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Day 349: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 8 (same type asked 6 times) See all 6 of this type

    62
    If the integral ∫010[sin⁡2πx]ex−[x]dx=αe−1+βe−12+γ\int_{0}^{10} \frac{\lbrack \sin2\pi x\rbrack}{e^{x- \lbrack x\rbrack}}dx=\alpha e^{- 1}+\beta e^{-\frac{1}{2}}+\gamma, where α,β,γ\alpha,\beta,\gamma are integers and [x]\lbrack x\rbrack denotes the greatest integer less than or equal to xx, then the value of α+β+γ\alpha+\beta+\gamma is equal to:

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  2. Question 2

    Application of Integrals. Asked once: 2021 Paper 17 (same type asked 5 times) See all 5 of this type

    69
    The area of the region bounded by y−x=2y-x= 2 and x2=yx^{2}= y is equal to :-

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  3. Question 3

    Limits and Continuity. Asked once: 2021 Paper 6 (same type asked 5 times) See all 5 of this type

    85
    Let f:R→Rf:R \rightarrow R and g:R→Rg:R \rightarrow R be defined as f(x)={x+a,x<0∣x−1∣,x≥0f(x) =\left\{ \begin{matrix} x+a, & x< 0 \\ |x- 1|, & x\geq 0 \end{matrix} \right. and
    g(x)={x+1,x<0(x−1)2+b,x≥0g(x) =\left\{ \begin{matrix} x+ 1, & x< 0 \\ (x- 1)^{2}+b, & x\geq 0 \end{matrix} \right.
    where a,ba,b are non-negative real numbers. If (gof)(x) is continuous for all x∈Rx\in R, then a+ba+b is equal to

  4. Question 4

    Relations and Functions. Asked once: 29 Jan 2023 (same type asked 5 times) See all 5 of this type

    79
    Let f:R→Rf:R \rightarrow R be a function such that f(x)=x2+2x+1x2+1f(x) =\frac{x^{2}+ 2x + 1}{x^{2}+ 1}. Then

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  5. Question 5

    Three Dimensional Geometry. Asked once: 31 Jan 2023 (same type asked 5 times) See all 5 of this type

    88
    Let the line L:x−12=y+1−1=z−31L:\frac{x - 1}{2}=\frac{y + 1}{- 1}=\frac{z - 3}{1} intersect the plane 2x+y+3z=162x + y + 3z = 16 at the point PP. Let the point QQ be the foot of perpendicular from the point R(1,−1,−3)R(1, - 1, - 3) on the line LL. If α\alpha is the area of triangle PQRPQR, then α2\alpha^{2} is equal to