CUET Mathematics 2024 - If e^y=x^x, then which of the following is true ? | PYQs + Solutions

CUET Mathematics 2024

Calculus

Medium

$y \frac{d^{2} y}{d x^{2}}=1$

$\frac{d^{2} y}{d^{2}}-y=0$

$\frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}=0$

$y \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+1=0$

✅ Correct Option: 4

Related questions:

The second order derivative of which of the following functions is $5^{\mathrm{x}}$ ?

Let $[x]$ denote the greatest integer function. Then match List-I with List-II:

List-I	List-II
(A) $\|x - 1\| + \|x - 2\|$	(I) is differentiable everywhere except at $x = 0$
(B) $x - \|x\|$	(II) is continuous everywhere
(C) $x - [x]$	(III) is not differentiable at $x = 1$
(D) $x \, \|x\|$	(IV) is differentiable at $x = 1$

If $f(x)$ , defined by $f(x)=\left\{\begin{array}{lll}k x+1 & \text { if } & x \leq \pi \\ \cos x & \text { if } & x>\pi\end{array}\right.$ is continuous at $x=\pi$ , then the value of $k$ is :

CUET Mathematics 2024 PYQs

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