PYQ Vault

Day 8: CBSE Class 10 Maths

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

  1. Question 1

    Introduction to Trigonometry. Asked 3 times: 2023, 2024*, 2025 (* = numbers or wording changed that year)

    28 (b)
    Prove that : (1cos⁡A−cos⁡A)(1sin⁡A−sin⁡A)=1tan⁡A+cot⁡A\left(\dfrac{1}{\cos A} - \cos A\right)\left(\dfrac{1}{\sin A} - \sin A\right) = \dfrac{1}{\tan A + \cot A}

  2. Question 2

    Introduction to Trigonometry. Asked 3 times: 2023, 2024, 2025* (* = numbers or wording changed that year)

    30 (a)
    Prove that : cos⁡θ−2cos⁡3θsin⁡θ−2sin⁡3θ+cot⁡θ=0\dfrac{\cos\theta - 2\cos^3\theta}{\sin\theta - 2\sin^3\theta} + \cot\theta = 0.

  3. Question 3

    Quadratic Equations. Asked 3 times: 2022*, 2024*, 2025 (* = numbers or wording changed that year)

    35 (a)
    A two-digit number is such that the product of its digits is 12. When 36 is added to this number, the digits interchange their places. Find the number.

  4. Question 4

    Triangles. Asked 3 times: 2023, 2024, 2025

    34 (b)
    Sides AB and BC and median AD of triangle ABC are respectively proportional to sides PQ and QR and median PM of ΔPQR\Delta PQR. Show that ΔABC∼ΔPQR\Delta ABC \sim \Delta PQR.

  5. Question 5

    Triangles. Asked 3 times: 2023*, 2024, 2025 (* = numbers or wording changed that year)

    34 (a)
    In the given figure, PA, QB and RC are perpendicular to AC. If PA = x units, QB = y units and RC = z units, prove that 1x+1z=1y\dfrac{1}{x} + \dfrac{1}{z} = \dfrac{1}{y}.