Download App

DETERMINANTS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDETERMINANTS5 Marks
Question
Solve the following determinant equations:
$\begin{vmatrix}1&1&\text{x}\\\text{p}+1&\text{p}+1&\text{p}+\text{x}\\3&\text{x}+1&\text{x}+2\end{vmatrix}=0$
✓

Answer

Let $\begin{vmatrix}1&1&\text{x}\\\text{p}+1&\text{p}+1&\text{p}+\text{x}\\3&\text{x}+1&\text{x}+2\end{vmatrix}=0$
$=\begin{vmatrix}1&1&\text{x}\\\text{p}&\text{p}&\text{p}\\3&\text{x}+1&\text{x}+2\end{vmatrix}$ [Applying $R_2\rightarrow R_2 - R_1$]
$=\text{p}\begin{vmatrix}1&1&\text{x}\\1&1&1\\3&\text{x}+1&\text{x}+2\end{vmatrix}$
$=\text{p}\begin{vmatrix}1&1&\text{x}\\1&1&1\\2&\text{x}&2\end{vmatrix}$
$=\text{p}\begin{vmatrix}0&1&\text{x}\\0&1&1\\2-\text{x}&\text{x}&2\end{vmatrix}$ [Applying $C_1 \rightarrow C_2 - C_1$​​​​​​​]
$=\text{p}\left\{(2-\text{x})\times\begin{vmatrix}1&\text{x}\\1&1 \end{vmatrix}\right\}$ [Expanding along $C_1$]
$=\text{p}(2-\text{x})(1-\text{x})=0$
$\text{x}=1,2$

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 "5 Marks Questions" 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

Maximize Z = 50x + 30y
Subject to
$2\text{x}+\text{y}\leq18$
$3\text{x}+2\text{y}\leq34$
$\text{x},\text{y}\geq0$
→
Integrate the function $\frac{1}{{\sqrt {8 + 3x - {x^2}} }}$
→
Minimise Z = x + 2y
subject to $2\text{x}+\text{y}\geq3,\ \text{x}+2\text{y}\geq6,\ \text{x},\ \text{y}\geq0.$
Show that the minimum of Z occurs at more than two points.
→
Three bags contain a number of red and white balls as follows: Bag $1 : 3$ red balls, Bag $2 : 2$ red balls and $1$ white ball Bag $3 : 3$ white balls.
The probability that bag i will be chosen and a ball is selected from it is $\frac{\text{i}}{6}, i = 1, 2, 3$. What is the probability that:
  1. A red ball will be selected?
  2. A white ball is selected?
→
Find the coordinates of a point on the parabola $y = x^2+ 7x + 2$ which is closest to the strainght line $y = 3x -3$.
→
If $\text{y}\sqrt{1-\text{x}^2}+\text{x}\sqrt{1-\text{y}^2}=1,$ prove that $\frac{\text{dy}}{\text{dx}}=-\sqrt{\frac{1-\text{y}^2}{1-\text{x}^2}}$
→
Find: $\int\frac{3\text{x}+5}{\text{x}^2+3\text{x}-18}\text{ dx}.$
→
Find the second order derivatives of the following functions:
$\text{y}=\tan^{-1}\text{x}$
→
Find the maximum area of an isosceles triangle inscribed in the ellipse $\frac{\text{x}^{2}}{16} + \frac{\text{y}^{2}}{9} = 1$ with its vertex at one end of the major axis.
→
Evaluate the following integrals:
$\int(4\text{x}+1)\sqrt{\text{x}^2-\text{x}-2}\text{dx}$
→