CUET Mathematics - f(x)=cases|x|/x,&x0\\1,&x=0cases g(x)=casesx(1/x),&x0\\0,&x=0cases Then at the origin, which one of the following is true? | PYQs + Solutions

CUET Mathematics 2025 13 May Shift 2

Calculus

Medium

core

$f(x)$ is continuous, but $g(x)$ is not continuous

$g(x)$ is continuous, but $f(x)$ is not continuous

Both $f(x)$ and $g(x)$ are continuous

Neither $f(x)$ nor $g(x)$ is continuous

✅ Correct Option: 2

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If $x^2 - y^2 = t - \frac{1}{t}$ , and $x^4 + y^4 = t^2 + \frac{1}{t^2}$ , then which of the following is correct?

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If $x^m y^n = (x + y)^{m+n}$ , then $\frac{d^2y}{dx^2}$ is equal to:

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Let $e^y(x+1) = 1$ . Then which of the following are TRUE?

(A) $\frac{d^2y}{dx^2} = -\frac{1}{(x+1)^2}$

(B) $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$

(D) $\left.\frac{d^2y}{dx^2}\right|_{x=0} = 1$

(E) $\left.\frac{d^2y}{dx^2}\right|_{x=1} = \frac{1}{4}$

Choose the correct answer from the options given below:

CUET Mathematics 2025 13 May Shift 2 PYQs