PYQ Vault

Day 106: CBSE Class 10 Maths

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

  1. Question 1

    Polynomials. Asked once: 2025 (same type asked 3 times)

    24 (b)
    If ‘α\alpha’ and ‘β\beta’ are the zeroes of the polynomial p(y)=y2−5y+3p(y) = y^2 - 5y + 3, then find the value of α4β3+α3β4\alpha^4\beta^3 + \alpha^3\beta^4.

  2. Question 2

    Probability. Asked once: 2025 (same type asked 3 times)

    22
    All the face cards are removed from the pack of 52 cards and a card is drawn at random from the remaining cards. Find the probability that the card so drawn is (i) a spade. (ii) not an ace.

  3. Question 3

    Real Numbers. Asked once: 2025 (same type asked 3 times)

    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) : Unit digit of 3n3^n cannot be an even number for any natural number n. Reason (R) : 2 is not a prime factor of 3n3^n for any natural number n.

    Tap an option to check your answer.

  4. Question 4

    Real Numbers. Asked once: 2025 (same type asked 3 times)

    26 (b)
    Let p, q and r be three distinct prime numbers. Check whether p⋅q⋅r+qp \cdot q \cdot r + q is a composite number or not. Further, give an example for 3 distinct primes p, q, r such that (i) p⋅q⋅r+1p \cdot q \cdot r + 1 is a composite number. (ii) p⋅q⋅r+1p \cdot q \cdot r + 1 is a prime number.

  5. Question 5

    Real Numbers. Asked once: 2026 (same type asked 3 times)

    31
    The dimensions of a window are 156 cm ×\times 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.