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Day 82: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked 2 times: 4 Apr 2024*, 24 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    66
    For some n≠10n \neq 10, let the coefficients of the 5th ,6th 5^{\text{th~}},6^{\text{th~}} and 7th 7^{\text{th~}} terms in the binomial expansion of (1+x)n+4(1 + x)^{n + 4} be in A.P. Then the largest coefficient in the expansion of (1+x)n+4(1 + x)^{n + 4} is :

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  2. Question 2

    Conic Sections. Asked 2 times: 27 Jun 2022*, 24 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    145
    If the equation of the parabola with vertex V(32,3)V\left( \frac{3}{2},3 \right) and the directrix x+2y=0x + 2y = 0 is αx2+βy2−γxy−30x−60y+225=0\alpha x^{2}+ \beta y^{2}- \gamma xy - 30x - 60y + 225 = 0, then α+β+γ\alpha + \beta + \gamma is equal to:

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  3. Question 3

    Permutations and Combinations. Asked 2 times: 4 Apr 2024*, 24 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    141
    Group A consists of 7 boys and 3 girls, while group BB consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group AA and the remaining 3 from group BB, is equal to:

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  4. Question 4

    Complex Numbers. Asked 2 times: 11 Apr 2023*, 24 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    56
    If α\alpha and β\beta are the roots of the equation 2z2−3z−2i=02z^{2}- 3z - 2i = 0, where i=−1i =\sqrt{- 1}, then 16. Re(α19+β19+α11+β11α15+β15)⋅Im(α19+β19+α11+β11α15+β15)Re\left( \frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}} \right)\cdot Im\left( \frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}} \right) is equal to

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  5. Question 5

    Vector Algebra. Asked 2 times: 10 Apr 2023*, 23 Jan 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    57
    Let the arc AC of a circle subtend a right angle at the centre O . If the point B on the arcACarcAC, divides the arcACarcAC such that  length of arcAB length of arcBC=15\frac{\text{~length of~}arcAB}{\text{~length of~}arcBC}=\frac{1}{5}, and OC→=αOA→+βOB→\overrightarrow{OC}= \alpha\overrightarrow{OA}+ \beta\overrightarrow{OB}, then α+2(3−1)β\alpha +\sqrt{2}(\sqrt{3}- 1)\beta is equal to

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