CBSE Class 10 Mathematics 2026 — Set 5

Questions in this 2026 Mathematics paper (Set 5)

All 38 questions from this set, exactly as asked. Try each one, then open the question-paper PDF above for the complete paper.

1. 1.
   The value of k for which the equation kx2 – 6x – 4 = 0 has real and equal roots, is

   • (a) 9/4
   • (b) –4
   • (c) –9/4
   • (d) –2
2. 2.
   The line segment joining the points P(–4, –2) and Q(10, 4) is divided by y-axis in the ratio

   • (a) 2 : 5
   • (b) 1 : 2
   • (c) 2 : 1
   • (d) 5 : 2
3. 3.
   If the zeroes of a polynomial p(x) are –3 and 8, then p(x) equals

   • (a) x2 + 5x – 4
   • (b) (x + 3) (–x + 8)
   • (c) a(x2 + 5x – 24)
   • (d) x2 – 24
4. 4.
   In the given figure, PQ is tangent to the circle with centre O. S is a point on the circle such that ∠SQT = 55°. The m∠QPS is

   • (a) 55°
   • (b) 20°
   • (c) 35°
   • (d) 70°
5. 5.
   Devansh proved that ABC ~ PQR using SAS similarity criteria. If he found ∠C = ∠R, then which of the following was proved true ?

   • (a) AC/AB = PR/PQ
   • (b) BC/AC = PR/QR
   • (c) AC/BC = PR/PQ
   • (d) AC/BC = PR/QR
6. 6.
   While calculating mean of a grouped frequency distribution, step deviation method was used (x – a)/h = u. It was found that x̄ = 64, h = 5 and a = 62.5. The value of ū is

   • (a) 0.5
   • (b) 1.5
   • (c) 0.3
   • (d) 7.5
7. 7.
   A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use π = 3.14)

   • (a) 314√2 cm2
   • (b) 314 cm2
   • (c) 3140/3 cm2
   • (d) 3140√2 cm2
8. 8.
   If an represents nth term of the A.P. –15/4, –10/4, –5/4, ……, then value of a16 – a12 is

   • (a) 4
   • (b) 5/4
   • (c) 5
   • (d) 25/4
9. 9.
   The value of p for which roots of the quadratic equation x2 – px + 6 = 0 are rational, is

   • (a) 1
   • (b) –5
   • (c) 25
   • (d) √5
10. 10.
    Which of the following can not be the probability of an event ?

    • (a) 39/100
    • (b) 0.001/20
    • (c) 10/0.2
    • (d) 10%
11. 11.
    A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that it is either a ten or a king is

    • (a) 1/26
    • (b) 2/13
    • (c) 1/13
    • (d) 8/26
12. 12.
    A camping tent in hemispherical shape of radius 1.4 m, has a door opening of area 0.50 m2. Outer surface area of the tent is

    • (a) 11.78 m2
    • (b) 12.32 m2
    • (c) 11.82 m2
    • (d) 12.86 m2
13. 13.
    An arc of length 2.2 cm subtends an angle θ at the centre of the circle with radius 2.8 cm. The value of θ is

    • (a) 50°
    • (b) 60°
    • (c) 45°
    • (d) 30°
14. 14.
    For an acute angle θ, if sin θ = 1/9, then value of (9 cosec θ + 1)/(9 cosec θ – 1) is

    • (a) 0
    • (b) 80/81
    • (c) 1
    • (d) 82/80
15. 15.
    In the given figure, PQ || YZ such that XP : PY = 2 : 3. If PQ = 5 cm, then YZ equals

    • (a) 12.5 cm
    • (b) 10 cm
    • (c) 15 cm
    • (d) 7.5 cm
16. 16.
    Meena calculates that the probability of her winning the first prize in a lottery is 0.08. If total 800 tickets were sold, the number of tickets bought by her, is

    • (a) 64
    • (b) 640
    • (c) 100
    • (d) 10
17. 17.
    A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as 60°. If AB = 5√3 m, then length of the wire is

