PYQ Vault

Day 1: CBSE Class 10 Maths

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

  1. Question 1

    Introduction to Trigonometry. Asked 4 times: 2023*, 2024, 2025*, 2026 (* = numbers or wording changed that year)

    28
    Prove that : sin⁡θ−cos⁡θ+1sin⁡θ+cos⁡θ−1=1sec⁡θ−tan⁡θ\dfrac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \dfrac{1}{\sec\theta - \tan\theta}

  2. Question 2

    Polynomials. Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)

    5
    If α\alpha and β\beta are two zeroes of a polynomial f(x)=px2−2x+3pf(x) = px^2 - 2x + 3p and α+β=αβ\alpha + \beta = \alpha\beta, then value of p is :

    Tap an option to check your answer.

  3. Question 3

    Probability. Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)

    29
    Two different coins are tossed simultaneously. What is the probability of getting : (i) at least one head ? (ii) at most one tail ? (iii) a head and a tail ?

  4. Question 4

    Probability. Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)

    9
    Three coins are tossed together. The probability of getting exactly one head, is :

    Tap an option to check your answer.

  5. Question 5

    Real Numbers. Asked 4 times: 2023*, 2024*, 2025*, 2026 (* = numbers or wording changed that year)

    24 (a)
    Prove that 2+352 + 3\sqrt{5} is an irrational number given that 5\sqrt{5} is irrational number.