PYQ Vault

Day 46: CBSE Class 10 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Polynomials. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    21
    If α\alpha, β\beta are the zeroes of the quadratic polynomial px2+qx+rpx^2 + qx + r, then find the value of α3β+β3α\alpha^3\beta + \beta^3\alpha.

  2. Question 2

    Polynomials. This type asked 3 times: 2023, 2025, 2026. This one: 2025

    21
    If the zeroes of the polynomial x2+ax+bx^2 + ax + b are in the ratio 3:43 : 4, then prove that 12a2=49b12a^2 = 49b.

  3. Question 3 (case study, 4 parts)

    Probability. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :
    37 (i)
    Find the probability that the drawn card is a face card.
    37 (ii)
    Find the probability that the drawn card is either a king or a queen.
    37 (iii) (a)
    Do you think that the probability of getting a queen was higher if none of the cards were dropped ? Justify your answer.
    37 (iii) (b)
    Find the probability that the drawn card is a jack. Compare it with the probability when none of the cards were dropped. In which case is the probability of getting a jack higher ?

  4. Question 4

    Quadratic Equations. This type asked 3 times: 2024, 2025, 2026. This one: 2024

    35 (b)
    The side of a square exceeds the side of another square by 4 cm and the sum of the areas of the two squares is 400 cm2\text{cm}^2. Find the sides of the squares.

  5. Question 5

    Real Numbers. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    3
    For any natural number nn, 6n6^n ends with the digit :

    Tap an option to check your answer.