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Day 620: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2021 Paper 1

    72
    If the tangent to the curve y=x3y=x^{3} at the point P(t,t3)P\left( t,t^{3} \right) meets the curve again at QQ, then the ordinate of the point which divides PQPQ internally in the ratio 1:21:2 is :

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  2. Question 2

    Conic Sections. Asked once: 4 Apr 2024

    164
    Consider a hyperbola HH having centre at the origin and foci on the xx-axis. Let C1C_{1} be the circle touching the hyperbola HH and having the centre at the origin. Let C2C_{2} be the circle touching the hyperbola HH at its vertex and having the centre at one of its foci. If areas (in sq. units) of C1C_{1} and C2C_{2} are 36π36\pi and 4π4\pi, respectively, then the length (in units) of latus rectum of HH is

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  3. Question 3

    Definite Integration. Asked once: 29 Jul 2022

    155
    If [t]\lbrack t\rbrack denotes the greatest integer ≤t\leq t, then the value of ∫01[2x−∣3x2−5x+2∣+1]dx\int_{0}^{1} \left\lbrack 2x -\left| 3x^{2}- 5x + 2 \right|+ 1 \right\rbrack dx is:

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  4. Question 4

    Sequences and Series. Asked once: 26 Jul 2022

    66
    Consider two [G.Ps](http://G.Ps). 2,22,23,…2,2^{2},2^{3},\ldots and 4,42,43,…4,4^{2},4^{3},\ldots of 60 and nn terms respectively. If the geometric mean of all the 60+n60 + n terms is (2)2258(2)^{\frac{225}{8}}, then ∑k=1nk(n−k)\sum_{k = 1}^{n} k(n - k) is equal to:

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  5. Question 5

    Conic Sections. Asked once: 4 Apr 2024

    77
    A square is inscribed in the circle x2+y2−10x−6y+30=0x^{2}+y^{2}- 10x - 6y + 30 = 0. One side of this square is parallel to y=x+3y = x + 3. If (xi,yi)\left( x_{i},y_{i} \right) are the vertices of the square, then ∑(xi2+yi2)\sum\left( x_{i}^{2}+y_{i}^{2} \right) is equal to :

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