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Day 205: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 23 Jan 2025 (same type asked 2 times) See all 2 of this type

    64
    If π2≤x≤3π4\frac{\pi}{2}\leq x\leq\frac{3\pi}{4}, then cos⁡−1(1213cos⁡x+513sin⁡x)\cos^{- 1}\left( \frac{12}{13}\cos x+\frac{5}{13}\sin x \right) is equal to

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  2. Question 2

    Probability. Asked once: 2021 Paper 5 (same type asked 2 times) See all 2 of this type

    75
    A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is:

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  3. Question 3

    Relations and Functions. Asked once: 29 Jan 2024 (same type asked 2 times) See all 2 of this type

    63
    If f(x)={2+2x,−1≤x<01−x3,0≤x≤3;g(x)={−x,−3≤x≤0x,0<x≤1 f(x) =\left\{ \begin{matrix} 2 + 2x, - 1 \leq x < 0 \\ 1 -\frac{x}{3},0 \leq x \leq 3 \end{matrix};g(x) =\left\{ \begin{matrix} - x, - 3 \leq x \leq 0 \\ x,0 < x \leq 1 \end{matrix} \right.\ \right., then range of (fog(x))(fog(x)) is

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  4. Question 4

    Application of Derivatives. Asked once: 25 Jun 2022 (same type asked 2 times) See all 2 of this type

    178
    Let f(x)=∣(x−1)(x2−2x−3)∣+x−3,x∈Rf(x) =\left| (x- 1)\left( x^{2}- 2x- 3 \right) \right|+x- 3,x\in R. If mm and MM are respectively the number of points of local minimum and local maximum of ff in the interval (0,4)(0,4), then m+Mm + M is equal to

  5. Question 5

    Probability. Asked once: 29 Jan 2023 (same type asked 2 times) See all 2 of this type

    169
    Let S={w1,w2,…….}S =\left\{ w_{1},w_{2},\ldots\ldots. \right\} be the sample space associated to a random experiment. Let (wn)=\left( w_{n} \right)= P(wn−1)2,n≥2\frac{P\left( w_{n - 1} \right)}{2},n \geq 2. Let A={2k+3l:k,l∈N}\mathbf{A = \{ 2k + 3l:k,l \in N\}} and B={wn:n∈A}B =\left\{ w_{n}:n \in A \right\}. Then P(B)P(B) is equal to

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