ICSE Maths 2017

ICSE Class 10 Maths 2017 — all 35 questions from the paper

The complete question list from the ICSE Class 10 Mathematics 2017 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 2017 paper

1. Q1.The discriminant of 3x² − 2x + 1/3 = 0 is:A) 0B) 4C) −4D) 8/3
2. Q2.The maturity value of a recurring deposit of ₹250 per month for 2 years at 10% p.a. is ₹6,000 + Interest. The interest earned is:A) ₹625B) ₹600C) ₹650D) ₹500
3. Q3.Two dice are thrown together. The probability of getting the same number on both dice is:A) 1/6B) 1/3C) 1/36D) 5/36
4. Q4.The slope of the line passing through (0, 0) and (−3, 3) is:A) −1B) 1C) 0D) Undefined
5. Q5.If A = [[2, x], [0, 1]] and B = [[1, 0], [3, 1]], and AB = [[8, 2], [3, 1]], then x is:A) 1B) 2C) 3D) 4
6. Q6.If the tangent from point P to a circle with centre O makes an angle of 30° with OP, then the angle between the two tangents from P is:A) 30°B) 60°C) 90°D) 120°
7. Q7.If x − 1 is a factor of x² − 5x + k, then k equals:A) 4B) −4C) 6D) −6
8. Q8.₹100 shares at ₹120 means the shares are:A) At a premium of ₹20B) At a discount of ₹20C) At parD) Below par by ₹120
9. Q9.If cosec θ = √2, then θ equals:A) 30°B) 45°C) 60°D) 90°
10. Q10.The total surface area of a cube of side 4 cm is:A) 96 cm²B) 64 cm²C) 48 cm²D) 16 cm²
11. Q11.If x/3 = y/4, then (4x − 3y)/(4x + 3y) equals:A) 0B) 1C) 7/24D) 1/7
12. Q12.The greatest integer x such that 2(x + 3) < 3x + 5, x ∈ Z, and x ≤ 5 is:A) 5B) 4C) 3D) 1
13. Q13.Mr. Sinha is a registered dealer. He buys raw material for ₹50,000 (plus GST at 18%) and sells finished goods for ₹80,000 (plus GST at 18%). His tax liability is:A) ₹5,400B) ₹14,400C) ₹9,000D) ₹3,600
14. Q14.If the first quartile (Q₁) of a data set is 20 and the third quartile (Q₃) is 50, the interquartile range is:A) 30B) 70C) 35D) 15
15. Q15.The coordinates of the point which divides the line segment joining (2, 3) and (7, 8) internally in the ratio 2:3 are:A) (4, 5)B) (5, 6)C) (3, 4)D) (4.5, 5.5)
16. Q16.Solve: 3x² − 11x + 10 = 0 by factorization. The roots are:A) x = 2 and x = 5/3B) x = −2 and x = −5/3C) x = 5 and x = 2/3D) x = 10/3 and x = 1
17. Q17.The sum of the first 10 multiples of 6 is:A) 330B) 300C) 360D) 390
18. Q18.If A = [[1, 3], [2, 4]] and B = [[1, 2], [3, 4]], is AB = BA?A) No, AB ≠ BAB) Yes, AB = BAC) Only if A = BD) Cannot be determined
19. Q19.Find the equation of the line through (2, −1) and parallel to the line joining (3, 4) and (−2, 1).A) 3x − 5y − 11 = 0B) 3x + 5y − 11 = 0C) 5x − 3y − 11 = 0D) 3x − 5y + 11 = 0
20. Q20.If a/b = c/d = e/f, prove that each ratio = (a + c + e)/(b + d + f). This is called:A) Addendo propertyB) Alternendo propertyC) Componendo propertyD) Subtrahendo property
21. Q21.A dealer in Delhi supplies goods worth ₹6,000 to a dealer in Agra. If IGST is 28%, the amount to be paid by the dealer in Agra is:A) ₹7,680B) ₹7,080C) ₹6,840D) ₹7,200
22. Q22.The mean of the following distribution is 15.5. Find the missing frequency p.
    
    Class: 0-5, 5-10, 10-15, 15-20, 20-25, 25-30
    Frequency: 2, 7, p, 10, 3, 1
    
    The value of p is:A) 7B) 8C) 5D) 6
23. Q23.A solid iron pole is in the shape of a cylinder surmounted by a cone. The height of the cylinder is 220 cm and the cone is 60 cm. The radius is 7 cm. The total weight if 1 cm³ of iron weighs 8 g is approximately:A) 311.52 kgB) 280 kgC) 350 kgD) 400 kg
24. Q24.Evaluate without tables: 2 tan²45° + cos²30° − sin²60°.A) 2B) 3C) 1D) 0
25. Q25.Cards numbered 3 to 27 are placed in a box. A card is drawn at random. The probability that the number is a perfect square is:A) 3/25B) 4/25C) 1/5D) 2/25
26. Q26.Prove: √((1 + sinA)/(1 − sinA)) = secA + tanA. The LHS can be simplified by multiplying by:A) √((1 + sinA)/(1 + sinA))B) √((1 − sinA)/(1 − sinA))C) cosA/cosAD) secA/secA
27. Q27.The coordinates of A are (−2, 3) and B is (4, 1). Find the equation of the perpendicular bisector of AB.A) 3x − y − 1 = 0B) 3x + y − 1 = 0C) x − 3y + 1 = 0D) x + 3y − 1 = 0
28. Q28.A man invests ₹5,000 in ₹100 shares at par paying 6% dividend. He sells when the shares are at ₹110 and reinvests in ₹50 shares at ₹55 paying 8%. The change in income is:A) Increase of ₹100B) Decrease of ₹100C) No changeD) Increase of ₹200
29. Q29.Mrs. Goswami deposits ₹1,000 per month for 1 year in a recurring deposit at 8% p.a. Her maturity value is:A) ₹12,520B) ₹12,000C) ₹12,480D) ₹12,960
30. Q30.Given: 15 − 7x > 2x − 27, x ∈ N. The smallest value of x is:A) 1B) 2C) 3D) 5
31. Q31.Construct a △ABC with AB = 5 cm, BC = 6 cm, and ∠ABC = 60°. Draw the circumscribed circle. What is the first step after constructing the triangle?A) Draw perpendicular bisectors of two sidesB) Draw angle bisectorsC) Draw altitudesD) Draw medians
32. Q32.From a point on the ground, the angles of elevation of the bottom and top of a transmission tower on a 20 m building are 45° and 60° respectively. The height of the tower is:A) 20(√3 − 1) mB) 20√3 mC) 20(√3 + 1) mD) 40 m
33. Q33.In a circle with centre O, ∠BAC = 40° where BC is a chord. The ∠BOC (central angle) is:A) 80°B) 40°C) 20°D) 100°
34. Q34.Rain water is collected in a conical vessel of diameter 5.6 m and depth 3 m. It is poured into a cylindrical vessel of diameter 2.8 m. The water level rises to:A) 1 mB) 2 mC) 3 mD) 4 m
35. Q35.Factorize x³ − 2x² − 5x + 6 completely.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 2017 paper

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