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Day 102: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. This type asked 2 times: 30 Jan 2023, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 2 of this type

    51
    Given below two statements : Statement I: 2513+2013+813+31325^{13} + 20^{13} + 8^{13} + 3^{13} is divisible by 7. Statement II : The integral part of (7+43)25(7 + 4\sqrt{3})^{25} is an odd number. In the light of the above statements, choose the correct answer from the options given below:

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  2. Question 2

    Conic Sections. This type asked 2 times: 4 Apr 2025, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 2 of this type

    59
    An ellipse has its center at (1,−2)(1, - 2), one focus at (3,−2)(3, - 2) and one vertex at (5,-2). Then the length of its latus rectum is :

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  3. Question 3

    Indefinite Integration. This type asked 2 times: 28 Jan 2025, 28 Jan 2026 S2. This one: 28 Jan 2026 S2 See all 2 of this type

    69
    Let f(x)=∫ dxx(23)+2x(12)f(x) =\int_{}^{}\ \frac{dx}{x^{\left( \frac{2}{3} \right)}+ 2x^{\left( \frac{1}{2} \right)}} be such that f(0)=−26+24log⁡e(2)f(0) = - 26 + 24\log_{e}(2). If f(1)=a+blog⁡e(3)f(1) =a+b\log_{e}(3), where a,b∈Za,b\in Z, then a+ba + b is equal to:

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  4. Question 4

    Conic Sections. This type asked 2 times: 1 Feb 2024, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 2 of this type

    72
    For some θ∈(0,π2)\theta \in \left( 0,\frac{\pi}{2} \right), let the eccentricity and the length of the latus rectum of the hyperbola x2−y2sec⁡2θ=8x^{2} - y^{2}\sec^{2}\theta = 8 be e1e_{1} and l1\mathcal{l}_{1}, respectively, and let the eccentricity and the length of the latus rectum of the ellipse x2sec⁡2θ+y2=6x^{2}\sec^{2}\theta + y^{2} = 6 be e2e_{2} and l2\mathcal{l}_{2}, respectively. If e12=e22(sec⁡2θ+1)e_{1}^{2} = e_{2}^{2}\left( \sec^{2}\theta + 1 \right), then (l1l2e1e2)tan⁡2θ\left( \frac{\mathcal{l}_{1}\mathcal{l}_{2}}{e_{1}e_{2}} \right)\tan^{2}\theta is equal to ____\_\_\_\_ .

  5. Question 5

    Permutations and Combinations. This type asked 2 times: 25 Jun 2022, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 2 of this type

    57
    Let S={1,2,3,4,5,6,7,8,9}S\mathbf{= \{ 1,2,3,4,5,6,7,8,9\}}. Let xx be the number of 9 -digit numbers formed using the digits of the set S such that only one digit is repeated, and it is repeated exactly twice. Let yy be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,

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