CBSE Maths 2017

CBSE Class 10 Maths 2017 — all 30 questions from the paper

The complete question list from the CBSE 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.If the product of zeroes of the polynomial ax² − 6x − 6 is 4, find the value of a.A) -3/2B) 3/2C) -2/3D) 2/3
2. Q2.If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots, then find the value of p.A) 3B) 5C) 15D) 1
3. Q3.The first three terms of an AP respectively are 3y − 1, 3y + 5 and 5y + 1. Find the value of y.A) 5B) 3C) 4D) 2
4. Q4.In ΔPQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠QPR.A) 30°B) 45°C) 60°D) 90°
5. Q5.Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ. If ∠PTQ = 80°, find ∠OPQ.A) 40°B) 80°C) 50°D) 20°
6. Q6.A die is thrown once. Find the probability of getting a number less than or equal to 4.A) 1/3B) 2/3C) 1/2D) 5/6
7. Q7.Given that HCF(306, 657) = 9, find LCM(306, 657).A) 22338B) 22338C) 22338D) 22338
8. Q8.Show that the pair of equations 2x + 3y = 5 and 4x + 6y = 15 is inconsistent. What type of system is this?A) Consistent with unique solutionB) Consistent with infinitely many solutionsC) Inconsistent (no solution)D) Dependent
9. Q9.Which term of the AP 3, 15, 27, 39, ... will be 132 more than its 54th term?A) 65thB) 60thC) 68thD) 72nd
10. Q10.The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, −5) and R(−3, 6), find the coordinates of P.A) (16, 8)B) (−8, −4)C) (8, 4)D) (4, 2)
11. Q11.If sec4A = cosec(A − 20°) where 4A is an acute angle, find the value of A.A) 22°B) 20°C) 18°D) 25°
12. Q12.A solid metallic hemisphere of radius 8 cm is melted and recast into a right circular cone of base radius 6 cm. Find the height of the cone.A) 28.44 cmB) 32 cmC) 24 cmD) 18 cm
13. Q13.Prove that 3 + √5 is irrational, given that √5 is irrational.A) RationalB) IrrationalC) IntegerD) Whole number
14. Q14.Two taps running together can fill a tank in 3(1/13) hours. If one tap takes 3 hours more than the other to fill the tank, find the time each tap takes to fill the tank separately.A) 5 and 8 hoursB) 4 and 7 hoursC) 6 and 9 hoursD) 3 and 6 hours
15. Q15.Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.A) 10 notes of ₹50 and 15 notes of ₹100B) 15 notes of ₹50 and 10 notes of ₹100C) 5 notes of ₹50 and 20 notes of ₹100D) 20 notes of ₹50 and 5 notes of ₹100
16. Q16.If the sum of the first n terms of an AP is 3n² + 5n, find the AP and its 25th term.A) 8, 14, 20, ...; a₂₅ = 152B) 5, 11, 17, ...; a₂₅ = 149C) 8, 14, 20, ...; a₂₅ = 152D) 5, 8, 11, ...; a₂₅ = 77
17. Q17.If the centroid of triangle with vertices (a, −2), (7, b) and (−4, 8) is (4, −1), find a and b.A) a = 5, b = −9B) a = −5, b = 9C) a = 9, b = −5D) a = 5, b = 9
18. Q18.Prove that: (sinθ − cosθ + 1)/(sinθ + cosθ − 1) = 1/(secθ − tanθ).A) Uses sin²θ + cos²θ = 1B) Uses sec²θ − tan²θ = 1C) Uses cosec²θ − cot²θ = 1D) Uses 1 + cot²θ = cosec²θ
19. Q19.Prove that the tangent to a circle is perpendicular to the radius at the point of contact. Using this, if tangents PA and PB from P to a circle of radius 4 cm are inclined at 60°, find PA.A) 4√3 cmB) 8 cmC) 4 cmD) 2√3 cm
20. Q20.The following table gives the daily income of 50 workers:
    Income (₹): 100–120 (f=12), 120–140 (f=14), 140–160 (f=8), 160–180 (f=6), 180–200 (f=10). Find the mean daily income.A) ₹145.20B) ₹142.00C) ₹148.40D) ₹150.00
21. Q21.Find the values of k for which the quadratic equation (3k + 1)x² + 2(k + 1)x + 1 = 0 has equal roots.A) k = 0 or k = 1B) k = 1 or k = −1C) k = 0 or k = 3D) k = 2 or k = −1
22. Q22.Two dice are thrown at the same time. Find the probability of getting different numbers on both dice.A) 5/6B) 1/6C) 2/3D) 25/36
23. Q23.A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.A) 8 km/hB) 6 km/hC) 4 km/hD) 10 km/h
24. Q24.If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. Using this, in ΔABC, D is the midpoint of AB, E is a point on AC such that AE = (1/4)AC. If DE is produced to meet BC at F, find BF/BC.A) 2/3B) 1/3C) 1/2D) 3/4
25. Q25.The angles of depression of the top and bottom of a building 50 m high as observed from the top of a tower are 30° and 60° respectively. Find the height of the tower.A) 75 mB) 50 mC) 100 mD) 25(√3 + 1) m
26. Q26.A well of diameter 4 m is dug 21 m deep. The earth taken out is spread evenly all around the well to form a 3 m wide embankment. Find the height of the embankment.A) 4/3 mB) 2 mC) 3 mD) 7/3 m
27. Q27.The median of the following data is 525. Find the values of x and y if the total frequency is 100.
    Class: 0–100 (f=2), 100–200 (f=5), 200–300 (f=x), 300–400 (f=12), 400–500 (f=17), 500–600 (f=20), 600–700 (f=y), 700–800 (f=9), 800–900 (f=7), 900–1000 (f=4). The value of x is:A) 9B) 15C) 12D) 6
28. Q28.Two customers are visiting a shop in the same week (Monday to Saturday). Each is equally likely to visit on any day. What is the probability that both visit on the same day?A) 1/6B) 1/36C) 1/3D) 5/6
29. Q29.Prove that the diagonals of a trapezium divide each other proportionally. In trapezium ABCD with AB ∥ DC, if AB = 2DC and the diagonals intersect at O, then OA/OC is:A) 2B) 1/2C) 4D) 1
30. Q30.Find the area of the shaded region where ABCD is a square of side 14 cm and four equal semicircles are drawn inside. (Use π = 22/7)A) 42 cm²B) 56 cm²C) 28 cm²D) 84 cm²

Worked solutions from the CBSE 2017 paper

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