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}

(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 6× in all

6 Apr 2024, Shift 1 · Q25Let $r_k=\frac{\int_0^1\left(1-x^7\right)^k dx}{\int_0^1\left(1-x^7\right)^{k+1}dx}$ , $k \in \mathbb{N}$ . Then the value of…HardNumerical value
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
1 Feb 2024, Shift 2 · Q10If $\int_0^{\frac{\pi}{3}}\cos^4x\,dx=a\pi+b\sqrt{3}$ , where $a$ and $b$ are rational numbers, then $9a+8b$ is equal to :MediumSingle correct
25 Jun 2022, Shift 2 · Q12If $b_n = \int_0^{\frac{\pi}{2}} \frac{\cos^2 nx}{\sin x}\,dx$ , $n \in \mathbb{N}$ , thenHardSingle correct
25 Feb 2021, Shift 2 · Q64If $I_n = \int_{\pi/4}^{\pi/2} \cot^n x \, dx$ , then :HardSingle 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.