CBSE Maths 2020

CBSE Class 10 Maths 2020 — all 30 questions from the paper

The complete question list from the CBSE Class 10 Mathematics 2020 board examination is below. Every question can be attempted in the timed interactive test above, with visual step-by-step solutions and AI coaching after each answer. Three fully worked solutions from this paper follow the question list.

Questions from the 2020 paper

1. Q1.If HCF(336, 54) = 6, find LCM(336, 54).A) 3024B) 2024C) 4024D) 1512
2. Q2.Find the nature of roots of the quadratic equation 2x² − 4x + 3 = 0.A) Real and equalB) Real and distinctC) No real rootsD) Rational roots
3. Q3.Find the 11th term from the last of the AP: 10, 7, 4, ..., −62.A) -32B) -35C) -29D) -26
4. Q4.If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, then the other two sides are divided in:A) Equal ratioB) Same ratioC) Different ratioD) Cannot be determined
5. Q5.If tanα = 5/12 and tanβ = 4/3, find tan(α + β). Actually — simpler: if tan2A = cot(A − 18°), where 2A is an acute angle, find A.A) 36°B) 18°C) 24°D) 54°
6. Q6.A box contains cards numbered 6 to 50. A card is drawn at random. The probability that it has a two-digit number is:A) 40/45B) 41/45C) 44/45D) 39/45
7. Q7.Find the zeroes of the quadratic polynomial 6x² − 3 − 7x and verify the relationship between zeroes and coefficients.A) 3/2 and −1/3B) −3/2 and 1/3C) 3/2 and 1/3D) −3/2 and −1/3
8. Q8.Find the values of k for which the pair of equations kx + 3y = k − 3 and 12x + ky = k has no solution.A) k = 6B) k = −6C) k = ±6D) k = 6 only (excluding −6)
9. Q9.Find the ratio in which the point P(−4, 6) divides the line segment joining A(−6, 10) and B(3, −8).A) 2 : 7B) 7 : 2C) 2 : 9D) 9 : 2
10. Q10.Evaluate: (5cos²60° + 4sec²30° − tan²45°)/(sin²30° + cos²30°)A) 67/12B) 11/12C) 73/12D) 55/12
11. Q11.Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Using this, if O is the centre and PQ is a chord of a circle of radius 5 cm such that OP ⊥ PQ, find PQ if OQ = 13 cm.A) 24 cmB) 12 cmC) 10 cmD) 18 cm
12. Q12.The distribution below gives the weight of 30 students of a class. Find the median weight.
    Weight (kg): 40–45 (f=2), 45–50 (f=3), 50–55 (f=8), 55–60 (f=6), 60–65 (f=6), 65–70 (f=3), 70–75 (f=2).A) 56.67 kgB) 55.00 kgC) 57.50 kgD) 54.17 kg
13. Q13.Prove that √5 is irrational. Hence prove that 3 − 2√5 is irrational. What is 3 − 2√5?A) RationalB) IrrationalC) IntegerD) Whole number
14. Q14.If α and β are zeroes of the polynomial p(x) = 2x² + 5x + k, and α² + β² + αβ = 21/4, find the value of k.A) 2B) -2C) 3D) -3
15. Q15.A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.A) 7/15B) 5/9C) 3/7D) 7/9
16. Q16.Find two consecutive positive integers whose sum of squares is 365.A) 13 and 14B) 12 and 13C) 14 and 15D) 11 and 12
17. Q17.The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?A) 38 terms, sum = 6973B) 38 terms, sum = 7000C) 37 terms, sum = 6790D) 39 terms, sum = 7150
18. Q18.In ΔABC, AD ⊥ BC. Prove that AB² + CD² = AC² + BD². If AB = 13, AD = 12, BD = 5, find AC.A) √(153)B) √193C) √181D) √169
19. Q19.If the point C(−1, 2) divides internally the line segment joining A(2, 5) and B in the ratio 3 : 4, find the coordinates of B.A) (−5, −2)B) (5, 2)C) (−3, −1)D) (3, 1)
20. Q20.Prove that: (1 + tan²A)/(1 + cot²A) = [(1 − tanA)/(1 − cotA)]² = tan²A. What does the expression simplify to?A) sin²AB) cos²AC) tan²AD) 1
21. Q21.Draw a circle of radius 3 cm. From a point 5 cm from the centre, construct a tangent. What is the length of each tangent?A) 4 cmB) 3 cmC) 5 cmD) √34 cm
22. Q22.A box contains 20 cards numbered from 1 to 20. A card is drawn at random. The probability that the number on the card is a prime number is:A) 2/5B) 3/10C) 7/20D) 1/4
23. Q23.A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream. Find the speed of the stream.A) 6 km/hB) 4 km/hC) 8 km/hD) 5 km/h
24. Q24.If the sum of the first n terms of an AP is 4n − n², what is the first term and common difference?A) a = 3, d = −2B) a = 4, d = −1C) a = 3, d = −1D) a = 2, d = −2
25. Q25.Sides AB and AC and median AD of ΔABC are proportional to sides PQ and PR and median PM of ΔPQR. Then ΔABC ~ ΔPQR. If AB = 6, AC = 8, AD = 5, PQ = 9, then PM is:A) 7.5B) 6C) 10D) 8
26. Q26.The shadow of a tower standing on a level ground is found to be 40 m longer when the sun's altitude is 30° than when it is 60°. Find the height of the tower.A) 20√3 mB) 40√3 mC) 20 mD) 30√3 m
27. Q27.A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm and its base radius is 3.5 cm, find the total surface area of the article.A) 374 cm²B) 297 cm²C) 374.5 cm²D) 396 cm²
28. Q28.The following table shows the ages of patients admitted in a hospital during a year:
    Age: 5–15 (f=6), 15–25 (f=11), 25–35 (f=21), 35–45 (f=23), 45–55 (f=14), 55–65 (f=5).
    Find the mode of the data.A) 36.8 yearsB) 34.0 yearsC) 38.5 yearsD) 33.3 years
29. Q29.A die is thrown twice. Find the probability that the sum of the numbers appearing is 7.A) 1/6B) 5/36C) 7/36D) 1/12
30. Q30.If the areas of two similar triangles are 81 cm² and 49 cm² respectively, and the altitude of the bigger triangle is 4.5 cm, find the corresponding altitude of the smaller triangle.A) 3.5 cmB) 3.0 cmC) 2.5 cmD) 4.0 cm

Worked solutions from the CBSE 2020 paper

Start the test above to see visual step-by-step solutions for all 30 questions — free, with AI coaching when you get stuck.