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Day 282: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 2021 Paper 20 (same type asked 3 times) See all 3 of this type

    76
    If α,β\alpha,\beta are the distinct roots of x2+bx+c=0x^{2}+bx+c= 0, then lim⁡x→βe2(x2+bx+c)−1−2(x2+bx+c)(x−β)2\lim_{x\rightarrow\beta} \frac{e^{2\left( x^{2}+bx+c \right)}- 1 - 2\left( x^{2}+bx+c \right)}{(x-\beta)^{2}} is equal to:

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  2. Question 2

    Relations and Functions. Asked once: 2021 Paper 1 (same type asked 3 times) See all 3 of this type

    66
    Let f:R→Rf:R\rightarrow R be defined as f(x)=2x−1f(x) = 2x- 1 and g:R−{1}→Rg:R\mathbf{- \{ 1\} \rightarrow}R be defined as g(x)=x−12x−1g(x) =\frac{x-\frac{1}{2}}{x- 1}. Then the composition function f(g(x))f(g(x)) is:

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  3. Question 3

    Sequences and Series. Asked once: 31 Jan 2023 (same type asked 3 times) See all 3 of this type

    89
    Let a1,a2,…,ana_{1},a_{2},\ldots,a_{n} be in A.P. If a5=2a7a_{5}= 2a_{7} and a11=18a_{11}= 18, then 12(1a10+a11+1a11+a12+⋯+1a17+a18)12\left( \frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+ \cdots +\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}} \right) is equal to

  4. Question 4

    Differential Equations. Asked once: 27 Jan 2024 (same type asked 3 times) See all 3 of this type

    83
    If the solution of the differential equation (2x+3y−2)dx+(4x+6y−7)dy=0,y(0)=3(2x+ 3y- 2)dx+ (4x+ 6y- 7)dy= 0,y(0) = 3, is αx+βy+3log⁡e∣2x+3y−γ∣=6\alpha x+\beta y+ 3\log_{e}|2x+ 3y-\gamma| = 6, then α+2β+3γ\alpha+ 2\beta+ 3\gamma is equal to

  5. Question 5

    Limits and Continuity. Asked once: 2021 Paper 17 (same type asked 3 times) See all 3 of this type

    71
    The value of lim⁡x→0(x1−sin⁡x8−1+sin⁡x8)\lim_{x\rightarrow 0} \left( \frac{x}{\sqrt[8]{1 - \sin x}-\sqrt[8]{1 + \sin x}} \right) is equal to:

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