CUET Mathematics - If xsqrt(1 + y) + ysqrt(1 + x) = 0, where |x| < 1, |y| < 1 and x ≠ y, then | PYQs + Solutions

CUET Mathematics 2025 21 May Shift 1

Calculus

Hard

core

$\frac{dy}{dx} = \sqrt{\frac{1 + y}{1 + x}}$

$(1 + x)^2 \frac{dy}{dx} + 1 = 0$

$(1 + x^2) \frac{dy}{dx} + 1 = 0$

$(1 + x)^2 \frac{dy}{dx} = 1$

✅ Correct Option: 2

Related questions:

2 June Shift 1

If $y = \frac{1}{\sqrt[3]{1-x^3}}$ then $\frac{dy}{dx}$ is equal to

13 May Shift 2

$f(x)=\begin{cases}\dfrac{|x|}{x},&x\ne0\\1,&x=0\end{cases}$

$g(x)=\begin{cases}x\sin\left(\dfrac{1}{x}\right),&x\ne0\\0,&x=0\end{cases}$

Then at the origin, which one of the following is true?

13 May Shift 2

If $x = \frac{1-t}{1+t}$ and $y = \frac{3t}{1+t}$ , then $\frac{d^2y}{dx^2}$ is equal to

CUET Mathematics 2025 21 May Shift 1 PYQs