Mathematics · 2019
JEE Main · 10 April 2019, Shift 1 · Q64
If Δ_1= |x, sin θ, cos θ; - sin θ, -x, 1; cos θ, 1, x| and Δ_2= |x, sin 2 θ, cos 2 θ; - sin 2 θ, -x, 1; cos 2 θ, 1, x|, x ≠ 0; then for all θ ∈(0,…
If $\displaystyle \Delta_1=\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|$ and
$$\Delta_2=\left|\begin{array}{ccc}
x & \sin 2 \theta & \cos 2 \theta \\
-\sin 2 \theta & -x & 1 \\
\cos 2 \theta & 1 & x
\end{array}\right|, x \neq 0 ; \text { then }
$$
for all $\displaystyle \theta \in\left(0, \frac{\pi}{2}\right)$ :
Official answer
(2)
$\displaystyle \Delta_1+\Delta_2=-2 x^3$
More from Matrices and Determinants
- Let A=[a_i j] be a square matrix of order 3 such that a_i j=2^j-i, for all i, j=1,2,3. Then, the matrix A^2+A^3+…+A^10 is equal to:2022
- Let A= (2, -1; 0, 2). If B=I-^5 C_1(adj A)+^5 C_2(adj A)^2-…-^5 C_5(adj A)^5, then the sum of all elements of the matrix B is2022
- If for some α and β in R, the intersection of the following three planes x+4 y-2 z=1; x+7 y-5 z=β; x+5 y+α z=5 is a line in R^3, then α+β is equal to:2020
- If α ≠ a, β ≠ b, γ ≠ c and |α, b, c; a, β, c; a, b, γ| =0, then a/(α-a)+b/(β-b)+(γ)/(γ-c) is equal to:2024
- The values of λ and μ for which the system of linear equations x+y+z=2; x+2 y+3 z=5; x+3 y+λ z=μ has infinitely many solutions are, respectively:2020
- Let A= (1, 2; -2, -5). Let α, β ∈ R be such that α A^2+β A=2 I. Then α+β is equal to2022
- Let A=[a_i j] and B=[b_i j] be two 3 × 3 real matrices such that b_i j=(3)^(i+j-2) a_j i, where i, j=1,2,3. If the determinant of B is 81, then the…2020
- Let p and p+2 be prime numbers and let Δ= |p!, (p+1)!, (p+2)!; (p+1)!, (p+2)!, (p+3)!; (p+2)!, (p+3)!, (p+4)!| Then the sum of the maximum values of…2022
JEE Main 2019 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.