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Day 257: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 27 Jul 2022 (same type asked 4 times) See all 4 of this type

    81
    For k∈Rk \in R, let the solutions of the equation
    cos⁡(sin⁡−1(xcot⁡(tan⁡−1(cos⁡(sin⁡−1x)))))=k,0<∣x∣<12\cos\left( \sin^{- 1}\left( x\cot\left( \tan^{- 1}\left( \cos\left( \sin^{- 1}x \right) \right) \right) \right) \right)= k,0 < |x| <\frac{1}{\sqrt{2}}
    be α\alpha and β\beta, where the inverse trigonometric functions take only principal values. If the solutions of the equation x2−bx−5=0x^{2}- bx - 5 = 0 are 1α2+1β2\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}} and αβ\frac{\alpha}{\beta}, then bk2\frac{b}{k^{2}} is equal to

  2. Question 2

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

    73
    Let Sk=1+2+…..+KKS_{k}=\frac{1 + 2 + \ldots.. + K}{K} and ∑j=1nSj2=nA(Bn2+Cn+D)\sum_{j = 1}^{n} S_{j}^{2}=\frac{n}{A}\left( Bn^{2}+ Cn + D \right), where A,B,C,D∈NA,B,C,D \in N and AA has least value. Then

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  3. Question 3

    Conic Sections. Asked once: 2 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    74
    Let a circle C have its center in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line x+y=1x + y = 1 is 14\sqrt{14}, then the square of the radius of C is ____\_\_\_\_ .

  4. Question 4

    Conic Sections. Asked once: 22 Jan 2025 (same type asked 4 times) See all 4 of this type

    70
    Let the foci of a hyperbola be (1,14)(1,14) and (1,−12)(1, - 12). If it passes through the point (1,6)(1,6), then the length of its latus-rectum is :

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  5. Question 5

    Trigonometric Equations. Asked once: 2021 Paper 14 (same type asked 4 times) See all 4 of this type

    50
    The sum of all roots of sin⁡x+sin⁡2x+sin⁡3x+sin⁡4x=0\sin x+ \sin2x+ \sin3x+ \sin4x= 0 lying in [0,2π]\lbrack 0,2\pi\rbrack is

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