Let a function f(x)=+(^2+5+6)|x|+|x|^4, where , and are real number. Then the function f(x) is differentiable at x=0 if Option 1: =-2 or =-3 or both Option 2: =4,=4 Option 3: =0 Option 4: =3,=6,=4

The answer is '=-2 or =-3 or both'. View full solution:

CUET Mathematics - Let a function f(x)=+(^2+5+6)|x|+|x|^4, where , and are real number. Then the function f(x) is differentiable at x=0 if | PYQs + Solutions

CUET Mathematics 2026 22nd May Shift 1

Calculus

Medium

core

$\beta=-2$ or $\beta=-3$ or both

$\alpha=4,\beta=4$

$\gamma=0$

$\alpha=3,\beta=6,\gamma=4$

✅ Correct Option: 1

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30 May Shift 3

Which of the following statements are correct ?

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(B) If $f : R \to R$ then $f(x) = |x|$ is continuous everywhere but not differentiable at $x = 0$ .

(D) Let $f : R \to R$ then $f(x) = |x - 1| + |x - 2|$ is continuous everywhere but not differentiable at exactly 2 points.

(E) If $f : R \to R$ then $f(x) = \cot x$ is continuous everywhere.

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22 May Shift 3

Match List - I with List - II.

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(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

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26th May Shift 2

If $y = x^3\log(3x^2+6)$ , then $\dfrac{dy}{dx} =$