CBSE Maths 2018

CBSE Class 10 Maths 2018 — all 30 questions from the paper

The complete question list from the CBSE Class 10 Mathematics 2018 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 2018 paper

1. Q1.If the HCF of 65 and 117 is expressible in the form 65m − 117, then the value of m is:A) 2B) 1C) 3D) 4
2. Q2.Find the value of k so that the quadratic equation 3x² − kx + 38 = 0 has two equal roots.A) ±√456B) ±√(456)C) ±√114D) ±19√2
3. Q3.What is the common difference of the AP 1/p, (1−p)/p, (1−2p)/p, ... ?A) 1B) 1/pC) −1D) −p
4. Q4.In ΔABC, right-angled at B, AB = 5 cm and ∠ACB = 30°. Find the length of BC.A) 5√3 cmB) 10 cmC) 5/√3 cmD) 10√3 cm
5. Q5.If a number x is chosen at random from the numbers −3, −2, −1, 0, 1, 2, 3, what is the probability that x² ≤ 4?A) 3/7B) 5/7C) 4/7D) 6/7
6. Q6.If the midpoint of the line segment joining A(3, 4) and B(k, 6) is P(x, y) and x + y = 10, find the value of k.A) 7B) 5C) 3D) 9
7. Q7.Find the zeroes of the polynomial 4s² − 4s + 1 and verify the relationship.A) 1/2 and 1/2B) 1 and 1C) −1/2 and −1/2D) 1/4 and 1
8. Q8.Find the value of p for which the system 2x + py = −5 and 3x + 3y = −6 has a unique solution.A) p ≠ 2B) p = 2C) p ≠ 3D) p = 3
9. Q9.Find the sum of the first 8 multiples of 3.A) 108B) 96C) 120D) 84
10. Q10.In the given figure, ΔABC is an equilateral triangle with side 2a. Find the length of the altitude AD.A) a√3B) 2a√3C) a√2D) a
11. Q11.If sin(A + B) = 1 and cos(A − B) = √3/2, where 0° ≤ A + B ≤ 90° and A ≥ B, find A and B.A) A = 60°, B = 30°B) A = 45°, B = 45°C) A = 75°, B = 15°D) A = 90°, B = 0°
12. Q12.The tangent at point C of a circle and a diameter AB when extended meet at P. If ∠PCA = 110°, find ∠CBA.A) 20°B) 30°C) 40°D) 70°
13. Q13.Prove that √3 is irrational. Using this, prove that 2 + 5√3 is irrational.A) RationalB) IrrationalC) IntegerD) Whole number
14. Q14.Find the zeroes of the polynomial p(x) = x² − x − 6 and verify the relationship between zeroes and coefficients.A) 3 and −2B) −3 and 2C) 6 and −1D) −6 and 1
15. Q15.Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. Find the speeds of the two cars.A) 60 km/h and 40 km/hB) 70 km/h and 30 km/hC) 50 km/h and 50 km/hD) 80 km/h and 20 km/h
16. Q16.A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in ₹) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ₹90, find the number of articles produced.A) 6B) 5C) 10D) 15
17. Q17.The first and last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find the number of terms and the common difference.A) n = 16, d = 8/3B) n = 10, d = 40/9C) n = 20, d = 40/19D) n = 16, d = 40/15
18. Q18.If the ratio of the sum of the first n terms of two APs is (7n + 1) : (4n + 27), find the ratio of their mth terms.A) (14m − 6) : (8m + 23)B) (7m + 1) : (4m + 27)C) (14m + 1) : (8m + 27)D) (7m − 6) : (4m + 23)
19. Q19.Find the area of a triangle formed by the points A(5, 2), B(4, 7) and C(7, −4).A) 2 sq unitsB) 1 sq unitC) 4 sq unitsD) 3 sq units
20. Q20.Prove that: tanθ/(1 − cotθ) + cotθ/(1 − tanθ) = 1 + secθcosecθ. The expression equals:A) 1 + tanθ + cotθB) 1 + secθcosecθC) secθ + cosecθD) 2 + tanθcotθ
21. Q21.PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at point T. Find the length TP.A) 20/3 cmB) 10/3 cmC) 16/3 cmD) 8/3 cm
22. Q22.The following distribution gives the daily income of 50 workers:
    Income (₹): 200–250 (f=12), 250–300 (f=14), 300–350 (f=8), 350–400 (f=6), 400–450 (f=10). Find the mean income using the assumed mean method.A) ₹295B) ₹305C) ₹310D) ₹285
23. Q23.A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 48 minutes less. Find the original speed of the train.A) 45 km/hB) 40 km/hC) 50 km/hD) 36 km/h
24. Q24.In ΔABC, the bisector of ∠B meets AC at D. A line through C parallel to BD meets AB extended at E. Prove that BD/CE = AD/DC. If AB = 6 cm, AC = 8 cm, find BD : CE given AD : DC = AB : BC. Find BC.A) BC cannot be determined from given infoB) BC = 4 cmC) BC = 10 cmD) BC = 12 cm
25. Q25.From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.A) 3(√3 + 1) mB) 3(√3 − 1) mC) 3√3 mD) 6 m
26. Q26.A container shaped like a right circular cylinder having radius 6 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and radius 3 cm having a hemispherical shape on the top. Find the number of such cones which can be filled.A) 10B) 12C) 15D) 8
27. Q27.The following frequency distribution shows the monthly consumption of electricity of 68 consumers:
    Usage (units): 65–85 (f=4), 85–105 (f=5), 105–125 (f=13), 125–145 (f=20), 145–165 (f=14), 165–185 (f=8), 185–205 (f=4). Find the median.A) 137 unitsB) 140 unitsC) 135 unitsD) 142 units
28. Q28.A game consists of tossing a one-rupee coin 3 times and noting its outcome each time. Hanif wins if all tosses give the same result (three heads or three tails) and loses otherwise. What is the probability of Hanif losing?A) 3/4B) 1/4C) 1/2D) 7/8
29. Q29.Points A(−1, y) and B(5, 7) lie on a circle with centre O(2, −3y). Find the values of y and hence the radius of the circle.A) y = −1, r = √(9 + 64) = √73B) y = 1, r = √10C) y = −1, r = √(9 + 16) = 5D) y = −1, r = √(9 + 64)
30. Q30.If the polynomial x⁴ − 6x³ + 16x² − 25x + 10 is divided by (x² − 2x + k), the remainder is (x + a). Find k and a.A) k = 5, a = −5B) k = 7, a = −3C) k = 3, a = −7D) k = 5, a = 5

Worked solutions from the CBSE 2018 paper

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