Download App

STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right| = $
  • A
    $1$
  • B
    $0$
  • C
    $x$
  • ✓
    $xy$
✓

Answer

Correct option: D.
$xy$
d
(d) $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right| = \left| {\,\begin{array}{*{20}{c}}0&0&1\\{ - x}&x&1\\0&{ - y}&{1 + y}\end{array}\,} \right| = xy,$

[${C_1} \to {C_1} - {C_2}$    ;  ${C_2} \to {C_2} - {C_3}$]

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $x_0, y_0$ be fixed real numbers such that $x_0^2+y_0^2 > 1$. If $x, y$ are arbitrary real numbers such that $x^2+y^2 \leq 1$, then the minimum value of $\left(x-x_0\right)^2+\left(y-y_0\right)^2$ is
→
$x\sqrt {1 + y} + y\sqrt {1 + x} = 0$, then ${{dy} \over {dx}} = $
→
Let $A, B, C$ be three sets of complex number defined as $A = \left\{ {z:{I_m}z \ge 1} \right\},\,B = \left\{ {z:\left| {z - 2 - i} \right| = 3} \right\},$$\,C = \left\{ {z:{R_e}\left( {\left( {1 - i} \right)z} \right) = \sqrt 2 } \right\}$ . If $z$ be any point in $A \cap B \cap C$ , then ${\left| {z + 1 - i} \right|^2} + {\left| {z - 5 - i} \right|^2}$ lies between 
→
The value of $x$ that satisfies the relation $x = 1 - x + x^2 - x^3 + x^4 - x^5 + ......... \infty$
→
Let $p\left( x \right)$ be a function defined on $R$ such that $p'\left( x \right) = p'\left( {1 - x} \right),$ for all $x \in \left[ {0,1} \right]$ $p\left( 0 \right) = 1,p\left( 1 \right) = 41.$ then $\mathop \smallint \limits_0^1 p\left( x \right)dx = $
→
The value of the integral, $\int_{1}^{3}\left[ x ^{2}-2 x -2\right] dx ,$ where $[x]$ denotes the greatest integer less than or equal to $x$, is :
→
Let $A, B$ and $C$  be three events, which are pair-wise independence and $\bar E$  denotes the complement of an event $E$ . If $P(A \cap B \cap C) = 0$  and  $P(C) > 0,$ then $P[(\bar A \cap \bar B)|\,C]$ is equal to
→
The value of $\frac{e^{-\frac{\pi}{4}}+\int \limits_0^{\frac{\pi}{4}} e^{-x} \tan ^{50} x d x}{\int \limits_0^{\frac{\pi}{4}} e^{-x}\left(\tan ^{49} x+\tan ^{51} x\right) d x}$ is
→
A square is inscribed in the circle $x^2 + y^2 - 6x + 8y -103 = 0$ with its sides parallel to the coordinate axes. Then the distance of the vertex of the square which is nearest to the origin is
→
If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is
→