CBSE Class 10 Mathematics 2026 — Set 4

Questions in this 2026 Mathematics paper (Set 4)

All 43 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   If the quadratic equation 9x² + 8kx + 16 = 0 has real and equal roots, then the value of k is

   • (a) 3
   • (b) –3
   • (c) –4
   • (d) 3/2
2. 2.
   It is given that △ABC ~ △EDF. Which of the following is not true ?

   • (a) Perimeter of △ABC / Perimeter of △EDF = AB/ED
   • (b) AB/ED = AC/EF
   • (c) ∠A = ∠D, ∠C = ∠F
   • (d) (AB + BC)/AC = (DE + DF)/EF
3. 3.
   The nth term of an A.P. is √2 n + 1. Its common difference is

   • (a) √2
   • (b) √2 n
   • (c) 1
   • (d) √2 + 1
4. 4.
   If PQ and PR are tangents to the circle with centre O and radius 4 cm such that ∠QPR = 90º, then the length OP is

   • (a) 4 cm
   • (b) 4√2 cm
   • (c) 8 cm
   • (d) 2√2 cm
5. 5.
   Observe the graph of polynomial p(x). Number of zeroes of p(x) is

   • (a) 5
   • (b) 4
   • (c) 6
   • (d) 3
6. 6.
   In the given figure, DE || BC. If AD/DB = 1/3 and AC = 6 cm, then length AE is

   • (a) 1.5 cm
   • (b) 1 cm
   • (c) 2 cm
   • (d) 3 cm
7. 7.
   In the given figure, a circle is centred at (1, 2). The diameter of the circle is

   • (a) 4
   • (b) 2√2
   • (c) √5
   • (d) 2√5
8. 8.
   The value of k for which the system of linear equations x/2 – y/3 = 5 and 2x + ky = 7 is inconsistent, is

   • (a) 3/4
   • (b) 4/3
   • (c) 1/3
   • (d) 3
9. 9.
   A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is

   • (a) 77/4 cm²
   • (b) 77 cm²
   • (c) 154 cm²
   • (d) 77/8 cm²
10. 10.
    Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is

    • (a) 2/9
    • (b) 7/36
    • (c) 1/4
    • (d) 2/3
11. 11.
    When sin A = 1/3, the value of cot A is

    • (a) 2√2/3
    • (b) 2√2
    • (c) 1/(2√2)
    • (d) √3
12. 12.
    (1 – tan²A)/(1 – cot²A) equals to :

    • (a) tan²A
    • (b) –1
    • (c) – tan²A
    • (d) cot²A
13. 13.
    Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is

    • (a) 2πr³
    • (b) 3πr³
    • (c) 5πr³
    • (d) 4πr³
14. 14.
    PQ is tangent to a circle with centre O. If ∠POR = 65º, then m∠PTR is

    • (a) 65º
    • (b) 58.5º
    • (c) 57.5º
    • (d) 45º
15. 15.
    The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ) is

    • (a) √(a² + b²)
    • (b) a² – b²
    • (c) √(a² – b²)
    • (d) a² + b²
16. 16.
    An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is r/2, then h : 2r equals

    • (a) 1 : 8
    • (b) 1 : 2
    • (c) 1 : 1
    • (d) 2 : 1
17. 17.
    Arc PQ subtends an angle θ at the centre of the circle with radius 6.3 cm. If PQ = 11 cm, then the value of θ is

    • (a) 10º
    • (b) 60º
    • (c) 45º
    • (d) 100º
18. 18.
    Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

