Match List-I with List-II, List-I, List-II, Parametric Curve, dy/dx =, (A) x = t, y = t^2, (I) 3/2t, (B) x = t^2, y = t^3, (II) 2t, (C) x = t^3, y = t^2, (III) 1/2t, (D) x = t^2, y = t, (IV) 2/3t, Choose the correct answer from the options given below: Option 1: (A) - (I), (B) - (III), (C) - (II), (D) - (IV) Option 2: (A) - (I), (B) - (II), (C) - (III), (D) - (IV) Option 3: (A) - (II), (B) - (I), (C) - (IV), (D) - (III) Option 4: (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Answer: (A) - (II), (B) - (I), (C) - (IV), (D) - (III). Solution: Use dy/dx = (dy/dt)/(dx/dt). (A) 2t/1 = 2t. (B) 3t^2/2t = 3/2t. (C) 2t/3t^2 = 2/3t. (D) 1/2t.

Calculus

Continuity & Differentiability

Easy

applied

Match List-I with List-II

List-I List-II
Parametric Curve $\dfrac{dy}{dx} =$
(A) $x = t, y = t^2$ (I) $\dfrac{3}{2}t$
(B) $x = t^2, y = t^3$ (II) $2t$
(C) $x = t^3, y = t^2$ (III) $\dfrac{1}{2t}$
(D) $x = t^2, y = t$ (IV) $\dfrac{2}{3t}$

Choose the correct answer from the options given below:

List-I	List-II
Parametric Curve	$\dfrac{dy}{dx} =$
(A) $x = t, y = t^2$	(I) $\dfrac{3}{2}t$
(B) $x = t^2, y = t^3$	(II) $2t$
(C) $x = t^3, y = t^2$	(III) $\dfrac{1}{2t}$
(D) $x = t^2, y = t$	(IV) $\dfrac{2}{3t}$

(A) - (I), (B) - (III), (C) - (II), (D) - (IV)

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (II), (B) - (I), (C) - (IV), (D) - (III)

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

✅ Correct Option: 3

Use $\frac{dy}{dx} = \frac{dy/dt}{dx/dt}$ .

(A) $\frac{2t}{1} = 2t$ .

(B) $\frac{3t^2}{2t} = \frac{3}{2}t$ .

(D) $\frac{1}{2t}$ .

2026: 26 May Shift 2

Let $f(x) = |3-x| + (3+x)$ be a function, then which of the following statements are TRUE?

A. $f(x)$ is continuous at $x=3$

B. $f(x)$ is continuous at $x=-3$

C. $f(x)$ is differentiable at $x=3$

D. $f(x)$ is differentiable at $x=-3$

Choose the correct answer from the options given below:

2026: 18 May Shift 2

For the function $(ex)^y=e^x$ ;

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $y$ is equal to	I. $\dfrac{1-\log_e x}{x(1+\log_e x)^3}$
B. value of $\dfrac{dy}{dx}$	II. $\dfrac{x}{1+\log_e x}$
C. value of $\dfrac{d^2y}{dx^2}$	III. $\dfrac{\log_e x}{(1+\log_e x)^2}$
D. $x^y$ is equal to	IV. $e^{x-y}$

Choose the correct answer from the options given below:

2025: 21 May Shift 1

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

2025: 22 May Shift 2

If $x = e^t$ and $y = e^{2t}$ then $\frac{d^2y}{dx^2} =$

2025: 2 June Shift 1

If $y = \sin^{-1}x$ , then $(1-x^2)\frac{d^2y}{dx^2}$ is equal to

2026: 19 May Shift 1

If $y = 500e^{7x} + 600e^{-7x}$ , then $\frac{d^2y}{dx^2}$ equals :

Solution

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