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Day 210: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 2021 Paper 23 (same type asked 2 times) See all 2 of this type

    68
    If α=lim⁡x→π/4tan⁡3x−tan⁡xcos⁡(x+π4)\alpha=\lim_{x\rightarrow\pi/4} \frac{\tan^{3}x- \tan x}{\cos\left( x+\frac{\pi}{4} \right)} and β=lim⁡x→0(cos⁡x)cot⁡x\beta=\lim_{x\rightarrow 0} (\cos x)^{\cot x} are the roots of the equation, ax2+bx−4=0ax^{2}+bx- 4 = 0, then the ordered pair (a,b)(a,b) is:

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  2. Question 2

    Probability. Asked once: 25 Jan 2023 (same type asked 2 times) See all 2 of this type

    73
    Let MM be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space S={x∈Z:x(66−x)≥59M}S =\left\{ x\in Z:x(66 - x) \geq\frac{5}{9}M \right\} and the event A={x∈S:x\mathbf{A = \{ x \in S:x} is a multiple of 3}\}. Then P(A)P(A) is equal to

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  3. Question 3

    Sequences and Series. Asked once: 26 Jul 2022 (same type asked 2 times) See all 2 of this type

    83
    The series of positive multiples of 3 is divided into sets: {3},{6,9,12},{15,18,21,24,27},…\mathbf{\{ 3\},\{ 6,9,12\},\{ 15,18,21,24,27\},\ldots} Then the sum of the elements in the 11th 11^{\text{th~}} set is equal to

  4. Question 4

    Trigonometric Identities. Asked once: 28 Jun 2022 (same type asked 2 times) See all 2 of this type

    170
    If cot⁡α=1\cot\alpha= 1 and sec⁡β=−53\sec\beta= -\frac{5}{3}, where π<α<3π2\pi<\alpha<\frac{3\pi}{2} and π2<β<π\frac{\pi}{2}<\beta<\pi, then the value of tan⁡(α+β)\tan(\alpha+\beta) and the quadrant in which α+β\alpha+\beta lies, respectively are

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  5. Question 5

    Differentiation. Asked once: 24 Jan 2023 (same type asked 2 times) See all 2 of this type

    78
    Let f(x)={x2sin⁡(1x),x≠00,x=0f(x)=\begin{cases} x^{2}\sin\left(\frac{1}{x}\right), & x\neq 0 \\ 0, & x=0 \end{cases} Then at x=0x=0

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