JEE Main 2025 — Determinants Questions with Solutions

The system of equations $\begin{aligned} & x+y+z=6 \\ & x+2 y+5 z=9, \\ & x+5 y+\lambda z=\mu, \end{aligned}$ has no so…

If the system of linear equations aligned & 3 x+y+β z=3 \ & 2 x+α y-z=-3 \ & x+2 y+z=4aligned has infinitely many solut…

If the system of equations $\begin{aligned} & x+2 y-3 z=2 \\ & 2 x+\lambda y+5 z=5 \\ & 14 x+3 y+\mu z=33 \end{aligned}…

If the system of equations aligned & (λ-1) x+(λ-4) y+λ z=5 \ & λ x+(λ-1) y+(λ-4) z=7 \ & (λ+1) x+(λ+2) y-(λ+2) z=9align…

Let the system of equations $\begin{aligned} & x+5 y-z=1 \\ & 4 x+3 y-3 z=7 \\ & 24 x+y+\lambda z=\mu \end{aligned} \la…

Let M and m respectively be the maximum and the minimum values of f(x)= |arrayccc 1+ ² x & ² x & 4 4 x \ ² x & 1+ ² x &…

For some a, b, let f(x)= |arrayccca+( x)/(x) & 1 & ~b \ a & 1+( x)/(x) & ~b \ a & 1 & ~b+( x)/(x)array |, x ≠ 0, x → ₀…

If y(x)= |arrayccc x & x & x+ x+1 \ 27 & 28 & 27 \ 1 & 1 & 1array |, x R, then (d² y)/(d x²)+y is equal to

If the system of equations $\begin{aligned} & 2 x-y+z=4 \\ & 5 x+\lambda y+3 z=12 \\ & 100 x-47 y+\mu z=212 \end{aligne…

If the system of linear equations : $\begin{aligned} & x+y+2 z=6 \\ & 2 x+3 y+\mathrm{a} z=\mathrm{a}+1 \\ & -x-3 y+\ma…