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Day 241: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 26 Jul 2022 (same type asked 6 times) See all 6 of this type

    79
    tan⁡(2tan⁡−115+sec⁡−152+2tan⁡−118)\tan\left( 2\tan^{- 1}\frac{1}{5}+\sec^{- 1}\frac{\sqrt{5}}{2}+ 2\tan^{- 1}\frac{1}{8} \right) is equal to:

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  2. Question 2

    Complex Numbers. Asked once: 4 Apr 2025 (same type asked 6 times) See all 6 of this type

    73
    Let A={z∈C:∣z−2−i∣=3}A = \{ z \in C:|z - 2 - i| = 3\}, B={z∈C:Re(z−iz)=2}B = \{ z \in C:Re(z - iz) = 2\} and S=A∩BS = A \cap B. Then ∑z∈S∣z∣2\sum_{z \in S}^{} |z|^{2} is equal to .

  3. Question 3

    Sequences and Series. Asked once: 30 Jan 2023 (same type asked 6 times) See all 6 of this type

    84
    Let ∑n=0∞n3((2n)!)+(2n−1)(n!)(n!)((2n)!)=ae+be+c\sum_{n = 0}^{\infty} \frac{n^{3}((2n)!) + (2n - 1)(n!)}{(n!)((2n)!)}= ae +\frac{b}{e}+ c, where a,b,c∈Za,b,c \in Z and e=∑n=0∞1n!e =\sum_{n = 0}^{\infty} \frac{1}{n!} Then a2−b+ca^{2}- b + c is equal to

  4. Question 4

    Matrices. Asked once: 22 Jan 2025 (same type asked 6 times) See all 6 of this type

    129
    For a 3×33 \times 3 matrix M , let trace (M)(M) denote the sum of all the diagonal elements of M . Let A be a 3×33 \times 3 matrix such that ∣A∣=12|A| =\frac{1}{2} and trace (A)=3(A) = 3. If B=adj(adj(2A))B = adj(adj(2A)), then the value of ∣B∣+trace(B)|B| + trace(B) equals:

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  5. Question 5

    Permutations and Combinations. Asked once: 31 Jan 2024 (same type asked 6 times) See all 6 of this type

    151
    The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

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