Mathematics · 2025
JEE Main · 22 January 2025, Shift 2 · Q4
If the system of linear equations: x+y+2 z=6; 2 x+3 y+ a z= a +1; -x-3 y+ b z=2 b where a, b ∈ R, has infinitely many solutions, then 7 a +3 b is…
If the system of linear equations :
$$\begin{aligned}
& x+y+2 z=6 \\
& 2 x+3 y+\mathrm{a} z=\mathrm{a}+1 \\
& -x-3 y+\mathrm{b} z=2 \mathrm{~b}
\end{aligned}
$$
where $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbf{R}$, has infinitely many solutions, then $\displaystyle 7 \mathrm{a}+3 \mathrm{~b}$ is equal to :
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 16$
More from Matrices and Determinants
- Let A= [1, 1, 2; -2, 0, 1; 1, 3, 5]. Then the sum of all elements of the matrix adj(adj(2(adj A)^-1)) is equal to:2026
- For some a, b, let f(x)= |a+(sin x)/x, 1, b; a, 1+(sin x)/x, b; a, 1, b+(sin x)/x|, x ≠ 0, lim_x → 0 f(x)=λ+μ a+ν b. Then (λ+μ+ν)^2 is equal to:2025
- If the system of equations 2 x+λ y+3 z=5; 3 x+2 y-z=7; 4 x+5 y+μ z=9 has infinitely many solutions, then (λ^2+μ^2) is equal to:2025
- If the system of equations 2 x-y+z=4; 5 x+λ y+3 z=12; 100 x-47 y+μ z=212, has infinitely many solutions, then μ-2 λ is equal to2025
- Let A= [2, 2+p, 2+p+q; 4, 6+2 p, 8+3 p+2 q; 6, 12+3 p, 20+6 p+3 q]. If det(adj(adj(3 A)))=2^m · 3^n, m, n ∈ N, then m+n is equal to2025
- Among the statements: I: If |1, cos α, cos β; cos α, 1, cos γ; cos β, cos γ, 1| = |0, cos α, cos β; cos α, 0, cos γ; cos β, cos γ, 0|, then cos^2 α+…2026
- Let A= [cos θ, 0, - sin θ; 0, 1, 0; sin θ, 0, cos θ]. If for some θ ∈(0, π), A^2=A^T, then the sum of the diagonal elements of the matrix…2025
- Let f(x)=∫ (7 x^10+9 x^8)/((1+x^2+2 x^9)^2) d x, x>0, lim_x → 0 f(x)=0 and f(1)=1/4. If A= [0, 0, 1; 1/4, f^′(1), 1; α^2, 4, 1] and B=adj(adj A) be…2026
JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.