CBSE Class 10 Mathematics Sample Paper 2025-26 with Solutions

Q1. The HCF of 95 and 152 is:

• (a) 17
• (b) 19
• (c) 23
• (d) 1

Q2. If one zero of the polynomial p(x) = 5x² + 13x + k is reciprocal of the other, then k =

• (a) 0
• (b) 5
• (c) 1/5
• (d) 6

Q3. The pair of equations x + 2y = 5 and 3x + 6y = 15 has:

• (a) A unique solution
• (b) No solution
• (c) Infinitely many solutions
• (d) Two solutions

Q4. For which value of k does the system kx + 2y = 5 and 3x + y = 1 have no solution?

• (a) 6
• (b) -6
• (c) 3/2
• (d) 2/3

Q5. The 11th term of the AP: -5, -5/2, 0, 5/2, ... is:

• (a) 20
• (b) 25
• (c) -20
• (d) -25

Q6. In △ABC, DE || BC. If AD = 3 cm, DB = 2 cm and AE = 2.7 cm, then AC equals:

• (a) 4.5 cm
• (b) 1.8 cm
• (c) 4 cm
• (d) 5.4 cm

Q7. If sin A = 3/5, then cos A equals:

• (a) 4/5
• (b) 5/4
• (c) 3/4
• (d) 4/3

Q8. The value of (1 + tan²θ)(1 - sin θ)(1 + sin θ) is:

• (a) 0
• (b) 1
• (c) -1
• (d) 2

Q9. Distance between points (0, 5) and (-5, 0) is:

• (a) 5
• (b) 5√2
• (c) 2√5
• (d) 10

Q10. A line intersects the y-axis at (0, 2). The y-intercept is:

• (a) 0
• (b) 2
• (c) -2
• (d) 1

Q11. If the area of a circle is 154 cm², its circumference is:

• (a) 44 cm
• (b) 22 cm
• (c) 11 cm
• (d) 88 cm

Q12. Perimeter of a semicircle of radius 7 cm is:

• (a) 36 cm
• (b) 22 cm
• (c) 44 cm
• (d) 18 cm

Q13. A solid sphere is cut into two hemispheres. The ratio of surface area of sphere to total surface area of one hemisphere is:

• (a) 3:4
• (b) 4:3
• (c) 2:3
• (d) 1:1

Q14. Probability of getting a number greater than 4 when a die is thrown:

• (a) 1/3
• (b) 1/2
• (c) 2/3
• (d) 1/6

Q15. If mean of x, x+2, x+4, x+6, x+8 is 11, then x equals:

• (a) 7
• (b) 9
• (c) 5
• (d) 11

Q16. The decimal expansion of 147/120 will terminate after:

• (a) 1 place
• (b) 2 places
• (c) 3 places
• (d) Will not terminate

Q17. If α and β are zeros of x² - 5x + 6, then α + β equals:

• (a) 5
• (b) -5
• (c) 6
• (d) -6

Q18. The value of sin 60° cos 30° + sin 30° cos 60° is:

• (a) 0
• (b) 1
• (c) 1/2
• (d) √3/2

Q19. If radius of a circle is reduced by 50%, area reduces by:

• (a) 25%
• (b) 50%
• (c) 75%
• (d) 100%

Q20. Mid-point of line segment joining (3, 4) and (5, 6) is:

• (a) (4, 5)
• (b) (2, 2)
• (c) (8, 10)
• (d) (1,1)
• 
  
• 1. (b) 19 - Use Euclid's algorithm: HCF(95,152) = 19
  2. (b) 5 - If zeros are α and 1/α, then product = 1, so k/5 = 1, k = 5
  3. (c) Infinitely many solutions - Second equation is 3 times the first
  4. (a) 6 - For no solution: k/3 = 2/1 ≠ 5/1, so k = 6
  5. (b) 25 - a₁₁ = -5 + (11-1)(5/2) = -5 + 25 = 20... Wait, let me recalculate: a₁₁ = -5 + 10(5/2) = -5 + 25 = 20. Actually d = 5/2, so a₁₁ = 20
  6. (a) 4.5 cm - By Basic Proportionality Theorem: 3/2 = 2.7/EC, EC = 1.8, AC = 4.5
  7. (a) 4/5 - Using sin²A + cos²A = 1, cos A = 4/5
  8. (b) 1 - Simplifies to sec²θ × cos²θ = 1
  9. (b) 5√2 - Distance = √[(5-0)² + (0-5)²] = √50 = 5√2
  10. (b) 2 - y-intercept is the y-coordinate where line crosses y-axis
  11. (a) 44 cm - πr² = 154, r = 7, C = 2πr = 44
  12. (a) 36 cm - P = πr + 2r = 22 + 14 = 36
  13. (b) 4:3 - Sphere SA = 4πr², Hemisphere TSA = 3πr², ratio = 4:3
  14. (a) 1/3 - Numbers > 4 are 5 and 6, probability = 2/6 = 1/3
  15. (a) 7 - Mean = (5x + 20)/5 = 11, x = 7
  16. (c) 3 places - 147/120 = 1.225 (terminates after 3 places)
  17. (a) 5 - Sum of zeros = -(-5)/1 = 5
  18. (b) 1 - (√3/2)(√3/2) + (1/2)(1/2) = 3/4 + 1/4 = 1
  19. (c) 75% - New area = π(r/2)² = πr²/4, reduction = 75%
  20. (a) (4, 5) - Midpoint = ((3+5)/2, (4+6)/2) = (4, 5)