10th Maths Model Exam 2026 Question Paper with Answers

Prepare effectively for your SSLC Tamil exam with this 10th Tamil Test Question Paper 1 from Padasalai. This model test paper follows the latest Tamil Nadu state board syllabus and includes a variety of question types—poetry, prose, grammar, and writing skills—to help students practice and improve their scores. Ideal for unit tests, quarterly exams, and public exam revision, the PDF can be downloaded free for classroom or self-study use.

Class: X

MODEL EXAMINATION 2026

MATHEMATICS Marks: 100

I. CHOOSE THE CORRECT ANSWER 14 × 1 = 14

1. If f: A → B is a bijective function and if n(B) = 7, then n(A) is equal to:
a) 7 b) 49 c) 1 d) 14

2. Let f(x) = x² - x, then f(x - 1) - f(x + 1) is:
a) 4x b) 2 - 2x c) 2 - 4x d) 4x - 2

3. If t_n is the n^th term of an A.P. then t_8n - t_n is:
a) (8n - 1)d b) (8n - 2)d c) (7n - 2)d d) 7nd

4. A system of three linear equations in three variables is inconsistent if their planes:
a) intersect only at a point b) intersect in a line c) coincide with each other d) do not intersect

5. Graph of a quadratic equation is a:
a) straight line b) circle c) parabola d) hyperbola

6. How many tangents can be drawn to the circle from an exterior point?
a) 1 b) 2 c) infinite d) 0

7. The area of a triangle formed by the points (-5, 0), (0, -5), and (5, 0) is _______ sq.unit.
a) 0 b) 25 c) 5 d) 10

8. The straight line given by the equation y = 11 is:
a) parallel to x-axis b) parallel to y-axis c) passing through origin d) passing through the point (0, 11)

9. If the ratio of the height of a tower and the length of its shadow is √3 : 1, then the angle of elevation of the sun has measure:
a) 45° b) 30° c) 90° d) 60°

10. The ratio of the volumes of a cylinder, a cone and a sphere if each has the same diameter and height is:
a) 1:2:3 b) 2:1:3 c) 1:3:2 d) 3:1:2

11. Which of the following values cannot be a probability of an event?
a) 0 b) 0.5 c) 1.05 d) 1

12. If the standard deviation of data is 5.6 and each value of data is added by 3, then the value of new S.D is:
a) 3.6 b) 8.6 c) 5.6 d) 1

13. The non diagonal elements in any unit matrix is:
a) 0 b) 1 c) m d) n

14. The sum of first n natural numbers are also called _______ number:
a) pyramid b) triangle c) circle d) none of these

II. ANSWER ANY 10 (Q.NO 28 IS COMPULSORY) 10 × 2 = 20

15. Find A × B, A × A if A = {m, n}, B = ∅.

16. Find 'k' if f ∘ f(k) = 5 where f(k) = 2k - 1.

17. If 1³ + 2³ + 3³ + ... + k³ = 44100, then find 1 + 2 + 3 + ... + k.

18. Find the zeros of x² + 8x + 12.

19. If A =

0	4	9
8	3	7

, B =

7	3	8
1	4	9

, find B - 5A.

20. If ΔABC is similar to ΔDEF such that BC = 3 cm, EF = 4 cm and area of ΔABC = 54 cm², find the area of ΔDEF?

21. Show that the points (-2, 5), (6, -1) and (2, 2) are collinear.

22. Find the intercepts made by 3x - y - 6 = 0 on the coordinate axes.

23. Prove that √[^{(1 + cos θ)}/_{(1 - cos θ)}] = cosec θ + cot θ.

24. If the ratio of radii of two spheres is 4:7, find the ratio of their volumes.

25. Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r units.

26. If the standard deviation of a data is 3.6 and each value of the data is divided by 3, then find the new variance and standard deviation.

27. Two coins are tossed together. What is the probability of getting different faces on the coins?

28. How many terms are in the A.P. -2, -4, -6, ... -100? (Compulsory)

III. ANSWER ANY 10 (Q.NO 42 IS COMPULSORY) 10 × 5 = 50

29. Let A = {x ∈ W | 0 < x < 2}, B = {x ∈ ℕ | 1 < x ≤ 4} and C = {3, 5}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C).

30. A function f: [-5, 9] → ℝ is defined as follows:

f(x) =
  • 6x + 1, -5 ≤ x < 2
  • 5x² - 1, 2 ≤ x < 6
  • 3x - 4, 6 ≤ x ≤ 9

Find: i) f(-3) + f(2) ii) f(7) - f(1) iii) ^{[2f(-2) - f(6)]}/_{[f(4) + f(-2)]}

31. The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms.

32. Find the HCF of 396, 504, 636.

33. Find the values of m and n if 36x⁴ - 60x³ + 61x² - mx + n is a perfect square.

34. If A =

5	2	9
1	2	8

, B =

1	7
1	2
5	-1

, verify (AB)^T = B^TA^T.

35. If the vertices of a quadrilateral are at A(-5, 7), B(-4, k), C(-1, -6), D(4, 5) and its area is 72 sq.units, find the value of k.

36. Two ships are sailing in the sea on either side of a lighthouse. The angle of elevation of the top of the lighthouse as observed from the ships are 30°, 45° respectively. If the lighthouse is 200 m high, find the distance between the two ships.

37. A girl wishes to prepare birthday caps in the form of right circular cones for her birthday party using a sheet of paper whose area is 5720 cm². How many caps can be made with radius 5 cm and height 12 cm?

39. The marks scored by the students in a slip test are given below. Find the standard deviation:

x	4	6	8	10	12
f	7	3	5	9	5

40. Three unbiased coins are tossed once. Find the probability of getting at most 2 tails or at least 2 heads.

41. If the roots of the equation (c² - ab)x² - 2(a² - bc)x + b² - ac = 0 are real and equal, prove that either a = 0 or a³ + b³ + c³ = 3abc.

42. A straight line cuts the coordinate axes at A and B. If the midpoint of AB is (3, 2), then find the equation of AB. (Compulsory)

IV. ANSWER THE FOLLOWING 2 × 8 = 16

42. a) Draw a triangle ABC of base BC = 8 cm, ∠A = 60° and the bisector of ∠A meets BC at D such that BD = 6 cm.

(OR)

b) Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw the two tangents to the circle from that point.

43. a) Graph the quadratic equation x² - 9x + 20 = 0 and state the nature of the solution.

(OR)

b) A bus is travelling at a uniform speed of 50 km/hr. Draw the distance-time graph and hence find:
(i) the constant of variation
(ii) how far will it travel in 90 minutes?
(iii) the time required to cover a distance of 300 km.