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Day 604: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 1 Feb 2023

    89
    Let a1=8,a2,a3,…,ana_{1}= 8,a_{2},a_{3},\ldots,a_{n} be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is

  2. Question 2

    Straight Lines. Asked once: 2021 Paper 22

    71
    If pp and qq are the lengths of the perpendiculars from the origin on the lines, xcsc⁡α−ysec⁡α=kcot⁡2αx\csc\alpha- y\sec\alpha= k\cot2\alpha and xsin⁡α+ycos⁡α=ksin⁡2αx\sin\alpha+ y\cos\alpha= k\sin2\alpha respectively, then k2k^{2} is equal to :

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  3. Question 3

    Application of Derivatives. Asked once: 2021 Paper 26

    90
    Let aa be an integer such that all the real roots of the polynomial 2x5+5x4+10x3+10x2+10x+102x^{5}+ 5x^{4}+ 10x^{3}+ 10x^{2}+ 10x+ 10 lie in the interval (a,a+1)(a,a+ 1). Then, ∣a∣|a| is equal to

  4. Question 4

    Complex Numbers. Asked once: 2021 Paper 15

    52
    Equation of circle Re(z2)+2(img(z))2+2Re(z)=0Re\left( z^{2} \right)+ 2(img(z))^{2}+ 2Re(z) = 0 where z=x+iyz=x+iy. A line passes through the vertex of parabola x2−6x+y+13=0x^{2}- 6x+y+ 13 = 0 and center of circle, then the yy intercept of the line is

  5. Question 5

    Conic Sections. Asked once: 9 Apr 2024

    88
    Let the centre of a circle, passing through the point (0,0),(1,0)(0,0),(1,0) and touching the circle x2+y2=9x^{2}+y^{2}= 9, be (h,k)(h,k). Then for all possible values of the coordinates of the centre (h,k),4( h2+k2)(h,k),4\left( {\text{ }h}^{2}+k^{2} \right) is equal to