PYQ Vault
EbooksTutor

Day 160: JEE Mains Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: 7 Apr 2025 (same type asked 4 times) See all 4 of this type

    134
    The number of solutions of the equation cos⁡2θcos⁡θ2+cos⁡5θ2=2cos⁡35θ2\cos2\theta \cos\frac{\theta}{2}+ \cos\frac{5\theta}{2}= 2\cos^{3}\frac{5\theta}{2} in [−π2,π2]\left\lbrack -\frac{\pi}{2},\frac{\pi}{2} \right\rbrack is :

    Tap an option to check your answer.

  2. Question 2

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

    48
    If x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 ellipse passes through (32,1),e=13\left( \sqrt{\frac{3}{2}},1 \right),e=\frac{1}{\sqrt{3}}. Circle centred at one of the focus and radius 23\frac{2}{\sqrt{3}}. These ellipse &\& circle intersect at two points. Find square of the distance between the two points.

    Tap an option to check your answer.

  3. Question 3

    Definite Integration. Asked once: 29 Jan 2023 (same type asked 4 times) See all 4 of this type

    159
    The value of the integral ∫1/22tan⁡−1xxdx\int_{1/2}^{2} \frac{\tan^{- 1}x}{x}dx is equal to

    Tap an option to check your answer.

  4. Question 4

    Sequences and Series. Asked once: 2 Apr 2026 S1 (same type asked 4 times) See all 4 of this type

    72
    If ∑k=1nak=6n3\sum_{k = 1}^{n} a_{k} = 6n^{3}, then ∑k=16(ak+1−ak36)2\sum_{k = 1}^{6} \left( \frac{a_{k + 1} - a_{k}}{36} \right)^{2} is equal to ____\_\_\_\_ .

  5. Question 5

    Straight Lines. Asked once: 28 Jan 2026 S1 (same type asked 4 times) See all 4 of this type

    56
    Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x+22y=4x+ 2\sqrt{2}y= 4. If the co-ordinates of the vertex A are (α,β)(\alpha,\beta), then the greatest integer less than or equal to ∣α+2β∣|\alpha+\sqrt{2}\beta| is

    Tap an option to check your answer.