    • (a) 34
    • (b) 43
    • (c) 38.5
    • (d) 41.5
19. 19.
    Assertion (A) : If probability of happening of an event is 0.2p, p > 0, then p can't be more than 5. Reason (R) : P(E̅) = 1 – P(E) for an event E. Options: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. (a) Both A and R are true and R is the…
20. 20.
    Assertion (A) : (√3 + √5) is an irrational number. Reason (R) : Sum of the any two irrational numbers is always irrational. Options: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true, but R is not the correct explanation of A. (C) A is true, but R is false. (D) A is false, but R is true. (a) Both A and R are true and R is the correct explanation of A (b)…
21. 21.
    Verify that roots of the quadratic equation (p – q)x² + (q – r)x + (r – p) = 0 are equal when q + r = 2p.
22. 22.
    D is a point on the side BC of △ABC such that ∠CAB = ∠CDA. Show that CA² = CB · CD.
23. 23.
    Prove that : √[(1 + sin A)/(1 – sin A)] = sec A + tan A
24. 24.
    Prove that 2 + 3√5 is an irrational number given that √5 is irrational number.
25. 25.
    α and β are the zeroes of the polynomial 5x² – 16x – 10. Find the value of α/β + β/α.
26. 26.
    In a class test, Veer scored 6 more than twice as many marks as Kevin scored. If one of them had scored 4 more marks, their total score would have been 40. Find the marks obtained by Veer and Kevin.
27. 27.
    Chord AB of a circle with centre O and radius 21 mm subtends an angle of 120º at the centre. Find the perimeters of the shaded region. (Use √3 = 1.73)
28. 28.
    Prove that : (sin θ – cos θ + 1)/(sin θ + cos θ – 1) = 1/(sec θ – tan θ)
29. 29.
    To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by a semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are 14 m × 25 m × 16 m.
30. 30.
    A bag contains 30 balls out of which 'm' number of balls are blue in colour.

    • (i) Find the probability that a ball drawn at random from the bag is not blue.
    • (ii) If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 5/4 times the probability of drawing a blue ball in the first case. Find the value of m.
31. 31.
    Find the greatest number less than 10,000 which is exactly divisible by 48, 60 and 65.
32. 32.
    A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.
33. 33.
    In the given figure, TP and TQ are tangents to a circle with centre M, touching another circle with centre N at A and B respectively. It is given that MQ = 13 cm, NB = 8 cm, BQ = 35 cm and TP = 80 cm.

    • (i) Name the quadrilateral MQBN.
    • (ii) Is MN parallel to PA ? Justify your answer.
    • (iii) Find length TB.
    • (iv) Find length MN.
34. 34.
    A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30º. From the bottom of the same building, the angle of elevation of kite is 45º. Find the length of the string and height of roof from the ground. (Use √3 = 1.73)
35. 35.
    The median of the following data is 50 and sum of all frequencies is 90 : Class: 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90; Frequency: p, 15, 25, 20, q, 8, 10. Find the values of p and q.
36. 36.
    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 = x, ∠PRQ = θ and ∠CRB = ϕ. Using law of reflection i.e. ∠PRT = ∠CRT, prove that θ = ϕ.
37. 37.
    (Continued from carom-board case study) Prove that △PQR ~ △CBR given that PQ is perpendicular to AB.
38. 38.
    (Continued from carom-board case study) Find the value of x using similarity of triangles. Given PS = 9 cm, PQ = 35 cm, BR = x, board side 65 cm.
39. 39.
    'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on a grid pattern of dots. There are 4 dots in the first square, 8 dots in the second square, 12 dots in the third square and so on. Show that the number of dots given above form an A.P. Write the first term and common difference. Also write the nth term of the A.P. formed.
40. 40.
    (Kolam case study) The pattern is expanded on a large ground. If total 220 dots are used, then find the number of squares formed.
41. 41.
    Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given: Point A : (–4, 2) Rajasthan High Court; Point B : (4, –4) Birla Mandir; Point C : (4, 3) Heera Bagh; Point D : (–5, –2) Amar Jawan Jyoti. Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ?
42. 42.
    (Jaipur map case study) There is a crossing on the X-axis which divides AD in a certain ratio. Find the ratio. A : (–4, 2), D : (–5, –2).
43. 43.
    (Jaipur map case study) Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer. B : (4, –4) Birla Mandir, C : (4, 3) Heera Bagh, D : (–5, –2) Amar Jawan Jyoti.

Class 10 Mathematics exam pattern (80 marks)

The theory paper carries 80 marks over 3 hours (38 questions, with internal choice in some). Section-wise structure:

Structure per the CBSE 2023-24 sample-paper design; question wording varies by set.

Prepare with

How to use these papers

1. 1Start chapter-wise early in the year — solve only the Mathematics questions from a chapter you have just finished.
2. 2Switch to full timed papers 2–3 months before the exam: one complete set in the real time limit, no notes.
3. 3Self-mark against the marking scheme, then fix every mistake with our free NCERT solutions.
4. 4Re-attempt your weakest chapters until the recurring question types feel routine.

CBSE Class 10 Mathematics 2026 paper — FAQ