JEE Main 2024 — Determinants Questions with Solutions

If f x = x 3 2 x 2 + 1 1 + 3 x 3 x 2 + 2 2 x x 3 + 6 x 3 − x 4 x 2 − 2 for all x ∈ ℝ , then 2 f 0 + f ' 0 is equal to

If the system of equations $\begin{array}{r} 11 x+y+\lambda z=-5 \\ 2 x+3 y+5 z=3 \\ 8 x-19 y-39 z=\mu \end{array}$ has…

If the system of equations 2 x + 3 y − z = 5 x + α y + 3 z = − 4 3 x − y + β z = 7 has infinitely many solutions, then…

Consider the system of linear equations x + y + z = 5 , x + 2 y + λ 2 z = 9 and x + 3 y + λ z = μ , where λ , μ ∈ R . T…

If the system of equations $\begin{aligned} & 2 x+7 y+\lambda z=3 \\ & 3 x+2 y+5 z=4 \\ & x+\mu y+32 z=-1 \end{aligned}…

If the system of equations $\begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & x+(\cos \alpha…

Let the system of equations x + 2 y + 3 z = 5 , 2 x + 3 y + z = 9 , 4 x + 3 y + λ z = μ have infinite number of solutio…

Consider the matrices : A= [arrayll2 & -5 \ 3 & marray ], B= [arrayl20 \ marray ] and X= [arraylx \ yarray ]. Let the s…

If α ≠ a, β ≠ b, γ ≠ c and |arraylllα & b & c \ a & β & c \ a & b & γarray |=0, then aα-a+bβ-b+γγ-c is equal to:

For α, β R and a natural number n, let Ar= |arraycccr & 1 & (n²)/(2)+α \ 2 r & 2 & n²-β \ 3 r-2 & 3 & (n(3 n-1))/(2)arr…