JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 2 April 2025, Shift 1, Maths Q14

Question 14 of 75 in this shift, Maths question 14 of 25, Section A.

Let

f:\mathbf{R}\to\mathbf{R}

be a twice differentiable function such that

(\sin x\cos y)(f(2x+2y)-f(2x-2y))=(\cos x\sin y)(f(2x+2y)+f(2x-2y))

, for all

x, y\in\mathbf{R}

. If

f'(0)=\frac{1}{2}

, then the value of

24f''\left(\frac{5\pi}{3}\right)

is :

(1)3
(2) $-3$ Official answer
(3)2
(4) $-2$

Official answer

Option 2

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Differentiability via Functional Equations

Same idea in other shifts

Asked 10× in all

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26 Jul 2022, Shift 1 · Q1Let $f : \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function such that $f\,(3x) - f\,(x) = x$ . If $f\,(8) = 7$ , then $f\,(14)$ is…MediumSingle correct
26 Jun 2022, Shift 2 · Q21Let $f : \mathbb{R} \rightarrow \mathbb{R}$ satisfy $f(x + y) = 2^x f(y) + 4^y f(x)$ , $\forall x, y \in \mathbb{R}$ . If $f(2) = 3$ , then…HardNumerical value
4 Aug 2021, Shift 2 · Q67Let $f:\mathbb{R}\to\mathbb{R}$ be twice differentiable and satisfy $f(x+y)=f(x)+f(y)$ . If $f'(0)=1$ , then which of the following is true?EasySingle correct
26 Feb 2021, Shift 1 · Q74Let $f$ be any function defined on $\mathbf{R}$ and let it satisfy the condition :…MediumSingle correct
18 Mar 2021, Shift 2 · Q90Let $f:\mathbb{R}\to\mathbb{R}$ satisfy the equation $f(x+y)=f(x)\cdot f(y)$ for all $x, y\in\mathbb{R}$ and $f(x)\neq0$ for any…MediumNumerical value
4 Sep 2020, Shift 1 · Q73Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y) = f(x) + f(y) + xy^2 + x^2y$ , for all real $x$ and $y$ . If…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.