# CBSE CLASS-10 MARCH 2018

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1 CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four sections A, B, C and D. iii. Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks each. iv. There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and 3 questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. v. Use of calculator is not permitted. SECTION A 1. What is the value of cos sin In an AP, if the common difference (d) = 4, and the seventh term (a 7 ) is 4, then find the first term. 3. Given ABC ~ PQR, if AB PQ = 1 3, then find ar ABC ar PQR 4. What is the HCF of smallest prime number and the smallest composite number?

2 5. Find the distance of a point P(x, y) from the origin. 6. If x = 3 is one root of the quadratic equation x 2 2kx 6 = 0, then find the value of k. SECTION B 7. Two different dice are tossed together. Find the probability: i. Of getting a doublet ii. Of getting a sum 10, of the numbers on the two dice. 8. Find the ratio in which P(4,m) divides the line segment joining the points A(2,3) and B (6, -3). Hence find m. 9. An integer is chosen at random between 1 and 100. Find the probability that it is: i. Divisible by 8 ii. Not divisible by In the figure., 1 ABCD is a rectangle. Find the values of x and y. 11. Find the sum of first 8 multiples of Given that 2 is irrational, prove that ( ) is an irrational number. SECTION -C 13. If A(-2,1) B(a,0) C, (4,b) and D(1,2) are the vertices of a parallelogram ABCD, find the values of a and b

3 If A (-5,7), B (-4,-5), C (-1, -6) and D(4,5) are the vertices of quadrilateral, find the area of the quadrilateral ABCD. 14. Find all zeroes of the polynomial (2x 4 9x 3 + 5x 2 + 3x 1) is two of its zeroes are (2 + 3) and (2 3). 15. Find the HCF and LCM of 404 and 96 and verify that HCF x LCM = Product of two given numbers. 16. Prove that the length of tangents drawn from an external point to a circle are equal. 17. Prove that the are of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal. If the area of two similar triangles are equal, prove that they are congruent 18. A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase it speed 100km/h from the usual speed. Find its usual speed. 19. The table below shown the salaries of 280 persons:

4 Salary (In thousand) No. of persons Calculate the median salary of the data. 20. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig.2. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article. A heap of rice in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

5 21. Find the area of the shaded region in Fig.3, where arcs drawn with the centres A, B, C and D intersect in pairs at mid-points P,Q, R and S of the sides AB, BC, CD and DA respectively of a square of side 12 cm, [Use π = 3.14] 22. If 4 tan θ = 3, evaluate ( 4 sinθ cosθ+1 4 sinθ+cosθ 1 ) If tan 2A = cot(a 18 0 ) where 2A is an angle, find the value of A. SECTION D 23. A observed from the top of a 100 m high light house from the sealevel, the angles of depression of two ship are 30 0 and If one ship is exactly behing the other on the same side of the height house, find the distance between the two ships. [Use ]

6 24. The diameter of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find: (i) The area of the metal sheet used to make the bucket. (ii) Why we should avoid the bucket made by ordinary plastic? 25. Prove that sina 2 sin3 A = tan A 2Cos 3 A cos A 26. The mean of the following distribution is 18. Frequency f of the class Class Frequency F 5 4 The following distribution gives the daily income of 50 workers of a factory : Daily income No. of workers Convert the distribution to less that type cumulative frequency distribution and draw its ogive. 27. A motor boat whose speed is 18km/hr in still water 1 hr more to go 24 km upstream than to return down stream to the same spot. Find the speed of the stream. A train travels at a certain average speed for a distance and then travels at a distance of 72 km at an average speed of 6km/hr more

7 than its original speed. It it takes 3 hours to complete total journey, what is the original average speed? 28. The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15. Find the numbers. 29. Draw a triangle ABC with BC = 6 cm and AB = 5 cm and ABC = Then construct a triangle whose sides are 3 4 of the corresponding sides of the ABC. 30. In an equilateral ABC is a point on side BC such that BD = 1 3 BC. Prove that 9 (AD) 2 = 7 (AB) 2. Prove that, in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

### 2. In an AP. if the common difference (d) = -4, and the seventh term (a7) is 4, then find the first term.

CBSE Board Class X Set 3 Mathematics Board Question Paper 2018 Time: 3 hrs. Marks: 80 Note: Please check that this question paper contains 11 printed pages. Code number given on the right hand side of

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