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Day 632: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 13

    47
    11n>10n+9n11^{n}>10^{n}+9^{n} number of integers satisfy the relation in {1,2,3,…,100}\left\{ 1,2,3,\ldots,100 \right\}

  2. Question 2

    Conic Sections. Asked once: 6 Apr 2023

    90
    Let the tangent to the curve x2+2x−4y+9=0x^{2}+ 2x - 4y + 9 = 0 at the point P(1,3)P(1,3) on it meet the yy-axis at AA. Let the line passing through PP and parallel to the line x−x - 3y=63y = 6 meet the parabola y2=4xy^{2}= 4x at BB. If BB lies on the line 2x−3y=82x - 3y = 8. then (AB)2(AB)^{2} is equal to

  3. Question 3

    Definite Integration. Asked once: 25 Jun 2022

    162
    If bn=∫0π2cos⁡2nxsin⁡xdx,n∈Nb_{n}=\int_{0}^{\frac{\pi}{2}} \frac{\cos^{2}nx}{\sin x}dx,n \in N, then

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  4. Question 4

    Sequences and Series. Asked once: 2021 Paper 9

    73
    If α,β\alpha,\beta are natural numbers such that 100α−199β=(100)(100)+(99)(101)+(98)(102)100^{\alpha}- 199\beta = (100)(100) + (99)(101) + (98)(102) +…..+(1)(199)+ \ldots.. + (1)(199), then the slope of the line passing through (α,β)(\alpha,\beta) and origin is :

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  5. Question 5

    Conic Sections. Asked once: 6 Apr 2023

    85
    Let the point ( p,p+1)p,p + 1) lie inside the region E={(x,y):3−x≤y≤9−x2,0≤x≤3}E =\left\{ (x,y):3 - x \leq y \leq\sqrt{9 -x^{2}},0 \leq x \leq 3 \right\} If the set of all values of pp is the interval (a,b)(a,b). then b2+b−a2b^{2}+ b -a^{2} is equal to