Determinant

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JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 1

If the system of equations $x+5y+6z=4$, $2x+3y+4z=7$, $x+6y+az=b$ has infinitely many solutions, then the point $(a,b)$ lies on the line

Determinant

$y-x=3$$x-y=3$$x+y=11$$x+y=12$

JEE Main 2021 (Online) 25th February Evening ShiftQuestion 2

The following system of linear equations $2x+3y+2z=9$ $3x+2y+2z=9$ $x-y+4z=8$

Determinant

does not have any solutionhas a unique solutionhas infinitely many solutionshas a solution $(\alpha,\beta,\gamma)$ satisfying $\alpha+\beta^{2}+\gamma^{3}=12$

JEE Main 2021 (Online) 25th July Evening ShiftQuestion 3

The number of distinct real roots of $\begin{vmatrix}\sin x&\cos x&\cos x\\\cos x&\sin x&\cos x\\\cos x&\cos x&\sin x\end{vmatrix}=0$ in the interval $-\frac{\pi}{4}\le x\le\frac{\pi}{4}$ is :

Determinant

$1$$2$$3$$4$

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 4

Consider the following system of equations : $x+2y-3z=a$ $2x+6y-11z=b$ $x-2y+7z=c$, where $a,b$ and $c$ are real constants. Then the system of equations :

Determinant

has a unique solution for all $a,b$ and $c$has a unique solution when $5a=2b+c$has infinite number of solutions when $5a=2b+c$has no solution for all $a,b$ and $c$

JEE Main 2021 (Online) 17th March Morning ShiftQuestion 5

The system of equations $kx+y+z=1$, $x+ky+z=k$ and $x+y+zk=k^{2}$ has no solution if $k$ is equal to :

Determinant

$0$$1$$-1$$-2$