If x = 2at, y = at^2, where 'a' is a constant, then (d^2 y)/dx^2 at x = 2 is : Option 1: 1 Option 2: 2a Option 3: 1/4 Option 4: 1/2a

Answer: 1/2a. Solution: From parametric form: dx/dt = 2a and dy/dt = 2at, so dy/dx = t. Then (d^2 y)/dx^2 = (d t)/dx = dt/dx = 1/2a. This value is independent of x.

Applied Mathematics

Calculus

Medium

If $x = 2at, y = at^2$ , where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :

$\frac{1}{4}$

$\frac{1}{2a}$

✅ Correct Option: 4

From parametric form: $\frac{dx}{dt} = 2a$ and $\frac{dy}{dt} = 2at$ , so $\frac{dy}{dx} = t$ . Then $\frac{d^2 y}{dx^2} = \frac{d t}{dx} = \frac{dt}{dx} = \frac{1}{2a}$ . This value is independent of x.

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If the fixed cost is ₹1000, then the cost of producing 200 units will be :

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Match List - I with List - II.

List - I (Functions)	List - II (Maximum value)
(A) $f(x) = -x^2, x \in (-\infty, \infty)$	(I) 8
(B) $f(x) = -x^2 + 1, x \in (-\infty, \infty)$	(II) 7
(C) $f(x) = x + 1, x \in [0, 6]$	(III) 1
(D) $f(x) = x^3, x \in [0, 2]$	(IV) 0

Choose the correct answer from the options given below :

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If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$

If x=2at,y=at2x = 2at, y = at^2x=2at,y=at2, where 'a' is a constant, then d2ydx2\frac{d^2 y}{dx^2}dx2d2y​ at x=2x = 2x=2 is :

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CUET Mathematics Past Year Questions (Topic-Wise)

If $x = 2at, y = at^2$ , where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :