CUET Mathematics 2024 - The second order derivative of which of the following functions is 5^x ? | PYQs + Solutions

CUET Mathematics 2024

Calculus

Easy

$5^{x} \log _{e} 5$

$5^{x}\left(\log _{e} 5\right)^{2}$

$\frac{5^{\mathrm{x}}}{\log _{\mathrm{e}} 5}$

$\frac{5^{\mathrm{x}}}{\left(\log _{\mathrm{e}} 5\right)^{2}}$

✅ Correct Option: 4

Related questions:

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 :

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

CUET Mathematics 2024 PYQs

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