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Day 583: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 26 Jun 2022

    81
    The sum of the cubes of all the roots of the equation x4−3x3−2x2+3x+1=10x^{4}- 3x^{3}- 2x^{2}+ 3x+ 1 = 10 is

  2. Question 2

    Relations and Functions. Asked once: 25 Jun 2022

    87
    Let f:R→Rf:R \rightarrow R be a function defined by f(x)=(2(1−x252)(2+x25))150f(x) =\left( 2\left( 1 -\frac{x^{25}}{2} \right)\left( 2 +x^{25} \right) \right)^{\frac{1}{50}}. If the function g(x)=f(f(f(x)))+f(f(x))g(x) = f(f(f(x))) + f(f(x)), the the greatest integer less than or equal to g(1)g(1) is

  3. Question 3

    Sequences and Series. Asked once: 29 Jan 2024

    61
    If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

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  4. Question 4

    Straight Lines. Asked once: 29 Jul 2022

    73
    Let the circumcentre of a triangle with vertices A(a,3),B(b,5)A(a,3),B(b,5) and C(a,b),ab>0C(a,b),ab > 0 be P(1,1)P(1,1). If the line APAP intersects the line BCBC at the point Q(k1,k2)Q\left( k_{1},k_{2} \right), then k1+k2k_{1}+k_{2} is equal to:

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  5. Question 5

    Three Dimensional Geometry. Asked once: 2021 Paper 6

    64
    If (x,y,z)(x,y,z) be an arbitrary point lying on a plane PP which passes through the point (42,0,0)(42,0,0), (0,42,0)(0,42,0) and (0,0,42)(0,0,42), then the value of expression
    3+x−11(y−19)2(z−12)2+y−19(x−11)2(z−12)23 +\frac{x- 11}{(y- 19)^{2}(z- 12)^{2}}+\frac{y- 19}{(x- 11)^{2}(z- 12)^{2}}
    +z−12(x−11)2(y−19)2−x+y+z14(x−11)(y−19)(z−12)+\frac{z - 12}{(x - 11)^{2}(y - 19)^{2}}-\frac{x + y + z}{14(x - 11)(y - 19)(z - 12)}

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