If x = 2 and y = 2, then the value of d^2y/dx^2 at = 0 is Option 1: -1/2 Option 2: -1 Option 3: 0 Option 4: 1

Answer: -1/2. Solution: x = 2,\ y = 2. dy/dx = (-2)/(2) = -. d^2y/dx^2 = -^2 * (d)/dx = -^2 * 1/(2) = -(^3)/2. At =0: -1/2.

Calculus

Continuity & Differentiability

Medium

If $x = 2\sin\theta$ and $y = 2\cos\theta$ , then the value of $\frac{d^2y}{dx^2}$ at $\theta = 0$ is

$-\frac{1}{2}$

$-1$

$0$

$1$

✅ Correct Option: 1

$x = 2\sin\theta,\ y = 2\cos\theta$ .

$\frac{dy}{dx} = \frac{-2\sin\theta}{2\cos\theta} = -\tan\theta$ .

$\frac{d^2y}{dx^2} = -\sec^2\theta \cdot \frac{d\theta}{dx} = -\sec^2\theta \cdot \frac{1}{2\cos\theta} = -\frac{\sec^3\theta}{2}$ .

At $\theta=0$ : $-\frac{1}{2}$ .

2026: 29 May Shift 2

A function f(x) is defined by $f(x)=\begin{cases}x^2+\alpha x+\beta: & 0\leq x<2\\3x+2 : & 2\leq x\leq4\\2\alpha x+5\beta :& 4<x\leq8\end{cases}$ . If function f(x) is continuous on [0, 8], then value of $2\alpha+3\beta$ is

2026: 21 May Shift 2

If a function $f(x) = \begin{cases}\lambda(x^2-2x), & x \le 0\\4x+1, & x>0\end{cases}$ then

2025: 27 May Shift 1

If $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots + \infty}}}$ then $\frac{dy}{dx}$ equals to

2026: 19 May Shift 2

Match the LIST-I with LIST-II

	LIST-I Curve $y = f(x)$ , where $f(x)$ is		LIST-II Nature / derivative / value of $y = f(x)$
A.	$x\vert x \vert$	I.	$y'$ is 2 for all $x \in R^+$ (set of positive real numbers)
B.	$x + \vert x \vert$	II.	$y'$ is 2 for all $x \in R^-$ (set of negative real numbers)
C.	$x - \vert x \vert$	III.	$f(-5) = -1$
D.	$\dfrac{x}{\vert x \vert}$	IV.	$(0, 0)$ is the point of inflection

Choose the correct answer from the options given below:

2023: 23 May Shift 3

If $y = \sin^{-1}\left(\frac{1-x^2}{1+x^2}\right)$ then $\frac{dy}{dx} =$

2026: 18 May Shift 2

If $x=\log_e t$ and $y=\dfrac{1}{t}$ , then $\dfrac{d^2y}{dx^2}$ at $t=0.1$ is

If x=2sin⁡θx = 2\sin\thetax=2sinθ and y=2cos⁡θy = 2\cos\thetay=2cosθ, then the value of d2ydx2\frac{d^2y}{dx^2}dx2d2y​ at θ=0\theta = 0θ=0 is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $x = 2\sin\theta$ and $y = 2\cos\theta$ , then the value of $\frac{d^2y}{dx^2}$ at $\theta = 0$ is