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Day 305: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 29 Jun 2022 (same type asked 6 times) See all 6 of this type

    86
    50tan⁡(3tan⁡−1(12)+2cos⁡−1(15))+50\tan\left( 3\tan^{- 1}\left( \frac{1}{2} \right)+ 2\cos^{- 1}\left( \frac{1}{\sqrt{5}} \right) \right)+ 42tan⁡(12tan⁡−1(22))4\sqrt{2}\tan\left( \frac{1}{2}\tan^{- 1}(2\sqrt{2}) \right) is equal to

  2. Question 2

    Complex Numbers. Asked once: 1 Feb 2024 (same type asked 6 times) See all 6 of this type

    66
    Let S={z∈C:∣z−1∣=1\mathbf{S = \{ z \in C:|z - 1| = 1} and (2−1)(z+zˉ)−i(z−zˉ)=22}(\sqrt{2}- 1)(z +\bar{z}) - i(z -\bar{z}) = 2\sqrt{2}\}. Let z1, z2z_{1},\ z_{2} ∈S\in S be such that ∣z1∣=max⁡z∈S∣z∣\left| z_{1} \right|=\max_{z \in S} |z| and ∣z2∣=min⁡z∈S∣z∣\left| z_{2} \right|=\min_{z \in S} |z|. Then ∣2z1−z2∣2\left| \sqrt{2}z_{1}-z_{2} \right|^{2} equals:

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  3. Question 3

    Sequences and Series. Asked once: 2021 Paper 24 (same type asked 6 times) See all 6 of this type

    75
    Let Sn=1⋅(n−1)+2⋅(n−2)+3⋅(n−3)+….+S_{n}= 1 \cdot (n- 1) + 2 \cdot (n- 2) + 3 \cdot (n- 3) + \ldots. + (n−1)⋅1,n≥4(n - 1) \cdot 1,n \geq 4. The sum ∑n=4∞(2Snn!−1(n−2)!)\sum_{n= 4}^{\infty} \left( \frac{2S_{n}}{n!}-\frac{1}{(n- 2)!} \right) is equal to:

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  4. Question 4

    Matrices. Asked once: 10 Apr 2023 (same type asked 6 times) See all 6 of this type

    156
    If A=15!6!7![5!6!7!6!7!8!7!8!9!]A =\frac{1}{5!6!7!}\begin{bmatrix} 5! & 6! & 7! \\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}, then ∣adj(adj(2A))∣|adj(adj(2A))| is equal to:

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  5. Question 5

    Permutations and Combinations. Asked once: 11 Apr 2023 (same type asked 6 times) See all 6 of this type

    66
    The number of triplets (x,y,z)(x,y,z). where x,y,zx,y,z are distinct non negative integers satisfying x+y+z=15x + y + z = 15, is

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