k}, & \text{if x}=1\\3\text{k}, & \text{if x}=2\\0, & \text{otherwise}\end{cases}$
Determine the value of ‘k’.
→
Find the value of $\lambda$ is the vectors $2\hat{\text{i}}+\lambda\hat{\text{j}}+3\hat{\text{k}}$ and $3\hat{\text{i}}+2\hat{\text{j}}-4\hat{\text{k}}$ are perpendicular to each other.
→