ICSE Maths 2016

ICSE Class 10 Maths 2016 — all 35 questions from the paper

The complete question list from the ICSE 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.The quadratic equation whose roots are 3 and −3 is:A) x² − 9 = 0B) x² + 9 = 0C) x² − 6x + 9 = 0D) x² + 6x + 9 = 0
2. Q2.A man deposits ₹100 per month for 10 months in a bank. The bank pays interest at 5% p.a. The interest earned on the recurring deposit is:A) ₹22.92B) ₹25.00C) ₹20.83D) ₹27.50
3. Q3.A bag has 5 white and 3 black balls. A ball is drawn at random. The probability that it is white is:A) 5/8B) 3/8C) 5/3D) 3/5
4. Q4.The line passing through (−2, 6) and (4, −3) has its x-intercept at:A) 2B) −2C) 4D) 0
5. Q5.If A = [[a, b], [c, d]], then the transpose of A is:A) [[a, c], [b, d]]B) [[d, −b], [−c, a]]C) [[a, b], [c, d]]D) [[d, c], [b, a]]
6. Q6.In a circle, the angle between a tangent and a chord drawn from the point of tangency equals:A) The angle in the alternate segmentB) Twice the angle in the alternate segmentC) Half the central angleD) 90°
7. Q7.If f(x) = x³ − 6x² + 11x − 6, then f(1) equals:A) 0B) 1C) −1D) 6
8. Q8.A man bought 200 shares of face value ₹10 at par. The company pays a dividend of 8%. His annual income is:A) ₹160B) ₹80C) ₹200D) ₹320
9. Q9.The value of sin 30° + cos 60° is:A) 1B) 0C) 1/2D) √3
10. Q10.A sphere has a surface area of 616 cm². Its radius is (use π = 22/7):A) 7 cmB) 14 cmC) 3.5 cmD) 21 cm
11. Q11.The mean proportional between 9 and 25 is:A) 15B) 17C) 12D) 20
12. Q12.If x ∈ W (whole numbers) and 2x − 3 < 5, the solution set is:A) {0, 1, 2, 3}B) {1, 2, 3}C) {0, 1, 2, 3, 4}D) {1, 2, 3, 4}
13. Q13.A shopkeeper sells goods worth ₹20,000 to a consumer. The CGST rate is 9%. The SGST charged is:A) ₹1,800B) ₹900C) ₹3,600D) ₹1,200
14. Q14.For the data 3, 5, 7, 9, 11, the variance is:A) 8B) 10C) 4D) 16
15. Q15.The equation of a line with slope 2 and y-intercept −3 is:A) y = 2x − 3B) y = −2x + 3C) y = 2x + 3D) 2x + y = 3
16. Q16.Solve: x² − 3x − 10 = 0. The roots are:A) x = 5 and x = −2B) x = −5 and x = 2C) x = 10 and x = −1D) x = −10 and x = 1
17. Q17.The first term of an AP is 5 and the common difference is 3. Find the 20th term.A) 62B) 65C) 60D) 58
18. Q18.Given A = [[3, −2], [5, 1]] and B = [[−1, 4], [2, −3]], find A + 2B.A) [[1, 6], [9, −5]]B) [[5, −10], [1, 7]]C) [[1, 6], [7, −5]]D) [[−1, 6], [9, 5]]
19. Q19.The line joining (1, 5) and (−4, −5) is divided by the y-axis in the ratio:A) 1:4B) 4:1C) 1:5D) 5:1
20. Q20.Using componendo-dividendo, if (3a + 4b)/(3a − 4b) = 2, find a/b.A) 4B) 12C) 4/3D) 12/1
21. Q21.An article is sold within the same state for ₹12,000. If CGST = SGST = 6%, the total tax paid is:A) ₹1,440B) ₹720C) ₹360D) ₹2,160
22. Q22.The following table shows daily wages:
    
    Wages (₹): 50-60, 60-70, 70-80, 80-90, 90-100
    Workers: 10, 18, 22, 17, 13
    
    The mean wage is:A) ₹74.75B) ₹75.00C) ₹73.50D) ₹76.00
23. Q23.A solid metal cylinder of radius 14 cm and height 21 cm is melted and recast into small spheres of radius 3.5 cm. The number of spheres is:A) 72B) 54C) 36D) 108
24. Q24.If tan A = 5/12, find (sin A + cos A) × sec A.A) 17/12B) 12/13C) 5/13D) 169/156
25. Q25.Numbers 1 to 15 are each written on separate cards. A card is drawn at random. The probability that the number is a perfect cube is:A) 2/15B) 1/15C) 3/15D) 4/15
26. Q26.Prove: cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A. The LHS simplifies to:A) 2 sec AB) 2 cosec AC) sec A + tan AD) 2(1 + sin A)/cos A
27. Q27.Find the area of the triangle formed by the line 2x + 3y = 12 with the coordinate axes.A) 12 sq unitsB) 6 sq unitsC) 24 sq unitsD) 8 sq units
28. Q28.A man invests equal amounts in two different companies. Company A has ₹100 shares at ₹120 paying 10% dividend. Company B has ₹50 shares at ₹75 paying 15% dividend. If the total annual income is ₹1,100, the amount invested in each company is:A) ₹3,600B) ₹7,200C) ₹1,800D) ₹5,400
29. Q29.A man deposits ₹600 per month for 2 years at 10% p.a. in a recurring deposit. His maturity value is:A) ₹15,900B) ₹14,400C) ₹16,200D) ₹15,600
30. Q30.If 3x − 5 ≤ x + 3 < 5x − 1, find x when x ∈ R.A) 1 ≤ x ≤ 4B) x > 1 and x ≤ 4C) 1 < x ≤ 4D) −1 ≤ x ≤ 4
31. Q31.Construct a △ABC with BC = 5 cm, ∠B = 60°, ∠C = 75°. To draw the incircle, you need to find the:A) Incentre by drawing angle bisectorsB) Circumcentre by drawing perpendicular bisectorsC) Centroid by drawing mediansD) Orthocentre by drawing altitudes
32. Q32.A boy 1.5 m tall stands at a distance of 24 m from a building. The angle of elevation of the top of the building from his eyes is 60°. The height of the building is:A) (24√3 + 1.5) mB) 24√3 mC) (24/√3 + 1.5) mD) 25.5 m
33. Q33.In the figure, PQ and PR are tangents from P to a circle with centre O. If ∠QPR = 70°, then ∠QOR is:A) 110°B) 70°C) 140°D) 35°
34. Q34.A tent is in the form of a cylinder of diameter 4.2 m and height 4 m, surmounted by a cone of equal base and height 2.8 m. The canvas required for the tent (in m²) is approximately:A) 75.36 m²B) 63.25 m²C) 80.50 m²D) 70.00 m²
35. Q35.Factorize: x³ − 6x² + 11x − 6.A) (x − 1)(x − 2)(x − 3)B) (x + 1)(x + 2)(x + 3)C) (x − 1)(x − 2)(x + 3)D) (x − 1)(x + 2)(x − 3)

Worked solutions from the ICSE 2016 paper

Start the test above to see visual step-by-step solutions for all 35 questions — free, with AI coaching when you get stuck.