PYQ Vault

Day 37: CBSE Class 10 Maths

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

  1. Question 1

    Introduction to Trigonometry. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    21 (a)
    Prove that : tan⁡θ1+tan⁡2θ+cot⁡θ1+cot⁡2θ=2sin⁡θcos⁡θ\dfrac{\tan\theta}{1 + \tan^2\theta} + \dfrac{\cot\theta}{1 + \cot^2\theta} = 2\sin\theta\cos\theta.

  2. Question 2

    Introduction to Trigonometry. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    28 (A)
    If x=h+acos⁡θx = h + a\cos\theta, y=k+bsin⁡θy = k + b\sin\theta, then prove that : (x−ha)2+(y−kb)2=1\left(\dfrac{x - h}{a}\right)^2 + \left(\dfrac{y - k}{b}\right)^2 = 1

  3. Question 3

    Introduction to Trigonometry. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : tan⁡2θ\tan 2\theta is not defined at θ=45∘\theta = 45^\circ. Reason (R) : sin⁡90∘≠cos⁡90∘\sin 90^\circ \neq \cos 90^\circ.

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  4. Question 4

    Pair of Linear Equations in Two Variables. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    8
    The value of k for which the system of linear equations x2+y3=5\dfrac{x}{2} + \dfrac{y}{3} = 5 and 2x+ky=72x + ky = 7 is inconsistent, is

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  5. Question 5

    Pair of Linear Equations in Two Variables. This type asked 4 times: 2023, 2024, 2025, 2026. This one: 2026

    3
    The pair of linear equations 3x2+5y3=7\dfrac{3x}{2} + \dfrac{5y}{3} = 7 and 9x+10y=149x + 10y = 14, is :

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