NCERT CBSE 10th Mathematics Pre-Board Question Paper (2018-19)
Time: 3 hours
Subject Code: 041
- All questions are compulsory.
- This question paper consists of 30 questions divided into four Sections – A, B, C and D.
- 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. Section D contains 8 questions of 4 marks each.
- 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.
- Use of calculators is not permitted.
Question numbers 1 to 6 carry 1 mark each.
Question: 1. Write whether on simplification given an irrational or a rational number.
Question: 2. If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, find the values of a and b.
Question: 3. If one root of 5x² + 13 x + k = 0 is the reciprocal of the other root, then find value of k.
Question: 4. If ΔABC ∼ ΔQRP, ar(ΔABC) / ar(ΔQRP) = 9/4, and BC = 15 cm, then find PR.
Question: 5. A(5, 1); B(1, 5) and C(-3, -1) are the vertices of ΔABC. Find the length of median AD.
Question numbers 7 to 12 carry 2 marks each.
Question: 7. Given that √3 is an irrational number, prove that (2+√3) is an irrational number.
Question: 8. X is a point on the side BC of ΔABC. XM and XN are drawn parallel to AB and AC respectively meeting AB in N and AC in M. MN produced meets CB produced at T. Prove that TX² = TB × TC
Question: 9. In fig. (1), ABC is a triangle in which ∠B = 90°, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle.
Question: 10. Find the linear relation between x and y such that P(x,y) is equidistant from the points A(1, 4) and B(-1, 2).
Question: 11. A, B, C are interior angles of ΔABC. Prove that cosec(A+B/2) = sec C/2
Question: 12. A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the ratio between radius of their bases to their height is 3:4.
Question numbers 13 to 22 carry 3 marks each.
Question: 13. Using Euclid’ division algorithm find the HCF of the numbers 867 and 255.
Question: 14. Divide 27 into two parts such that the sum of their reciprocals is 3/20.
Question: 15. In an A.P id sum of its first n terms is 3n² and its kth term is 164, find the value of k.
Question: 16. If coordinates of two adjacent vertices of a parallelogram are (3, 2), (1, 0) and diagonals bisect each other at (2, -5), find coordinates of the other two vertices. OR If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units, find x.
Question: 17. In fig. (2) AB is a chord of length 8 cm of a circle of radius 5 cm. The tangents to the circle at A and B intersect at P. Find the length of AP.
OR Prove that the lengths of lengths of tangents drawn from an external point to a circle are equal.
Question: 18. Construct a triangle with sides 6 cm, 8 cm and 10 cm. Construct another triangle whose sides are 3/5 of the corresponding sides of original triangle.
Question: 19. Prove that
Question: 20. The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 48 hours. OR The side of a square is 10 cm. Find the area between inscribed and circumscribed circles of the square.
Question: 21. If sin (A + 2B) = √3/2 and cos (A+ 4B) = 0, A > B, and A + 4B < 90°, then find A and B.
Question: 22. By changing the following frequency distribution ‘to less than type’ distribution, draw its ogive.
Question number 23 to 30 carry 4 marks each.
Question: 23. For what values of m and n the following system of linear equations has infinitely many solutions. 3x + 4y = 12 (m + n) x + 2 (m – n) y = 5m – 1
Question: 24. Obtain all zeroes of 3x4 – 15x3 + 13x2 + 25x – 30, if two of its zeroes are √5/3 and – √5/3.
Question: 25. A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of slower train is 10 km/hr less than of faster train, find the speeds of two trains.
Solve for x
Question: 26. Prove that the ratio of the areas of two similar triangle is equal to the ratio of the squares of their corresponding sides.
Question: 27. The angle of elevation of the top a hill at the foot of a tower is 60° and the angle of depression from the top of tower to the foot of hill is 30°. If tower is 50 metre high find the height of the hill.
Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point in between them on the road, the angles of elevation of the top of poles are 60° and 30° respectively. Find the height of the poles and the distances of the from the poles.
Question: 28. A man donates 10 aluminum is of height 20 cm and has its upper and lowest ends of radius 36 cm and 21 cm respectively. Find the cost of preparing 10 buckets if the cost of aluminum sheet is Rs. 42 per 100 cm2. Write your comments on the act of the man.
Question: 29. Find the mean and mode for the following data: