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JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Differentiation

If

y (x) = sin x 271 cos x 281 sin x + cos x + 1 271

,

x \in R

, then

\frac{d ^{2} y}{d x ^{2}} + y

is equal to

(A)-1✓ Correct
(B)28
(C)27
(D)1

Answer: (A)

Solution

Applying the column operation

C_{3} \to C_{3} - C_{1}

reduces the determinant to

y (x) = sin x 271 cos x 281 1 + cos x 00 .

Expanding along the third column,

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

. Then

\frac{d y}{d x} = sin x

and

\frac{d ^{2} y}{d x ^{2}} = cos x

, so

\frac{d ^{2} y}{d x ^{2}} + y = cos x - (1 + cos x) = - 1

.

JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Single correct option

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