Class 10 Maths Answer Key - Basic | CBSE Exam 2025-26 Board Term 1

1. The HCF of 2² · 3³ and 3² · 2³ is :

• (a) 1
• (b) 2 · 3
• (c) 2² · 3²
• (d) 2³ · 3³

Answer is as follow: (d) 2³ · 3³

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2. A letter is selected from the letters of the word FEBRUARY. The probability that it is a vowel is :

• (a) 1/8
• (b) 2/8
• (c) 3/8
• (d) 3/7

Answer is as follow: (c) 3/8

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3. Which of the following numbers will not end with 0 for any natural number n?

• (a) 4 × n
• (b) 4ⁿ
• (c) 3ⁿ + 1
• (d) 10ⁿ + 1

Answer is as follow: (b) 4ⁿ

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4. The system of linear equations px + qy = r and p₁x + q₁y = r₁ has a unique solution, if :

• (a) p/q ≠ p₁/q₁
• (b) p/p₁ ≠ q/q₁
• (c) p/q₁ ≠ q/p₁
• (d) p/q/r ≠ p₁/q₁/r₁

Answer is as follow: (c) p/q₁ ≠ q/p₁

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5. Which of the equations among the following is/are quadratic equation(s)?

q₁: x² + x = (x + 1)², q₂: x − 1 = x² − 1, q₃: x = x², q₄: √x = x²√x + 1

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• (a) q₁ only
• (b) q₁, q₂ and q₃ only
• (c) q₂ and q₃ only
• (d) q₂ and q₄ only

Answer is as follow: (c) q₂ and q₃ only

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6. The discriminant of the quadratic equation ax² + x + a = 0 is :

• (a) √(1 − 4a²)
• (b) 1 − 4a²
• (c) 4a² − 1
• (d) √(4a² − 1)

Answer is as follow: (b) 1 − 4a²

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7. The distance between points (3, 0) and (0, −3) is :

• (a) 3 units
• (b) 6 units
• (c) √6 units
• (d) √18 units

Answer is as follow: (d) √18 units

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8. If △ABC ∼ △ADE in the adjoining figure, then which of the following is true?

• (a) AB/BE = AC/CD
• (b) AB/AD = AC/AE
• (c) AB/BC = AE/DE
• (d) AC/AD = AB/AE

Answer is as follow: (b) AB/AD = AC/AE

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9. In the adjoining figure, if EA ∥ SR and PE = x cm, then the value of 5x is :

• (a) 2.4 cm
• (b) 12 cm
• (c) 1.35 cm
• (d) 6.75 cm

Answer is as follow: (b) 12 cm

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10. Which of the following graphs represents a polynomial with both zeroes being positive?

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• (a)
• (b)
• (c)
• (d)

Answer is as follow:(c)

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11. The system of equations x = 2 and x = 3 has:

• (a) unique solution (2, 3)
• (b) two solutions (2, 0) and (3, 0)
• (c) no solution
• (d) infinitely many solutions

Answer is as follow:

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12. The numbers x, x + 4 and x + 8 are in A.P. with common difference:

• (a) x
• (b) 4 + x
• (c) 4
• (d) 0

Answer is as follow: (c) 4

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13. Which of the following statements is not true?

• (a) sin 0° = cos 0°
• (b) tan 30° = cot 60°
• (c) sin 30° = cos 60°
• (d) sin 45° = 1/sec 45°

Answer is as follow: (a) sin 0° = cos 0°

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14. If √3 sin A = cos A, then the measure of A is :

• (a) 90°
• (b) 60°
• (c) 45°
• (d) 30°

Answer is as follow: (d) 30°

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15. In the adjoining figure, the angle of elevation of the point C from the point B, is :

• (a) 30°
• (b) 45°
• (c) 22.5°
• (d) 67.5°

Answer is as follow: (a) 30°

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16. In the adjoining figure, the slant height of the conical part is :

• (a) 4 cm
• (b) 7 cm
• (c) 5 cm
• (d) 25 cm

Answer is as follow: (c) 5 cm

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17. The upper limit of the median class of the above data is :

• (a) 10
• (b) 20
• (c) 30
• (d) 40

Answer is as follow: (d) 40

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18. If for a data, median is 5 and mode is 4, then mean is equal to :

• (a) 7
• (b) 11
• (c) 11/2
• (d) 14/3

Answer is as follow: (c) 11/2

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19. Assertion (A): From a bag containing 5 red balls, 2 white balls and 3 green balls, the probability of drawing a non-white ball is 4/5.
Reason (R): For any event E, P(E) + P(not E) = 1

• (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.

Answer is as follow: Both (A) and (R) are true and (R) is the correct explanation of (A).

