SET - A

MT EDUCARE LTD.QUEST - I (Semi Prelim I)

(2017-18)Portion : Real Numbers, Polynomials, Introduction to Trigonometry, Triangles,Linear equations in two variable, Probability, Some application of Trigonometry,

and Co-ordinate Geometry

CBSE - X

• Please check that this question paper contains 5 printed pages.• Code number given on the right hand side of the question paper should be

written on the title page of the answer-book by the candidate.• Please check that this question paper contains 30 questions.• Please write down the serial number of the question before attempting it.

MATHEMATICS

General Instructions:i) All questions are compulsory.

ii) The question paper consists of 30 questions divided in 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,

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 three questions of 4 marks each. You have to attempt

only one of the alternnatives in all such questions.

v) Use of calculator is not permitted.

Time allowed : 3 hours Maximum Marks : 80

Series RLH

Roll No. Code No. 31/1

SET - A

SECTION - AQuestion number 1 to 6 carry 1 marks each.

1. Evaluate :sec 35º

cosec 55º.

2. One letter of English alphabet is chosen at random. Find the probabilitythat the letter chosen precedes p.

3. Express 5005 as a product of primes.

4. Given : DE || BCTo Find : EC

5. Find the area of triangle formed by the points A(5, 2), B(4, 7) and C(7, –4).

6. Tower AB stands vertically on the ground. From a pointC on the ground which is 15 m away from the foot B ofthe tower, the angle of elevation of the top A of the toweris found to be 60º. Find the height of the tower.

SECTION - BQuestion number 7 to 12 carry 2 marks each.

7. Find the values of y for which the distance between the points A(3, –1) andB(11, y) is 10 units.

8. Solve the pair of linear equations by substitution method:

x – y = 3;3x

+2y

= 6.

9. The HCF of two numbers is 16 and their product is 3072. Find their LCM.

10. Evaluate :2 2

2 2

sin 63º sin 27ºcos 17º cos 73º

.

... 2 ...

B C

D E

A

1.5

cm

1 cm

3 cm

A

B C60º

15 m

SET - A... 3 ...

11. In the adjoining figure, DE AC and DF AE.

Prove thatBF BE=FE EC

12. Five cards-the ten, jack, queen, king and ace of diamonds are wellshuffled with their face downwards. If the queen is drawn and put aside,what is the probability that the second card picked up is:(a) an ace (b) a queen

SECTION - CQuestion numbers 13 to 22 carry 3 marks each.

13. Find the co-ordinates of the points trisection of the line segmentjoining (4, –1) and (–2, –3).

14. The angle of elevation of the top of a building from the foot of a tower is30o and the angle of elevation of the top of tower from the foot of thebuilding is 60o. If the tower is 50 m, find the height of the building.

OR

14. A tree breaks due to the storm and the broken part bends so that thetop of the tree touches the ground making an angle of 300 with it. Thedistance from the foot of the tree to the point where the top touchesthe ground is 8 metres. Find the height of the tree.

15. On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainderwere x – 2 and –2x + 4 respectively. Find g(x).

16. The sum of the digits of a two digit number is 9. Also, nine times numberis twice the number obtained by reversing the order of thedigits. Find the number.

OR

16. The area of a rectangle gets reduced by 9 square units, if its length isreduced by 5 units and breadth is increased by 3 units. If we increasethe length by 3 units and the breadth by 2 units, the area increases by67 square units. Find the dimensions of the rectangle

17. Prove that the area of an equilateral triangle described on one side of asquare is equal to half the area of the equilateral triangle described onone of its diagonals.

A

D

B F E C

SET - A... 4 ...

18. If AD and PM are medians of ABC and PQR respectively where

ABC ~ PQR then prove thatAB AD=PQ PM .

19. Prove thatcos A – sin A + 1cos A + sin A – 1

= cosec A + cot A using the identity

cosec2A = 1 + cot2A.

OR

19. Prove the following : (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A

20. A die is thrown twice. What is the probability that:(i) 5 will not come up either time (ii) 5 will come up at least once

OR

20. A box contains 90 discs which are numbered from 1 to 90. If one disc isdrawn at random from the box, find the probability that it bears(i) a two - digit number (ii) a perfect square number(iii) a number divisible by 5

21. Find the value of k for which the given system has no solution:3x – 4y + 7 = 0; kx + 3y – 5 = 0

22. Divide 3x2 – x3 – 3x + 5 by x – 1 – x2 and verify by division algorithm.

SECTION - DQuestion numbers 23 to 30 carry 4 marks each.

23. In an equilateral triangle ABC, D is a point on side BC such that BD =1BC3

.

Prove that 9AD² = 7AB².

24. Aftab tells his daughter “Seven years ago, I was seven times as old asyou were then. Also, three years from now, I shall be three times as youwill be”. Represent this situation algebraically and graphically.

OR

24. Roohi travels 300 km to her home partly by train and partly by bus. Shetakes 4 hours if she travels 60 km by train and the remaining by bus. Ifshe travels 100 km by train and the remaining by bus, she takes 10minutes longer. Find the speed of the train and the bus separately.

SET - A

25. A straight highway leads to the foot of a tower. A man standing at the topof the tower observes a car at an angle of depression of 30o, which isapproaching the foot of the tower with a uniform speed. Six secondslater, angle of depression of the car is found to be 60o. Find the timetaken by the car to reach the foot of the tower from this point.

OR25. The angle of elevation of the top of a tower from two points at a distance

4m and 9m from the base of the tower and in the same straight line withit are complementary. Prove that the height of tower is 6m.

26. Prove that if a line is parallel to a side of a triangle and it intersects theother two sides in distinct points then the other two sides are divided inthe same ratio.

27. Use Euclid’s division lemma to show that the cube of any positive integeris of the form 9m, 9m + 1 or 9m + 8.

28. Name the type of quadrilateral formed, if any, by the points (–3, 5), (3, 1),(0, 3), (–1, –4). Give reasons for your answer.

29. Solve the pair of equations by reducing them to pair of linear equations:

13x y

+1

3 –x y =34

;1

2(3 )x y –

12(3 – )x y

= –18

OR

29. Solve :7 – 2x y

xy = 5;8 + 7x y

xy = 15

30. A 1.5 m tall boy is standing at some distance from a 30 m tall building.The angle of elevation from his eyes to the top of building increases from30o to 60o as he walks towards the building. Find the distance he walkedtowards the building. ( 3 = 1.73)

All the Best

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