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Day 24: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. This type asked 5 times: 25 Jun 2022, 30 Jan 2023, 31 Jan 2024, 9 Apr 2024, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 5 of this type

    52
    The sum of the coefficients of x499x^{499} and x500x^{500} in (1+x)1000+x(1+x)999+x2(1+x)998+……..+x1000(1 +x)^{1000}+x(1 +x)^{999}+x^{2}(1 +x)^{998}+ \ldots\ldots.. +x^{1000} is

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  2. Question 2

    Conic Sections. This type asked 5 times: 25 Jul 2022, 31 Jan 2024, 9 Apr 2024, 21 Jan 2026 S1, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 5 of this type

    60
    Let the ellipse E:x2144+y2169=1E:\frac{x^{2}}{144}+\frac{y^{2}}{169}= 1 and the hyperbola H:x216−y2λ2=−1H:\frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}= - 1 have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H , then the value of 24(e+L)24(e + L) is :

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  3. Question 3

    Definite Integration. This type asked 5 times: 2021 Paper 7, 2021 Paper 12, 25 Jul 2022, 8 Apr 2023, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 5 of this type

    63
    Let [ • ] denote the greatest integer function. Then ∫−π2π2(12(3+[x])3+[sin⁡x]+[cos⁡x])dx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{12(3 + \lbrack x\rbrack)}{3 + \lbrack \sin x\rbrack + \lbrack \cos x\rbrack} \right)dx is equal to:

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  4. Question 4

    Probability. This type asked 5 times: 2021 Paper 24, 4 Apr 2024, 7 Apr 2025, 21 Jan 2026 S2, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 5 of this type

    54
    The probability distribution of a random variable X is given below :
    XX4k4k307k\frac{30}{7}k327k\frac{32}{7}k347k\frac{34}{7}k367k\frac{36}{7}k387k\frac{38}{7}k407k\frac{40}{7}k6k6k
    P(X)P(X)215\frac{2}{15}115\frac{1}{15}215\frac{2}{15}15\frac{1}{5}115\frac{1}{15}215\frac{2}{15}15\frac{1}{5}115\frac{1}{15}
    If E(X)=26315E(X) =\frac{263}{15}, then P(X<20)P(X< 20) is equal to :

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  5. Question 5

    Vector Algebra. This type asked 5 times: 27 Jan 2024, 29 Jan 2024, 28 Jan 2025, 28 Jan 2026 S1, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 5 of this type

    67
    Let P be a point in the plane of the vector AB→=3i^+j^−k^\overrightarrow{AB}= 3\widehat{i}+\widehat{j}-\widehat{k} and AC→=i^−j^+3k^\overrightarrow{AC}=\widehat{i}-\widehat{j}+ 3\widehat{k} such that PP is equidistant from the lines AB and AC . If ∣AP→∣=52|\overrightarrow{AP}| =\frac{\sqrt{5}}{2}, then the area of the triangle ABPABP is :

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