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Day 322: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. Asked once: 29 Jun 2022 (same type asked 4 times) See all 4 of this type

    180
    Let f(x)f(x) and g(x)g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x))=8x2−2xf(g(x)) = 8x^{2}- 2x, and g(f(x))=4x2+6x+1g(f(x)) = 4x^{2}+ 6x + 1, then the value of f(2)+g(2)f(2) + g(2) is

  2. Question 2

    Permutations and Combinations. Asked once: 8 Apr 2023 (same type asked 4 times) See all 4 of this type

    84
    The largest natural number nn such that 3n3^{n} divides 66! Is

  3. Question 3

    Relations and Functions. Asked once: 2021 Paper 2 (same type asked 4 times) See all 4 of this type

    83
    If a+α=1,b+β=2a+\alpha= 1,b+\beta= 2 and af(x)+αf(1x)=bx+βx,x≠0af(x) +\alpha f\left( \frac{1}{x} \right)=bx+\frac{\beta}{x},x\neq 0, then the value of the expression
    f(x)+f(1x)x+1x is \frac{f(x) +f\left( \frac{1}{x} \right)}{x+\frac{1}{x}}\text{~is~}

  4. Question 4

    Three Dimensional Geometry. Asked once: 2021 Paper 3 (same type asked 4 times) See all 4 of this type

    62
    Let α\alpha be the angle between the lines whose direction cosines satisfy the equations l+m−n=0l + m - n = 0 and l2+m2−n2=0l^{2}+m^{2}-n^{2}= 0. Then the value of sin⁡4α+cos⁡4α\sin^{4}\alpha +\cos^{4}\alpha is:

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  5. Question 5

    Conic Sections. Asked once: 24 Jan 2025 (same type asked 4 times) See all 4 of this type

    60
    Let the product of the focal distances of the point (3,12)\left( \sqrt{3},\frac{1}{2} \right) on the ellipse x2a2+y2 b2=1,(a>b)\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,(a > b), be 74\frac{7}{4}. Then the absolute difference of the eccentricities of two such ellipses is

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