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Day 155: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 29 Jan 2024 (same type asked 5 times) See all 5 of this type

    64
    A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

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  2. Question 2

    Relations and Functions. Asked once: 31 Jan 2024 (same type asked 5 times) See all 5 of this type

    89
    Let A={1,2,3,4}\mathbf{A = \{ 1,2,3,4\}} and R={(1,2),(2,3),(1,4)}\mathbf{R = \{(1,2),(2,3),(1,4)\}} be a relation on AA. Let SS be the equivalence relation on A such that R⊂SR \subset S and the number of elements in SS is nn. Then, the minimum value of nn is

  3. Question 3

    Application of Derivatives. Asked once: 26 Jul 2022 (same type asked 5 times) See all 5 of this type

    156
    If the maximum value of aa, for which the function fa(x)=tan⁡−12x−3ax+7f_{a}(x) =\tan^{- 1}2x - 3ax + 7 is non-decreasing in (−π6,π6)\left( -\frac{\pi}{6},\frac{\pi}{6} \right), is aˉ\bar{a}, then faˉ(π8)f_{\bar{a}}\left( \frac{\pi}{8} \right) is equal to

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  4. Question 4

    Complex Numbers. Asked once: 27 Jul 2022 (same type asked 5 times) See all 5 of this type

    152
    Let SS be the set of all (α,β),π<α,β<2π(\alpha,\beta),\pi < \alpha,\beta < 2\pi, for which the complex number 1−isinα1+2isinα\frac{1 - isin\alpha}{1 + 2isin\alpha} is purely imaginary and 1+icosβ1−2icosβ\frac{1 + icos\beta}{1 - 2icos\beta} is purely real. Let Zαβ=sin⁡2α+icos2β,(α,β)∈SZ_{\alpha\beta}= \sin2\alpha + icos2\beta,(\alpha,\beta) \in S. Then ∑(α,β)∈S(iZαβ+1iZˉαβ)\sum_{(\alpha,\beta) \in S} \left( iZ_{\alpha\beta}+\frac{1}{i{\bar{Z}}_{\alpha\beta}} \right) is equal to:

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  5. Question 5

    Binomial Theorem. Asked once: 11 Apr 2023 (same type asked 5 times) See all 5 of this type

    166
    The sum of the coefficients of three consecutive terms in the binomial expansion of (1+x)n+2(1 + x)^{n + 2}, which are in the ratio 1:3:51:3:5, is equal to

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