CUET CUET Mathematics 2024 - If t=e^2 x and y= _e t^2, then d^2 yd x^2 is : | PYQs + Solutions | AfterBoards
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CUET Mathematics 2024

Calculus
>
Continuity & Differentiability

Medium

If t=e2xt=e^{2 x} and y=log⁡et2y=\log _{e} t^{2}, then d2ydx2\frac{d^{2} y}{d x^{2}} is :

Correct Option: 1
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CUET Mathematics 2024

If f(x)f(x), defined by f(x)={kx+1 if x≤πcos⁡x if x>πf(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=πx=\pi, then the value of kk is :

CUET Mathematics 2024

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

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

CUET Mathematics 2024

The second order derivative of which of the following functions is 5x5^{\mathrm{x}} ?

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