CUET Mathematics 2026 21st May Shift 1 PYQs

If $y = 500 e^{7x} + 600 e^{-7x}$ and $\frac{d^2 y}{dx^2} = ky$, then the value of k is :

If $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots + \infty}}}$ then $\frac{dy}{dx}$ equals to

A function defined as $f:R\to R$ satisfies $f(x+y)=f(x)f(y)$ and $f(x)\ne 0$ for all $x,y\in R$, where R is set of real numbers. If $f(x)$ is differentiable at $x=0$ and $f'(0)=2$, then $f'(x)$ is equal to