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JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 16 March 2021, Shift 2, Maths Q79

Question 79 of 90 in this shift, Maths question 19 of 30, Section A.

Let

f:S\to S

where

S=(0,\infty)

be a twice differentiable function such that

f(x+1)=xf(x)

. If

g:S\to\mathbf R

be defined as

g(x)=\log_e f(x)

, then the value of

|g''(5)-g''(1)|

is equal to :

(1) $\frac{205}{144}$ Official answer
(2) $\frac{197}{144}$
(3) $\frac{187}{144}$
(4)1

Official answer

Option 1

NTA final key.

Chapter: Application of Derivatives
Topic: Chain Rule
Idea tested: Differentiating Functional Equations

Same idea in other shifts

Asked 2× in all

13 Apr 2023, Shift 1 · Q1For the differentiable function $f : \mathbb{R}-\{0\} \rightarrow \mathbb{R}$ , let $3f(x)+2f\left(\frac{1}{x}\right)=\frac{1}{x}-10$ , then…MediumSingle correct

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.