2024 Slot 1 - If e^y=x^x, then which of the following is true ? | PYQs + Solutions

2024 Slot 1

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:

If $t=e^{2 x}$ and $y=\log _{e} t^{2}$ , then $\frac{d^{2} y}{d x^{2}}$ is :

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 $x = 1$

2024 Slot 1 PYQs