Let x=at^2, y=2at. If d^2y/dx^2+dy/dx=0 at t=3, then a is equal to: Option 1: 8 Option 2: 1/18 Option 3: 1/9 Option 4: 9

The answer is '1/18'. View full solution:

CUET Mathematics - Let x=at^2, y=2at. If d^2y/dx^2+dy/dx=0 at t=3, then a is equal to: | PYQs + Solutions

CUET Mathematics 2026 30th May Shift 1

Calculus

Medium

applied

$\frac{1}{18}$

$\frac{1}{9}$

✅ Correct Option: 2

Related questions:

12th May Shift 2

If $x=a(\theta+\sin\theta)$ , $y=a(1-\cos\theta)$ , then $\dfrac{d^2y}{dx^2}=$

16 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $f(x) = x \sin x$	(I) is not continuous at $x = -3$
(B) $f(x) = \frac{\vert x\vert }{x}, x \neq 0$ and $f(x) = 1 \text{ at } x = 0$	(II) is continuous everywhere
(C) $f(x) = x - [x]$ , $[x]$ denotes greatest integer function	(III) is not differentiable at $x = 1$
(D) $f(x) = e^{\vert x - 1\vert }$	(IV) is not continuous at $x = 0$

Choose the correct answer from the options given below:

13 May Shift 1

If $f(x) = x^3\log_e x$ , Then $f''(e^2)$ is equal to