Mathematics · 2026
JEE Main · 22 January 2026, Shift 2 · Q7
Let n be the number obtained on rolling a fair die. If the probability that the system x- ny +z=6; x+( n -2) y+( n +1) z=8; ( n -1) y+z=1 has a…
Let n be the number obtained on rolling a fair die. If the probability that the system
$$\begin{aligned}
& x-\mathrm{ny}+z=6 \\
& x+(\mathrm{n}-2) y+(\mathrm{n}+1) z=8 \\
& \quad(\mathrm{n}-1) y+z=1
\end{aligned}
$$
has a unique solution is $\displaystyle \frac{\mathrm{k}}{6}$, then the sum of k and all possible values of n is :
Official answer
From NTA’s final answer key for this paper.
(4)
$\displaystyle 22$
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
- Let A= [1, 2; 1, α] and B= [3, 3; β, 2]. If A^2-4 A+I=O and B^2-5 B-6 I=O, then among the two statements: (S1): [(B-A)(B+A)]^T= [13, 15; 7, 10] and…2026
- The sum of all possible values of θ ∈[0,2 π], for which the system of equations: x cos 3 θ-8 y-12 z=0; x cos 2 θ+3 y+3 z=0; x+y+3 z=0 has a…2026
- Consider the system of linear equations in x, y, z: x+2 y+t z=0, 6 x+y+5 t z=0, 3 x+t^2 y+f(t) z=0, where f: R → R is a differentiable function. If…2026
- If the system of equations x+5 y+6 z=4, 2 x+3 y+4 z=7, x+6 y+a z=b has infinitely many solutions, then the point (a, b) lies on the line2026
- Let A= [1, 0, 0; 3, 1, 0; 9, 3, 1] and B=[b_i j], 1 ≤ i, j ≤ 3. If B=A^99-I, then the value of (b_31-b_21)/(b_32) is:2026
- Let A= [1, 2, 7; 4, -2, 8; 3, 8, -7] and det(A-α I)=0, where α is a real number. If the largest possible value of α is p, then the circle…2026
- Let α, β ∈ R be such that the system of linear equations x+2 y+z=5; 2 x+y+α z=5; 8 x+4 y+β z=18 has no solution. Then (β)/(α) is equal to:2026
JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.