If x = 16at^(1/4) and y = 8at^(3/4) then dy/dx is equal to: Option 1: 3/2√t Option 2: √t Option 3: 8/17t^(5/4) Option 4: 17/(8t^(5/4))

Answer: 3/2√t. Solution: Differentiate both parametric equations with respect to t: dx/dt = 4a t^(-3/4) and dy/dt = 6a t^(-1/4). Then dy/dx = (6a t^(-1/4))/(4a t^(-3/4)) = 3/2t^(1/2) = 3/2√t.

Calculus

Continuity & Differentiability

Easy

common

If $x = 16at^{\frac{1}{4}}$ and $y = 8at^{\frac{3}{4}}$ then $\dfrac{dy}{dx}$ is equal to:

$\dfrac{3}{2}\sqrt{t}$

$\sqrt{t}$

$\dfrac{8}{17}t^{\frac{5}{4}}$

$\dfrac{17}{8t^{\frac{5}{4}}}$

✅ Correct Option: 1

Differentiate both parametric equations with respect to $t$ :

$\dfrac{dx}{dt} = 4a\,t^{-3/4}$ and $\dfrac{dy}{dt} = 6a\,t^{-1/4}$ .

Then $\dfrac{dy}{dx} = \dfrac{6a\,t^{-1/4}}{4a\,t^{-3/4}} = \dfrac{3}{2}t^{1/2} = \dfrac{3}{2}\sqrt{t}$ .

2025: 30 May Shift 1

Let $y = \cos(\sin x^2)$ , then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{\pi}}{2}$ is equal to

2025: 21 May Shift 1

If $f(x) = \begin{cases} \frac{\tan(\frac{\pi}{4} - x)}{\cot 2x} & , x ≠ \frac{\pi}{4} \\ 2K + 1 & , x = \frac{\pi}{4} \end{cases}$ is continuous at $x = \frac{\pi}{4}$ , then the value of K is equal to

2026: 19 May Shift 2

For the function $f(x) = -2|\log_e|x||$ , which of the following is true?

2025: 15 May Shift 1

The function $f: \mathbb{R} \to \mathbb{R}$ defined by

$f(x) = \begin{cases} x^2, & x \ge 1 \\ x, & x < 1 \end{cases}$

2023: 22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	$y = \log(\sin x)$	(I)	$\frac{d^2y}{dx^2} = -\frac{1}{x^2}$
(B)	$y = e^{(1 + \log x)}$	(II)	$\frac{d^2y}{dx^2} = 2$
(C)	$y = \log\lvert x \rvert$	(III)	$\frac{d^2y}{dx^2} = 0$
(D)	$y = x^2 + 4x - 1$	(IV)	$\frac{d^2y}{dx^2} = -\csc^2 x$

Choose the correct answer from the options given below :

2022: 16 July Shift 2

Match List I with List II

List I	List II
A. If $f(x) = 2x$ and $g(x) = \frac{x^2}{2} + 1$ , then $\frac{g(x)}{f(x)}$ is	I. discontinuous at exactly three points.
B. The function $f(x) = \frac{4-x^2}{4x-x^3}$ is	II. continuous everywhere
C. The function $f(x) = \lvert x \rvert + \lvert x-1 \rvert$ is	III. discontinuous at $x = 0$ .
D. The function $f(x) = \lvert \sin x \rvert$ is	IV. continuous at $x = 0$ and $x = 1$

Choose the correct answer from the options given below:

If x=16at14x = 16at^{\frac{1}{4}}x=16at41​ and y=8at34y = 8at^{\frac{3}{4}}y=8at43​ then dydx\dfrac{dy}{dx}dxdy​ is equal to:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $x = 16at^{\frac{1}{4}}$ and $y = 8at^{\frac{3}{4}}$ then $\dfrac{dy}{dx}$ is equal to: