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Day 111: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. This type asked 2 times: 2021 Paper 23, 8 Apr 2024. This one: 8 Apr 2024 See all 2 of this type

    172
    If α=lim⁡x→0+(etan⁡x−extan⁡x−x)\alpha =\lim_{x \rightarrow0^{+}} \left( \frac{e^{\sqrt{\tan x}}-e^{\sqrt{x}}}{\sqrt{\tan x}-\sqrt{x}} \right) and β=lim⁡x→0(1+sin⁡x)12cot⁡x\beta =\lim_{x \rightarrow 0} (1 + \sin x)^{\frac{1}{2}\cot x} are the roots of the quadratic equation ax2+bx−e=0ax^{2}+ bx -\sqrt{e}= 0, then 12 log⁡e(a+b)\log_{e}(a + b) is equal to

  2. Question 2

    Probability. This type asked 2 times: 25 Jan 2023, 8 Apr 2024. This one: 8 Apr 2024 See all 2 of this type

    70
    Let the sum of two positive integers be 24. If the probability, that their product is not less than 34\frac{3}{4} times their greatest positive product, is mn\frac{m}{n}, where gcd(m,n)=1gcd(m,n) = 1, then n−mn-m equals:

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  3. Question 3

    Sequences and Series. This type asked 2 times: 26 Jul 2022, 8 Apr 2024. This one: 8 Apr 2024 See all 2 of this type

    85
    Let the positive integers be written in the form: If the kth k^{\text{th~}} row contains exactly kk numbers for every natural number kk, then the row in which the number 5310 will be, is

  4. Question 4

    Trigonometric Identities. This type asked 2 times: 28 Jun 2022, 8 Apr 2024. This one: 8 Apr 2024 See all 2 of this type

    71
    If sin⁡x=−35\sin x= -\frac{3}{5}, where π<x<3π2\pi<x<\frac{3\pi}{2}, then 80(tan⁡2x−cos⁡x)80\left( \tan^{2}x- \cos x \right) is equal to:

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  5. Question 5

    Differentiation. This type asked 2 times: 24 Jan 2023, 6 Apr 2024. This one: 6 Apr 2024 See all 2 of this type

    61
    If f(x)={x3sin⁡(1x), x≠00, x=0f(x) =\left\{ \begin{matrix} x^{3}\sin\left( \frac{1}{x} \right) & ,\ x \neq 0 \\ 0 & ,\ x = 0 \end{matrix} \right., then

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