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20. Assertion (A): 7 × 2 + 3 is a composite number.
Reason (R): A composite number has more than two factors.

• (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.

Answer is as follow: (d) A is false but R is true.

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21. Find the coordinates of the point which divides the line segment joining the points A (-6, 10) and B (3, -8) in the ratio 2 : 7.

Answer is as follow:(−4,6)

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22. (A) One zero of a quadratic polynomial is twice the other. If the sum of zeroes is (-6), find the polynomial.

OR

(B) If one zero of the polynomial x² − 5x − c is (-1), find the value of c. Also, find the other zero.

Answer is as follow: x² +6x+8

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23. In the adjoining figure, AP = 1/2 AB and PQ ∥ BC. If CQ = 3 cm, then find the length of AC.

Answer is as follow: The length of AC is 6 cm.

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24. (A) Evaluate : sin²30° − cos²45° + cot²60°

Answer is as follow: The value is 1/12

OR

(B) If sin(A + 2B) = 2 cos 60° and A = 3B, find the measures of A and B.

Answer is as follow: A=54° and B=18°

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25. A box consists of 60 wall clocks, out of which 40 are good, 15 have minor defects and the remaining are broken. What is the probability that:

• (i) the box will be rejected?
• (ii) the clock has minor defect?

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26. Given that √5 is an irrational number, prove that 3 + 2√5 is also an irrational number.

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27. (A) Solve the following system of equations graphically: x + 3y = 6 and 2x − 3y = 12. Also, find the area of the triangle formed by the lines x + 3y = 6, x = 0 and y = 0.

OR

(B) One of the supplementary angles exceeds the other by 120°. Express this as a system of linear equations and find the angles.

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28. If the point P (x, y) is equidistant from the points (3, 6) and (-3, 4), obtain the relation between x and y. Hence, find the coordinates of point P if it lies on x-axis.

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29. (A) Prove that: (sin A − tan A) / (sin A + tan A) = (1 − sec A) / (1 + sec A)

OR

(B) If sin x = p, then prove that: (i) cot x = √(1 − p²) / p (ii) (1 + tan² x) / (1 + cot² x) = p² / (1 − p²)

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30. Prove that the lengths of tangents drawn from an external point to a circle are equal.

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31. In the adjoining figure, AB is the diameter of the circle with centre O. Two tangents p and q are drawn to the circle at points A and B respectively. Prove that p ∥ q. Further, a line CD touches the circle at E and ∠BCD = 110°. Find the measure of ∠ADC.

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32. (A) Express 24/(18−x) − 24/(18+x) = 1 as a quadratic equation in standard form and find the discriminant. Also, find the roots of the equation.

OR

(B) The sum of squares of two positive numbers is 100. If one number exceeds the other by 2, find the numbers.

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33. In the adjoining figure, △ABE ∼ △ACD. Prove that: (i) △ADE ∼ △ABC (ii) △BOD ∼ △COE

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34. (A) In the adjoining figure, △OAB is an equilateral triangle and the area of the shaded region is 750π cm². Find the perimeter of the shaded region.

OR

(B) Find the ratio of area of shaded region in figure (i) to that of figure (ii).

Answer is as follow:

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35. The mode of the following data is 3.286. Find the mean and median of the above data.

Answer is as follow:

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36. A watermelon vendor arranged the watermelons similar to shown in the adjoining picture. The number of watermelons in subsequent rows differ by ‘d’. The bottommost row has 101 watermelons and the topmost row has 1 watermelon. There are 21 rows from bottom to top. Based on the above information, answer the following questions :

• (i) Find the value of ‘d’.
• (ii) How many watermelons will be there in the 15th row from the bottom?
• (iii) (a) Find the total number of watermelons from bottom to top. OR
• (iii) (b) If the number of watermelons in the nth row from top is equal to the number of watermelons in the nth row from bottom, find the value of n.

Answer is as follow:

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37. Mishika and Sahaj created a bird-bath from a cylindrical log of wood by scooping out a hemispherical depression. Cylinder length is 2 m (0.6 m in earth) and diameter is 1.4 m.

• (i) Radius of depression?
• (ii) Volume of water in hemisphere in terms of π?
• (iii) (a) Total surface area of log above ground? OR
• (iii) (b) Volume of log above ground?

Answer is as follow:

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38. A flagstaff 7.32 m long is at the top of a 10 m tall building. Rope l₁ (to building top) makes 30°. Rope l₂ (to flagstaff top) makes θ.

• (i) Find x.
• (ii) Find θ.
• (iii) (a) Total length of ropes? OR
• (iii) (b) Which rope is longer and by how much?

Answer is as follow:

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CBSE 10th Result 2021



Last Updated on : March 26, 2026