Determinants

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Q JEE MAIN 2025

If the system of equations $$ \begin{aligned} & 2 x+\lambda y+3 z=5 \\ & 3 x+2 y-z=7 \\ & 4 x+5 y+\mu z=9 \end{aligned} $$...

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Q JEE MAIN_2025

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

JEE Main Physics Medium

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Q JEE MAIN 2023

Let the system of linear equations

has a unique solution $x=\alpha, y=\beta, z=\gamma$. Then the...

JEE Main Physics Medium

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Q JEE MAIN 223

For the system of linear equations $$ \begin{aligned} & 2 x+4 y+2 a z=b \\ & x+2 y+3 z=4 \\ & 2 x-5 y+2 z=8...

JEE Main Mathematics Easy

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Q JEE MAIN 2023

Let $D_k=\left|\begin{array}{ccc}1 & 2 k & 2 k-1 \\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2\end{array}\right|$. If $\sum_{k=1}^n D_k=96$, then| $n$...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

Let $A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2\end{array}\right]$. If |adj $(\operatorname{adj}(\operatorname{adj} 2 A)) \mid=(16)^n$, then...

JEE Main Mathematics Medium

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Q JEE MAIN 2023

For the system of linear equations 2x - y + 3z = 5 3x + 2y – z = 7 4x + 5y + az...

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Q JEE-Main 2023

If the system of equations
x + y + az = b
2x + 5y + 2z = 6
x + 2y + 3z =...

JEE Main Mathematics Easy

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Q JEE-Main 2024

Let αβγ=45;α,β,γ∈R. If x(α,1,2)+y(1,β,2) +z(2,3,γ)=(0,0,0) for some x,y,z∈R,xyz≠ 0, then 6α+4β+γ is equal to_____.

JEE Main Mathematics Medium

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Q JEE MAIN

Let $\lambda, \mu \in R$. If the system of equations $3 x+5 y+\lambda z=3$ 7x+11y-9z=2 $97 x+155 y-189 z=\mu$ has infinitely many solutions, then $...

JEE Main Mathematics Easy

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Determinants