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Day 35: JEE Mains Maths

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

  1. Question 1

    Conic Sections. This type asked 4 times: 29 Jan 2025, 2 Apr 2026 S1, 2 Apr 2026 S2, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 4 of this type

    72
    Let the centre of the circle x2+y2+2gx+2fy+25=0x^{2} + y^{2} + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x−y=42x - y = 4. Let the area of an equilateral triangle inscribed in the circle be 27327\sqrt{3}. Then the square of the length of the chord of the circle on the line x=1x = 1 is____\_\_\_\_ .

  2. Question 2

    Conic Sections. This type asked 4 times: 31 Jan 2023, 22 Jan 2025, 2 Apr 2025, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 4 of this type

    63
    Let the eccentricity e of a hyperbola satisfy the equation 6e2−11e+3=06e^{2}- 11e + 3 = 0. If the foci of the hyperbola are (3,5)(3,−4)(3,5)(3, - 4), then the length of its latus rectum is:

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  3. Question 3

    Trigonometric Equations. This type asked 4 times: 2021 Paper 14, 25 Jan 2023, 7 Apr 2025, 5 Apr 2026 S2. This one: 5 Apr 2026 S2 See all 4 of this type

    73
    If S={θ∈[−π,π]:cos⁡θcos⁡5θ2=cos⁡7θcos⁡7θ2}S = \left\{ \theta \in \lbrack - \pi,\pi\rbrack:\cos\theta \cos\frac{5\theta}{2} = \cos7\theta\cos\frac{7\theta}{2} \right\}, then n(S)n(S) is equal to .........

  4. Question 4

    Conic Sections. This type asked 4 times: 2021 Paper 14, 27 Jun 2022, 2 Apr 2026 S1, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    59
    Let a focus of the ellipse E:x2a2+y2b2=1E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 be S(4,0)S(4,0) and its eccentricity be 45\frac{4}{5}. If the point P(3,α)P(3,\alpha) lies on E and O is the origin, then the area of △POS\bigtriangleup POS is equal to :

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  5. Question 5

    Definite Integration. This type asked 4 times: 2021 Paper 26, 29 Jul 2022, 29 Jan 2023, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 4 of this type

    68
    The value of the integral ∫0∞log⁡e(x)x2+4dx\int_{0}^{\infty} \frac{\log_{e}(x)}{x^{2}+ 4}dx is:

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