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JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 13 April 2023, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

The value of

\dfrac{e^{-\frac{\pi}{4}}+\int_0^{\frac{\pi}{4}}e^{-x}\tan^{50}x\,dx}{\int_0^{\frac{\pi}{4}}e^{-x}\left(\tan^{49}x+\tan^{51}x\right)dx}

is

(1) $25$
(2) $49$
(3) $50$ Official answer
(4) $51$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Reduction Formulae in Definite Integrals

Same idea in other shifts

Asked 2× in all

8 Apr 2024, Shift 1 · Q11The value of $k\in\mathbb{N}$ for which the integral $I_n=\int_0^1(1-x^k)^n dx$ , $n\in\mathbb{N}$ , satisfies $147I_{20}=148I_{21}$ isHardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.