    • (a) 10 m
    • (b) 10√3 m
    • (c) 15 m
    • (d) (5/2)√3 m
18. 18.
    Simplest form of (sec A)/√(sec2A – 1) is

    • (a) sin A
    • (b) tan A
    • (c) cosec A
    • (d) cos A
19. 19.
    Assertion (A) : The system of linear equations 3x – 5y + 7 = 0 and –6x + 10y + 14 = 0 is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines. Select the correct answer: (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…
20. 20.
    Assertion (A) : H.C.F. (36 m2, 18 m) = 18 m, where m is a prime number. Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number. Select the correct answer: (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…
21. 21.
    Prove that 2 – 5√3 is an irrational number given that √3 is irrational.
22. 22.
    Vertices of a right triangle ABC with ∠B = 90° are A(3, 4), B(1, 1) and C(–8, 7). Find the value of tan A.
23. 23.
    In the given figure, AB || DE and AC || DF. Show that ABC ~ DEF. If BC = 10 cm, EB = CF = 5 cm and AB = 7 cm, then find the length DE.
24. 24.
    Evaluate : (sin³ 60° – tan 30°)/cos² 45°
25. 25.
    A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is 3/5, then find the number of yellow balls.
26. 26.
    A circle of diameter 20 cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.
27. 27.
    In an A.P., 15th term exceeds the 8th term by 21. If sum of first 10 terms is 55, then form the A.P.
28. 28.
    Prove that : tan θ/(1 – cot θ) + cot θ/(1 – tan θ) = 1 + tan θ + cot θ.
29. 29.
    A circle centered at (2, 1) passes through the points A(5, 6) and B(–3, K). Find the value(s) of K. Hence find length of chord AB.
30. 30.
    Solve the system of linear equations : x = 4 and 3x – 2y = 6 graphically.
31. 31.
    The dimensions of a window are 156 cm × 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.
32. 32.
    Venkat can row a boat in still water at the speed of 12 km/h. He ferries tourists 15 km upstream and 18 km downstream in 3 hours. Find the speed of the stream.
33. 33.
    D is the mid-point of side BC of ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD = DG. Prove that

    • (i) OBGC is a parallelogram.
    • (ii) EF || BC
    • (iii) AEF ~ ABC
34. 34.
    The mean of the following frequency distribution is 28. If sum of all frequencies is 100, then find the values of p and q : Class Interval: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60; Frequency: 12, p, 27, 20, q, 6.
35. 35.
    PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.
36. 36.
    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 + 136. Observe the diagram and based on above information, answer the following questions : (i) Write the co-ordinates of point A.
37. 36 (ii).
    (Case study 36, part ii) Find the span of the arch.
38. 36 (iii)(a).
    (Case study 36, part iii-a) Write the zeroes of the polynomial using diagram and verify the relationship between sum of zeroes and polynomials.
39. 36 (iii)(b).
    (Case study 36, part iii-b) Find the values of p(x) at x = 100 and x = –100. Are they same ?
40. 37 (i).
    A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter 7 cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are 24 cm × 12 cm × 17 cm. (i) Find the surface area of the bulb.
41. 37 (ii).
    (Case study 37, part ii) What could be the maximum diameter of the bulb if at least 1 cm space is left from each side ?
42. 37 (iii)(a).
    (Case study 37, part iii-a) Find the area of the fabric used if there is a fold of 2 cm on top and bottom edges.
43. 37 (iii)(b).
    (Case study 37, part iii-b) Find the space available inside the lamp.
44. 38 (i).
    Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank. From a window (W) of the building, the angle of elevation of top of the tank is 45° and angle of depression of its foot is 30°. (i) Write a relation between d (the…
45. 38 (ii).
    (Case study 38, part ii) Determine the value of h.
46. 38 (iii)(a).
    (Case study 38, part iii-a) Determine height of the water tank.
47. 38 (iii)(b).
    (Case study 38, part iii-b) Find the value of x and height of the window above ground level.

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