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CUET Mathematics 2024 PYQs

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CUET Mathematics 2024

Calculus

>

Continuity & Differentiability

Easy

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

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

Will be added.

Related questions:

CUET Mathematics 2024

f(x)

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

CUET Mathematics 2024

[x]

denote the greatest integer function. Then match List-I with List-II:

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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 $x = 1$

CUET Mathematics 2024

t=e^{2 x}

y=\log _{e} t^{2}

\frac{d^{2} y}{d x^{2}}