PYQ Vault

Day 190: CBSE Class 10 Maths

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

  1. Question 1

    Statistics. Asked once: 2025

    17
    Following data shows the marks obtained by 100 students in a class test :
    Marks obtained2029283342384325
    Number of students628241524120
    The median will be the average of which two observations ?

    Tap an option to check your answer.

  2. Question 2

    Surface Areas and Volumes. Asked once: 2026

    25
    1000 small thermocol balls of radius 0⋅50{\cdot}5 cm are kept in a spherical balloon of radius 20 cm. Find the volume of air in the balloon.

  3. Question 3 (case study, 4 parts)

    Triangles. Asked once: 2026

    Carom board is a very popular game. The board is a square of side length 65 cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position P with a striker. The disc, hits the boundary of the board at R and goes straight to pocket at corner C. It is given that PS = 9 cm, PQ = 35 cm, BR=xBR = x, ∠PRQ=α\angle PRQ = \alpha and ∠CRB=θ\angle CRB = \theta. Based on the above information, answer the following questions :
    36 (i)
    Using law of reflection i.e. ∠PRT=∠CRT\angle PRT = \angle CRT, prove that θ=α\theta = \alpha.
    36 (ii)
    Prove that ΔPQR∼ΔCBR\Delta PQR \sim \Delta CBR given that PQ is perpendicular to AB.
    36 (iii) (a)
    Find the value of xx using similarity of triangles.
    36 (iii) (b)
    If Area ΔPQRArea ΔCBR=PQ2CB2\dfrac{\text{Area } \Delta PQR}{\text{Area } \Delta CBR} = \dfrac{PQ^2}{CB^2}, then find the value of xx.

  4. Question 4

    Areas Related to Circles. Asked once: 2026

    27
    Chord AB of a circle with centre O and radius 21 mm subtends an angle of 120∘120^\circ at the centre. Find the perimeters of the shaded region. (Use 3=1.73\sqrt{3} = 1.73)

  5. Question 5

    Arithmetic Progressions. Asked once: 2025

    32 (a)
    An AP consists of ‘n’ terms whose nthn^{\text{th}} term is 4 and the common difference is 2. If the sum of ‘n’ terms of AP is −14-14, then find ‘n’. Also, find the sum of the first 20 terms.