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Day 147: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 25 Jul 2022 (same type asked 6 times) See all 6 of this type

    157
    lim⁡n→∞12n(11−12n+11−22n+11−32n+…..+11−2n−12n)\lim_{n \rightarrow \infty} \frac{1}{2^{n}}\left( \frac{1}{\sqrt{1 -\frac{1}{2^{n}}}}+\frac{1}{\sqrt{1 -\frac{2}{2^{n}}}}+\frac{1}{\sqrt{1 -\frac{3}{2^{n}}}}+ \ldots.. +\frac{1}{\sqrt{1 -\frac{2^{n}- 1}{2^{n}}}} \right) is equal to

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  2. Question 2

    Three Dimensional Geometry. Asked once: 24 Jan 2023 (same type asked 6 times) See all 6 of this type

    168
    If the foot of the perpendicular drawn from (1,9,7)(1,9,7) to the line passing through the point (3,2,1)(3,2,1) and parallel to the planes x+2y+z=0x + 2y + z = 0 and 3y−z=33y - z = 3 is (α,β,γ)(\alpha,\beta,\gamma), then α+β+γ\alpha + \beta + \gamma is equal to

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  3. Question 3

    Definite Integration. Asked once: 2021 Paper 19 (same type asked 6 times) See all 6 of this type

    64
    If the value of the integral ∫05x+[x]ex−[x]dx=αe−1+β\int_{0}^{5} \frac{x + \lbrack x\rbrack}{e^{x - \lbrack x\rbrack}}dx =\alpha e^{- 1}+\beta, where α,β∈R,5α+6β=0\alpha,\beta\in R,5\alpha+ 6\beta= 0, and [x]\lbrack x\rbrack denotes the greatest integer less than or equal to xx; then the value of (α+β)2(\alpha+\beta)^{2} is equal to:

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  4. Question 4

    Application of Integrals. Asked once: 21 Jan 2026 S2 (same type asked 5 times) See all 5 of this type

    61
    If the area of the region {(x,y):1−2x≤y≤4−x2\left\{ (x,y):1 - 2x \leq y \leq 4 -x^{2} \right., x≥0,y≥0}x \geq 0,y \geq 0\} is αβ,α,β,∈N,gcd(α,β)=1\frac{\alpha}{\beta},\alpha,\beta, \in N,gcd(\alpha,\beta) = 1, then the value of (α+β)(\alpha + \beta) is :

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  5. Question 5

    Limits and Continuity. Asked once: 26 Jul 2022 (same type asked 5 times) See all 5 of this type

    68
    If f(x)={x+a,x≤0∣x−4∣,x>0f(x) =\left\{ \begin{matrix} x + a, & x \leq 0 \\ |x - 4|, & x > 0 \end{matrix} \right. and
    g(x)={x+1,x<0(x−4)2+b,x≥0g(x) =\left\{ \begin{matrix} x + 1 & ,x < 0 \\ (x - 4)^{2}+ b, & x \geq 0 \end{matrix} \right.
    are continuous on R, then (gof) (2) + (fog) (-2) is equal to:

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