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Day 106: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. This type asked 2 times: 23 Jan 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 2 of this type

    63
    Considering the principal values of the inverse trigonometric functions, sin⁡−1(32x+121−x2),−12<x<12\sin^{- 1}\left( \frac{\sqrt{3}}{2}x+\frac{1}{2}\sqrt{1 -x^{2}} \right), -\frac{1}{2}<x<\frac{1}{\sqrt{2}}, is equal to.

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  2. Question 2

    Probability. This type asked 2 times: 2021 Paper 5, 4 Apr 2025. This one: 4 Apr 2025 See all 2 of this type

    148
    A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is 1150\frac{11}{50}, the n is equal to.

  3. Question 3

    Relations and Functions. This type asked 2 times: 29 Jan 2024, 4 Apr 2025. This one: 4 Apr 2025 See all 2 of this type

    51
    Let f, g:(1,∞)→Rf,\text{ }g:(1,\infty) \rightarrow\mathbb{R} be defined as f(x)=2x+35x+2f(x) =\frac{2x+ 3}{5x+ 2} and g(x)=2−3x1−xg(x) =\frac{2 - 3x}{1 -x}. If the range of the function f∘g:[2,4]→Rf\circ g:\lbrack 2,4\rbrack \rightarrow\mathbb{R} is [α,β]\lbrack\alpha,\beta\rbrack, then 1β−α\frac{1}{\beta-\alpha} is equal to.

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  4. Question 4

    Application of Derivatives. This type asked 2 times: 25 Jun 2022, 3 Apr 2025. This one: 3 Apr 2025 See all 2 of this type

    126
    Let f:R→Rf:R\rightarrow R be a function defined by f(x)=∣∣x+2∣−2∣x∣∣f(x) = \left| |x+ 2| - 2|x| \right|. If mm is the number of points of local minima and nn is the number of points of local maxima of ff, then m+nm+n is.

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  5. Question 5

    Probability. This type asked 2 times: 29 Jan 2023, 3 Apr 2025. This one: 3 Apr 2025 See all 2 of this type

    71
    All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number nn be denoted by WnW_{n}. Let the probability P(Wn)P\left( W_{n} \right) of choosing the word WnW_{n} satisfy P(Wn)=2P(Wn−1),n>1P\left( W_{n} \right) = 2P\left( W_{n - 1} \right),n > 1.If P(CDBEA)=2α2β−1,α,β∈NP(CDBEA) = \frac{2^{\alpha}}{2^{\beta} - 1},\alpha,\beta \in \mathbb{N}, then α+β\alpha + \beta is equal to: