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Day 594: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 26 Jun 2022

    156
    Consider a cuboid of sides 2x,4x2x,4x and 5x5x and a closed hemisphere of radius rr. If the sum of their surface areas is a constant kk, then the ratio x:rx:r, for which the sum of their volumes is maximum, is:

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  2. Question 2

    Application of Integrals. Asked once: 2021 Paper 10

    79
    The area bounded by the curve 4y2=x2(4−x)(x−2)4y^{2}=x^{2}(4 -x)(x- 2) is equal to :

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  3. Question 3

    Complex Numbers. Asked once: 25 Jun 2022

    80
    Let a circle CC in complex plane pass through the points z1=3+4i,z2=4+3iz_{1}= 3 + 4i,z_{2}= 4 + 3i and z3=5iz_{3}= 5i. If z(≠z1)z\left( \neq z_{1} \right) is a point on CC such that the line through zz and z1z_{1} is perpendicular to the line through z2z_{2} and z3z_{3}, then arg(z)arg(z) is equal to :

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  4. Question 4

    Conic Sections. Asked once: 24 Jan 2025

    149
    Let H1:x2a2−y2b2=1H_{1}:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1 and H2:−x2A2+y2B2=1H_{2}: -\frac{x^{2}}{A^{2}}+\frac{y^{2}}{B^{2}}= 1 be two hyperbolas having length of latus rectums 15215\sqrt{2} and 12512\sqrt{5} respectively. Let their eccentricities be e1=52e_{1}=\sqrt{\frac{5}{2}} and e2e_{2} respectively. If the product of the lengths of their transverse axes is 10010100\sqrt{10}, then 25e2225e_{2}^{2} is equal to _____\_\_\_\_\_

  5. Question 5

    Definite Integration. Asked once: 13 Apr 2023

    84
    Let for x∈R,S0(x)=xx \in R,S_{0}(x) = x,
    Sk(x)=Ckx+k∫0xSk−1(t)dt, where C0=1,Ck=1−∫01Sk−1(x)dx,k=1,2,3….. Then \begin{matrix} & S_{k}(x) =C_{k}x + k\int_{0}^{x} S_{k - 1}(t)dt\text{, where~} \\ & C_{0}= 1,C_{k}= 1 -\int_{0}^{1} S_{k - 1}(x)dx,k = 1,2,3\ldots..\text{~Then~} \end{matrix}
    S2(3)+6C3S_{2}(3) + 6C_{3} is equal to