JEE Main 2025 Apr 3 Shift 1, Mathematics Q11: Differentiation And Intergration In Determinants

JEE Main2025Apr 3, Shift 1Mathematics

If $y (x) = sin x cos x sin x + cos x + 1 272827111, x \in R$ , then $\frac{d ^{2} y}{d x ^{2}} + y$ is equal to

Solution

Subtract column 1 from column 3 (this leaves the determinant unchanged):

$y (x) = sin x cos x 1 + cos x 27280110 .$

Expand along the third column. Only the entry $1 + cos x$ contributes:

$y (x) = (1 + cos x) 272811 \cdot (+ 1) = (1 + cos x) (27 - 28) = - (1 + cos x) .$

Differentiate: $y^{'} = sin x, y^{''} = cos x .$

$y^{''} + y = cos x + [- (1 + cos x)] = - 1.$

Concept behind this question

Concept-wise practice with instant solutions on Fundamenthol.