JEE Advanced 2026 · Paper 2, Mathematics question 15

Question Stem for Question Nos. 15 and 16

Consider the curve $C_1$ given by
$$y=e^{-x}\qquad\text{for }x\in[0,10\pi],$$
and the curve $C_2$ given by
$$y=e^{-x}(\sin x+\cos x)\qquad\text{for }x\in[0,10\pi].$$
Let $n$ be the total number of points of intersection of the curves $C_1$ and $C_2$.

Suppose that $\alpha_1,\alpha_2,\dots,\alpha_n\in[0,10\pi]$ are the $x$-coordinates of the points of intersection of the curves $C_1$ and $C_2$ such that
$$\alpha_1<\alpha_2<\dots<\alpha_n.$$