PYQ Vault

Day 77: CBSE Class 10 Maths

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

  1. Question 1 (case study, 4 parts)

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

    An arch of a railway bridge, built on Chenab riverbed, is shown in the above diagram. It is a parabolic arch connecting two hills at P and Q. If the parabolic curve is represented by the polynomial p(x)=−0.0025x2−0.025x+136p(x) = -0.0025x^2 - 0.025x + 136. Observe the diagram and based on above information, answer the following questions :
    36 (i)
    Write the co-ordinates of point A.
    36 (ii)
    Find the span of the arch.
    36 (iii) (a)
    Write the zeroes of the polynomial using diagram and verify the relationship between sum of zeroes and polynomials.
    36 (iii) (b)
    Find the values of p(x)p(x) at x=100x = 100 and x=−100x = -100. Are they same ?

  2. Question 2

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

    17
    Which of the following statements is true for a polynomial p(x) of degree 3?

    Tap an option to check your answer.

  3. Question 3

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

    24
    α,β\alpha, \beta are zeroes of the polynomial p(x)=3x2−6x−5p(x) = 3x^2 - 6x - 5. Find the value of 1α2+1β2\dfrac{1}{\alpha^2} + \dfrac{1}{\beta^2}.

  4. Question 4

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

    25
    While shuffling a pack of 52 cards, one card was accidently dropped. Find the probability that the dropped card (i) is not a face card. (ii) is a black king.

  5. Question 5

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

    3
    For any natural number n, 5n5^n ends with the digit :

    Tap an option to check your answer.