If y = x_e(x/2+x), then x^3d^2y/dx^2 is equal to: Option 1: x/2+x Option 2: 2x/2+x Option 3: (2x/2+x)^2 Option 4: (x/2+x)^2

The answer is '(2x/2+x)^2'. View full solution:

CUET Mathematics - If y = x_e(x/2+x), then x^3d^2y/dx^2 is equal to: | PYQs + Solutions

CUET Mathematics 2026 21st May Shift 2

Calculus

Hard

core

$\dfrac{x}{2+x}$

$\dfrac{2x}{2+x}$

$\left(\dfrac{2x}{2+x}\right)^2$

$\left(\dfrac{x}{2+x}\right)^2$

✅ Correct Option: 3

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	LIST-I Curve $y = f(x)$ , where $f(x)$ is		LIST-II Nature / derivative / value of $y = f(x)$
A.	$x\vert x \vert$	I.	$y'$ is 2 for all $x \in R^+$ (set of positive real numbers)
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Match List - I with List - II.

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(A)	$x = 2at^2, y = at^4$	(I)	Inverse trignometric function
(B)	$f(x) = (2x + 3)^3$	(II)	Implicit function
(C)	$xy + y^2 = \tan(x + y)$	(III)	Parametric function
(D)	$y = \tan^{-1}\left(\frac{3x - x^3}{1 - 3x^2}\right), -\frac{1}{\sqrt{3}} < x < \frac{1}{\sqrt{3}}$	(IV)	Composite function

Choose the correct answer from the options given below :