SAMPLE PAPER PAPER
CLASS -X (MATHEMATICS)
Time : 3 Hours M.M.80
GENERAL INSTRUCTIONS :
1. All questions are compulsory.
2. There are four section A,B, C and D
3. Section A contains 10 questions of 1 mark each
4. Section B contains 5 questions of 2 marks each
5. Section C contains 10 questions of 3 marks each and
6. Section D contains 5 questions carrying 6 marks each
7. There is one internal choice in section B, three in section C and two in section D.
8. Use of calculator and mobile phone is not permitted
SECTION A
1. What is the nature of roots of quadratic equation 4x2 – 12x+9 = 0?
2. Find perimeter of the given shaded region.
3. The length of tangent from a point A at a distance of 5cm from centre of a circle is 4cm. What will be radius of the circle?
equal to the height of the tower.
4. A bag contains 5 red and 5 black balls. A ball is drawn at random from the bag. What is the probability of getting a red ball?
5. What is the distance between two parallel tangents of a circle of radius 4cms?
6. The height of a tower is 10m. Find the altitude of sun if the shadow of the tower is
SECTION B
7. From pocket money, child saves Re 1 first day, Re 2 second day, Re 3 third day and so on in a month. How much money will the child save in the month of February 2008?
8. All the Queens, Jacks and diamonds have been removed from a pack of 52 cards. The remaining cards have been reshuffled and a card is drawn at random. Find the probability that it is a 1) face card 2) black card.
1. Find the value of x for which the distance between the points P (2,-3) and Q (x,5) is 10 units.
SECTION C
10. How many terms of the AP 24, 21, 18, …………….must be taken so that thesum is 78? Explain the double answer.
11. The sum of the first 30 terms of an AP is equal to the sum of its first 20 terms.Show that the sum of the first 50 terms of the same AP is zero.
12. A boy chimbing a hill covers 60 m during the first minute, 54 m during thesecond minute and 48 m during the next miunte and so on. How many
metres will he climb in the eighth minute? Also find the distance climbed by
him in 8 minutes.
13. Find the ratio in which the join of the points (3, -1) and (8, 9) is divided by the line y – x + 2 = 0
14. Find the third vertex of a triangle if its two vertices are (- 1,4) and (5,2) and midpoint ofone side is (0,3).
15. Show that the points (5, 6), (1, 5), (2, 1) and (6, 2) are the vertices of a square.
16. It is proposed to add to a square lawn of side 42 m, two circular ends. The centre of each circle being the point of intersection of the diagonals of the square. Find the area of the whole lawn.
17. Prove that the opposite sides of a quadrilateral circumscribing a circle subtend a pair of supplementary angles at the centre of the circle.
SECTION D
18. The sum of first n terms an A.P is 3n2 +n. Find the A.P and also the nth term.
OR
Find the sum of all three digit number which leave remainder 3 when divided by 5.
19. Find out if the points A (-3,2), B (1,-3) and C (4,1) are the vertices of an isosceles right.
20. In what ratio does the points P (2,-5) divide the line segment joining
A(-3 ,5) and B (4,-9).
21. Construct a right angled ∆ABC right angled at B with AB =4cms and BC=6cms. Now draw a circle with AB as diameter. From C, draw tangents to this circle.
OR
Construct a right angled ∆ABC in which AB=4cms, BC=6cms and <ABC=60° such that each side of new triangle is 4/3 of the corresponding side of ∆ABC.
22. In the given figure, AB, AC and PQ are tangents to a circle and AB=5 cm. Find the perimeter of ∆APQ.
23. Find the area and perimeter of the shaded region in figure given below, where AP=PQ=QR=14 cm.
24. Two ships sailing on the sea are on either side of the light house. The angles of depression of the two ships as observed from the top of the light house are 60° and 45° respectively. If the distance between the two ships is
25. From the top of the tower, the angles of depression of two object on the same side of tower are a & b, (where a >b). If the distance between the objects are x m, show that height of the tower is
26. A group of girls planned a picnic. The budget for food was Rs.2400. Due to illness, 10 girls couldn’t go to the picnic and cost of food for each girl increased by Rs.8. How many girls had planned for picnic?
27. A train travels 360 km at a uniform speed. If the speed of the train had been 5 km / hr more, it would have taken one hour less for the same journey. Find the original speed of the train.
28. The slant height of a frustum of a cone is 4cm and the perimeters of its circular ends are 18cm and 6cm. Find the curved surface area of the frustum.