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Day 552: JEE Mains Maths

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

  1. Question 1

    Application of Integrals. Asked once: 15 Apr 2023

    88
    If the area bounded by the curve 2y2=3x2y^{2}= 3x, lines x+y=3,y=0x+y= 3,y= 0 and outside the circle (x−3)2+y2=2(x- 3)^{2}+y^{2}= 2 is AA, then 4(π+4A)4(\pi+ 4A) is equal to

  2. Question 2

    Binomial Theorem. Asked once: 29 Jun 2022

    177
    Let the coefficients of x−1x^{- 1} and x−3x^{- 3} in the expansion of (2x15−1x15)15,x>0\left( 2x^{\frac{1}{5}}-\frac{1}{x^{\frac{1}{5}}} \right)^{15},x > 0, be mm and nn respectively. If rr is a positive integer such mn2= 15Cr⋅2rmn^{2}=\ ^{15}C_{r}\cdot2^{r}, then the value of rr is equal to

  3. Question 3

    Complex Numbers. Asked once: 6 Apr 2023

    154
    Let a≠ba \neq b be two non-zero real numbers. Then the number of elements in the set X={z∈C:Re(az2+bz)=aX =\left\{ z \in C:Re\left( az^{2}+ bz \right)= a \right. and  Re(bz2+az)=b}\left. \ Re\left( bz^{2}+ az \right)= b \right\} is equal to

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  4. Question 4

    Conic Sections. Asked once: 4 Apr 2025

    74
    Let CC be the circle x2+(y−1)2=2,E1x^{2} + (y - 1)^{2} = 2,E_{1} and E2E_{2} be two ellipses whose centres lie at the origin and major axes lie on xx-axis and yy-axis respectively. Let the straight line x+y=3x + y = 3 touch the curves C , E1E_{1} and E2E_{2} at P(x1,y1),Q(x2,y2)P\left( x_{1},y_{1} \right),Q\left( x_{2},y_{2} \right) and R(x3,y3)R\left( x_{3},y_{3} \right) respectively. Given that PP is the mid-point of the line segment QR and PQ=223PQ = \frac{2\sqrt{2}}{3}, the value of 9(x1y1+x2y2+x3y3)9\left( x_{1}y_{1} + x_{2}y_{2} + x_{3}y_{3} \right) is equal to .

  5. Question 5

    Definite Integration. Asked once: 5 Apr 2024

    69
    The integral ∫0π4136sin⁡x3sin⁡x+5cos⁡xdx\int_{0}^{\frac{\pi}{4}} \frac{136\sin x}{3\sin x + 5\cos x}dx is equal to:

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