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Day 119: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Inverse Trigonometric Functions. This type asked 2 times: 25 Jan 2023, 1 Feb 2023. This one: 1 Feb 2023 See all 2 of this type

    166
    Let S={x∈R:0<x<1S =\left\{ x \in \mathbb{R}:0 < x < 1 \right. and  2tan⁡−1(1−x1+x)=cos⁡−1(1−x21+x2)}\left. \ 2\tan^{- 1}\left( \frac{1 - x}{1 + x} \right)=\cos^{- 1}\left( \frac{1 -x^{2}}{1 +x^{2}} \right) \right\}. If n(S)n(S) denotes the number of elements in SS then:

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  2. Question 2

    Definite Integration. This type asked 2 times: 2021 Paper 22, 31 Jan 2023. This one: 31 Jan 2023 See all 2 of this type

    169
    If ϕ(x)=1x∫π4x(42sin⁡t−3ϕ′(t))dt,x>0\phi(x) =\frac{1}{\sqrt{x}}\int_{\frac{\pi}{4}}^{x} \left( 4\sqrt{2}\sin t - 3\phi^{'}(t) \right)dt,x > 0, then ϕ′(π4)\phi^{'}\left( \frac{\pi}{4} \right) is equal to :

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  3. Question 3

    Inverse Trigonometric Functions. This type asked 2 times: 2021 Paper 11, 31 Jan 2023. This one: 31 Jan 2023 See all 2 of this type

    68
    Let y=f(x)y = f(x) represent a parabola with focus (−12,0)\left( -\frac{1}{2},0 \right) and directrix y=−12y = -\frac{1}{2}. Then S={x∈R:tan⁡−1(f(x))+sin⁡−1(f(x)+1)=π2}S =\left\{ x\in R:\tan^{- 1}(\sqrt{f(x)}) +\sin^{- 1}(\sqrt{f(x) + 1}) =\frac{\pi}{2} \right\} :

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  4. Question 4

    Permutations and Combinations. This type asked 2 times: 29 Jan 2023, 31 Jan 2023. This one: 29 Jan 2023 See all 2 of this type

    90
    If all the six digit numbers x1x2x3x4x5x6x_{1}x_{2}x_{3}x_{4}x_{5}x_{6} with 0<x1<x2<x3<x4<x5<x60 <x_{1}<x_{2}<x_{3}<x_{4}<x_{5}<x_{6} are arranged in the increasing order, then the sum of the digits in the 72th 72^{\text{th~}} number is

  5. Question 5

    Application of Derivatives. This type asked 2 times: 2021 Paper 5, 30 Jan 2023. This one: 30 Jan 2023 See all 2 of this type

    68
    The number of points on the curve y=54x5−135x4−70x3+180x2+210xy = 54x^{5}- 135x^{4}- 70x^{3}+ 180x^{2}+ 210x at which the normal lines are parallel to x+90y+2=0x + 90y + 2 = 0 is :

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