10th Maths Public Exam Answer Key March 2026 Download PDF

 

Covernment High School
10^th Std MATHS PUBLIC EXAM ANSWER KEY - March-26
Date: 25-03-2026

PART A (1 MARKS)

1. (a) (8,6)

8. (c) (3,5)

2. (d) quadratic

9. (b) Parallel to y axis

3. (b)

10. (a) 2

4. (c) 14280

11. (c) 4x Cm

5. (a) x=1, y=2, z=3

12. (a) 2:1

6. (d) 4 × 3

13. (b) 2

7. (a) 13m

14. (b) P

PART B (2 MARKS)

15. y = x + 3, x = {0,1,2,3,4,5}

R = {(0,3), (1,4), (2,5), (3,6), (4,7), (5,8)}
Domain = {0, 1, 2, 3, 4, 5}
Range = {3, 4, 5, 6, 7, 8}

16. R is not a function as t ∈ x does not have an image in y.

17. 71 ≡ x (mod 8)

71 - x = 8n ⇒ x = 71 - 8n
x = 71 - 8(8) = 71 - 64 ⇒ x = 7

18. S_∞ =

a1 - r

a = 9, r =

t₂t₁

=

39

⇒ r =

13

S_∞ =

91 - 1/3

⇒ S_∞ = 27/2

19.

x² - 16x² + 8x + 16

=

(x+4)(x-4)(x+4)(x+4)

=

x - 4x + 4

20. Let the numbers be x,

1x

x -

1x

=

245

⇒ 5(x² - 1) = 24x
5x² - 24x - 5 = 0 ⇒ (x - 5)(5x + 1) = 0
x = 5, -1/5

21. A =

1    3    5
0    2    4
1    1    3

22. BD = AB - AD = 5.6 - 1.4 = 4.2 cm

EC = 7.2 - 1.8 = 5.4 cm

ADDB

=

1.44.2

=

13

;

AEEC

=

1.85.4

=

13

ADDB

=

AEEC

∴ DE || BC

23. Slope =

y₂ - y₁x₂ - x₁

=

-6 - 1014 - 14

=

-160

Slope is undefined.

24.

x4

-

y6

= 1 ⇒ 3x - 2y = 12

25. √

1 + cosθ1 - cosθ

= √ (

1 + cosθ1 - cosθ

×

1 + cosθ1 + cosθ

)

=

1 + cosθsinθ

= cosecθ + cotθ

26. SD = √

n² - 112

= √

21² - 112

= √

44012

= √36.67 ⇒ SD ≈ 6.05

27. n(S) = 12, n(A) = 3

P(A) =

n(A)n(S)

=

312

= 1/4

28. Ratio =

a³πa³ / 6

=

6π

= 6 : π (or) 21 : 11

PART C (5 MARKS)

29. B ∩ C = {3} ⇒ A × (B ∩ C) = {(0,3), (1,3)}   --- (1)

(A × B) ∩ (A × C) = {(0,3), (1,3)}   --- (2)
From (1) & (2), A × (B ∩ C) = (A × B) ∩ (A × C)

30. fog(x) = 3x

(fog)oh = 3x²
fo(goh) = 3x²
∴ (fog)oh = fo(goh)

31. AP Series: 301, 308 ... 595

a = 301, d = 7, l = 595
n = [

l - ad

] + 1 ⇒ n = 43
S_n =

n2

(a + l) ⇒ S₄₃ = 19264

32. S = 3 + 33 + 333 + ... to n terms

=

39

(9 + 99 + ... to n terms)
=

13

[ (10-1) + (100-1) + ... ]
S =

10(10ⁿ - 1)27

-

n3

33. Matrices Calculation:

(AB)^T =

52   43
30   3

B^TA^T =

52   43
30   3

From above, (AB)^T = B^TA^T

34. Ceva's / Thales Application:

BDDC

×

CEEA

×

AFFB

= 1

35. Area of Quadrilateral: A(8,6), B(5,11), C(-5,12), D(-4,3)

Area =

12

| (x₁y₂...) - (y₁x₂...) |
=

12

(158) = 79 sq.units

36. Required Equations:

Eq of BE ⇒ 2x + 5y + 6 = 0
Eq of AD ⇒ 5x + y - 48 = 0

37. AB = 200m.

In ΔBAC, tan 30° ⇒ AD = 200m
DC = 200√3 = 346.4m
CD = AC + AD = 346.4 + 200 = 546.4m

38. Area = CSA of Cylinder = 2πrh

= 2 ×

227

× 1.4 × 3 = 26.4 m²
Total Area = 8 × 26.4 = 211.2 m²

39.

43

π(R³ - r³) =

13

πr₁²h

125 - r³ = 98 ⇒ r³ = 27 ⇒ r = 3 cm
Internal diameter = 6 cm

40. x̄ = 30, Σ(x - x̄)² = 112

σ = √

1126

⇒ σ = 4.32
CV =

σx̄

× 100 ⇒ CV = 14.4%

41. n(S) = 36, P(A) = 6/36, P(B) = 3/36, P(A∩B) = 1/36

P(A∪B) = P(A) + P(B) - P(A∩B)
= 2/9

42. α + β =

32

, αβ = -

12

x² - (α + β)x + αβ = 0 applied based on new roots.

PART D (8 MARKS)

43. (a) Geometry

- Draw the Rough Diagram
- Draw the ΔPQR
- Complete the Construction arcs.

44. (a) Graph: y = x² - 5x + 4

∴ The roots are real and unequal. (Based on plotting)

44. (b) Graph: y =

12

x (Direct Variation)

From the graph:
(i) x = 9 ⇒ y = 4.5
(ii) y = 7.5 ⇒ x = 15