CBSE Maths 2016

CBSE Class 10 Maths 2016 — all 30 questions from the paper

The complete question list from the CBSE Class 10 Mathematics 2016 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 2016 paper

1. Q1.For what value of k will the pair of equations kx + 3y = k − 3 and 12x + ky = k have no solution?A) -6B) 6C) ±6D) 0
2. Q2.The decimal expansion of the rational number 14587/1250 will terminate after how many decimal places?A) 1B) 2C) 3D) 4
3. Q3.In an AP, if the common difference d = −4, and the seventh term a₇ is 4, then a₁ is:A) 28B) −28C) 24D) −24
4. Q4.In ΔABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of sinA is:A) 7/25B) 24/25C) 7/24D) 24/7
5. Q5.A letter of the English alphabet is chosen at random. The probability that it is a letter of the word MATHEMATICS is:A) 4/13B) 8/26C) 9/26D) 11/26
6. Q6.If ΔABC ~ ΔDEF and ∠A = 47°, ∠E = 83°, then ∠C is:A) 50°B) 83°C) 47°D) 130°
7. Q7.Find the prime factorisation of 1005.A) 3 × 5 × 67B) 5 × 201C) 5 × 3 × 69D) 3 × 5 × 71
8. Q8.Find the value of p for which the quadratic equation px(x − 3) + 9 = 0 has two equal roots.A) 4B) 3C) 9D) 1
9. Q9.Find the 9th term from the end (towards the first term) of the AP 5, 9, 13, ..., 185.A) 153B) 149C) 157D) 145
10. Q10.Find the coordinates of the point which divides the join of (−1, 7) and (4, −3) in the ratio 2 : 3.A) (1, 3)B) (2, 1)C) (0, 5)D) (3, −1)
11. Q11.Evaluate: 2tan²45° + cos²30° − sin²60°A) 2B) 1C) 3D) 0
12. Q12.A tangent PQ at point P of a circle of radius 5 cm meets a line through the centre O at Q such that OQ = 13 cm. Find the length PQ.A) 12 cmB) 10 cmC) 8 cmD) √(194) cm
13. Q13.Use Euclid's division algorithm to find the HCF of 867 and 255.A) 51B) 3C) 17D) 255
14. Q14.If α and β are zeroes of the polynomial f(x) = x² − p(x + 1) − c, show that (α + 1)(β + 1) = 1 − c. The value of (α + 1)(β + 1) is:A) 1 − cB) 1 + cC) c − 1D) p + c
15. Q15.Solve the pair: ax + by = a − b and bx − ay = a + b. Find x and y.A) x = 1, y = −1B) x = −1, y = 1C) x = 1, y = 1D) x = a, y = b
16. Q16.The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.A) 90 m and 120 mB) 60 m and 90 mC) 80 m and 110 mD) 100 m and 130 m
17. Q17.The sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. Find the AP.A) -13, -8, -3, 2, ...B) -8, -3, 2, 7, ...C) -3, 2, 7, 12, ...D) 2, 7, 12, 17, ...
18. Q18.Show that the points (1, 7), (4, 2), (−1, −1) and (−4, 4) are the vertices of a square.A) It is a square with side √34B) It is a rhombusC) It is a rectangle but not a squareD) It is not a quadrilateral
19. Q19.If tanA = n/(n+1) and tanB = 1/(2n+1), prove that A + B = π/4. What is tan(A + B)?A) 1B) 0C) −1D) undefined
20. Q20.Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. If ABCD is such a quadrilateral and ∠AOB = 110°, find ∠COD.A) 70°B) 110°C) 90°D) 180°
21. Q21.The following distribution gives the daily wages of 50 workers:
    Wages (₹): 250–300 (f=12), 300–350 (f=14), 350–400 (f=8), 400–450 (f=6), 450–500 (f=10). Find the median wage.A) ₹318.75B) ₹325.00C) ₹312.50D) ₹330.00
22. Q22.Cards marked 1 to 20 are placed in a box and mixed thoroughly. One card is drawn at random. What is the probability that the number on the card is divisible by 2 or 3?A) 13/20B) 3/4C) 7/10D) 4/5
23. Q23.A shopkeeper buys some books for ₹80. If he had bought 4 more books for the same amount, each book would have cost ₹1 less. Find the number of books he bought.A) 16B) 20C) 12D) 8
24. Q24.The sum of the first 7 terms of an AP is 63 and the sum of its next 7 terms is 161. Find the 28th term of this AP.A) 57B) 60C) 63D) 54
25. Q25.State and prove the Basic Proportionality Theorem. In ΔABC, D and E are points on AB and AC such that DE ∥ BC. If AD = 3 cm, BD = 5 cm, AE = 4.5 cm, find CE.A) 7.5 cmB) 6 cmC) 5.5 cmD) 8 cm
26. Q26.The angle of elevation of the top of a tower from two points at distances a and b from the base and in the same straight line with it are complementary. Prove that the height of the tower is √(ab).A) h = √(ab)B) h = (a + b)/2C) h = ab/(a + b)D) h = √(a² + b²)
27. Q27.From a solid cylinder of height 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (Use π = 22/7)A) 17.6 cm²B) 15.4 cm²C) 18.48 cm²D) 12.32 cm²
28. Q28.The following data shows the life (in hours) of 400 lamps:
    Lifetime: 300–400 (f=14), 400–500 (f=56), 500–600 (f=60), 600–700 (f=86), 700–800 (f=74), 800–900 (f=62), 900–1000 (f=48). Find the modal lifetime.A) 653.3 hoursB) 666.7 hoursC) 640 hoursD) 670 hours
29. Q29.A bag contains 18 balls out of which x balls are red. If one ball is drawn at random, the probability that it is red is x/18. If 2 more red balls are put in the bag, the probability of drawing a red ball now becomes 9/8 times the previous probability. Find x.A) 8B) 6C) 10D) 12
30. Q30.A cone is cut by a plane parallel to its base at a height 2/3 from the base. What is the ratio of the volume of the smaller cone (frustum top) to the original cone?A) 1/27B) 8/27C) 1/3D) 4/9

Worked solutions from the CBSE 2016 paper

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