CUET Mathematics: CalculusContinuity & Differentiability. Free, no login required.

Q1:

2022: 23 Aug Shift 1

Continuity & Differentiability

Medium

Core

If x=at2x = at^2 and y=2aty = 2at, then the value of d2ydx2\frac{d^2y}{dx^2} is

( where t is a parameter )

Answer options
Option 4
Correct Answer
Explanation for 2022: 23 Aug Shift 1 MAT question 1

Q2:

2022: 25 May Shift 1

Continuity & Differentiability

Easy

Common

If y=1x+1y = \frac{1}{x+1}, then d2ydx2\frac{d^2y}{dx^2} at x=2x = 2 is:

Answer options
Option 3
Correct Answer
Explanation for 2022: 25 May Shift 1 MAT question 2

Q3:

2022: 25 May Shift 1

Continuity & Differentiability

Medium

Core

The derivative of sin⁡(tan⁡−1e2x)\sin(\tan^{-1} e^{2x}) with respect to xx is:

Answer options
Option 2
Correct Answer
Explanation for 2022: 25 May Shift 1 MAT question 3

Q4:

2022: 25 May Shift 1

Continuity & Differentiability

Hard

Core

If 1−x2+1−y2=a(x−y)\sqrt{1-x^2} + \sqrt{1-y^2} = a(x-y), then dydx=\frac{dy}{dx} =

Answer options
Option 2
Correct Answer
Explanation for 2022: 25 May Shift 1 MAT question 4

Q5:

2022: 25 May Shift 1

Continuity & Differentiability

Medium

Core

The function f(x)=x−1x(x2−1),x≠1,f(1)=1f(x) = \frac{x-1}{x(x^2-1)}, x \neq 1, f(1) = 1, is discontinuous at

Answer options
Option 3
Correct Answer
Explanation for 2022: 25 May Shift 1 MAT question 5