PYQ Vault
EbooksTutor

Day 27: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. This type asked 5 times: 2021 Paper 6, 2021 Paper 8, 4 Apr 2024, 3 Apr 2025, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 5 of this type

    75
    Let ABC be a triangle. Consider four points p1,p2p_{1},p_{2}, p3,p4p_{3},p_{4} on the side AB , five points p5,p6,p7,p8,p9p_{5},p_{6},p_{7},p_{8},p_{9} on the side BC and four points p10,p11,p12,p13p_{10},p_{11},p_{12},p_{13} on the side AC . None of these points is a vertex of the triangle ABC . Then the total number of pentagons, that can be formed by taking all the vertices from the points p1,p2,….p13p_{1},p_{2},\ldots.p_{13}, is ____\_\_\_\_ .

  2. Question 2

    Trigonometric Identities. This type asked 5 times: 2021 Paper 22, 25 Jun 2022, 27 Jun 2022, 8 Apr 2024, 22 Jan 2026 S1. This one: 22 Jan 2026 S1 See all 5 of this type

    74
    If cos⁡248∘−sin⁡212∘sin⁡224∘−sin⁡26∘=α+β52\frac{\cos^{2}48^{\circ} - \sin^{2}12^{\circ}}{\sin^{2}24^{\circ} - \sin^{2}6^{\circ}} = \frac{\alpha + \beta\sqrt{5}}{2}, where α,β∈N\alpha,\beta \in \mathbb{N}, then α+β\alpha + \beta is equal to ____\_\_\_\_ .

  3. Question 3

    Application of Integrals. This type asked 5 times: 25 Jul 2022, 27 Jan 2024, 29 Jan 2024, 28 Jan 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 5 of this type

    132
    If the area of the region {(x,y):1+x2≤y≤min⁡{x+7,11−3x}}\left\{ (x,y):1 +x^{2}\leq y \leq \min\{ x + 7,11 - 3x\} \right\} is A , then 3 A is equal to.

    Tap an option to check your answer.

  4. Question 4

    Complex Numbers. This type asked 5 times: 2021 Paper 20, 2021 Paper 23, 10 Apr 2023, 9 Apr 2024, 7 Apr 2025. This one: 7 Apr 2025 See all 5 of this type

    61
    Among the statements (S1): The set {z∈C−{−i}:∣z∣=1 and z−iz+i is purely real}\{z\in\mathbb{C}-\{-i\}:|z|=1\text{ and }\frac{z-i}{z+i}\text{ is purely real}\} contains exactly two elements, and (S2): The set {z∈C−{−1}:∣z∣=1 and z−1z+1 is purely imaginary}\{z\in\mathbb{C}-\{-1\}:|z|=1\text{ and }\frac{z-1}{z+1}\text{ is purely imaginary}\} contains infinitely many elements.

    Tap an option to check your answer.

  5. Question 5

    Conic Sections. This type asked 5 times: 27 Jun 2022, 28 Jun 2022, 27 Jul 2022, 24 Jan 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 5 of this type

    55
    Let PP be the parabola, whose focus is (−2,1)\left( - 2,1 \right) and directrix is 2x+y+2x+y+ 2=02 = 0. Then the sum of the ordinates of the points on P , whose abscissa is -2 , is.

    Tap an option to check your answer.