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Day 609: JEE Mains Maths

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

  1. Question 1

    Straight Lines. Asked once: 2021 Paper 17

    61
    The point P(a,b)P(a,b) undergoes the following three transformations successively: (a) reflection about the line y=xy=x. (b) translation through 2 units along the positive direction of xx-axis. (c) rotation through angle π4\frac{\pi}{4} about the origin in the anti-clockwise direction. If the co-ordinates of the final position of the point PP are (−12,72)\left( -\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}} \right), then the value of 2a+b2a+b is equal to:

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  2. Question 2

    Application of Derivatives. Asked once: 2021 Paper 19

    82
    Let aa and bb respectively be the points of local maximum and local minimum of the function f(x)=2x3−3x2−12xf(x) = 2x^{3}- 3x^{2}- 12x. If AA is the total area of the region bounded by y=f(x)y=f(x), the xx-axis and the lines x=ax = a and x=bx = b, then 4 A4\text{ }A is equal to

  3. Question 3

    Complex Numbers. Asked once: 2021 Paper 10

    81
    If f(x)f(x) and g(x)g(x) are two polynomials such that the polynomial P(x)=f(x3)+x g(x3)P(x) = f\left( x^{3} \right) + x\,g\left( x^{3} \right) is divisible by x2+x+1x^{2}+x+1, then P(1)P(1) is equal to

  4. Question 4

    Conic Sections. Asked once: 9 Apr 2024

    74
    Let a circle passing through (2,0)(2,0) have its centre at the point (h, k). Let ( xc,ycx_{c},y_{c} ) be the point of intersection of the lines 3x+5y=13x+ 5y= 1 and (2+c)x+(2 +c)x+ 5c2y=15c^{2}y= 1. If h=lim⁡c→1xch=\lim_{c\rightarrow 1} x_{c} and k=lim⁡c→1yck=\lim_{c\rightarrow 1} y_{c}, then the equation of the circle is:

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  5. Question 5

    Definite Integration. Asked once: 31 Jan 2023

    80
    Let α∈(0,1)\alpha \in (0,1) and β=log⁡e(1−α)\beta =\log_{e}(1 - \alpha). Let Pn(x)=x+x22+x33+⋯+xnn,x∈(0,1)P_{n}(x) = x +\frac{x^{2}}{2}+\frac{x^{3}}{3}+ \cdots +\frac{x^{n}}{n},x \in (0,1). Then the integral ∫0αt501−tdt\int_{0}^{\alpha} \frac{t^{50}}{1 - t}dt is equal to

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