CBSE X
Delhi
MATHS PAPER 2011
Time allowed: 180 minutes; Maximum Marks: 90
General Instructions: | |
1) | All questions are compulsory. |
2) | The question paper consists of thirty questions divided into 4 sections A, B, C and D. Section A comprises of ten questions of 01 mark each, Section B comprises of five questions of 02 marks each, Section C comprises ten questions of 03 marks each and Section D comprises of five questions of 06 marks each. |
3) | All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question. |
4) | There is no overall choice. However, internal choice has been provided in one question of 02 marks each, three questions of 03 marks each and two questions of 06 marks each. You have to attempt only one of the alternatives in all such questions. |
5) | In question on construction, drawing should be near and exactly as per the given measurements. |
6) | Use of calculators is not permitted. |
1. The point P which divides the line segment joining the points A (2, −5) and B (5, 2) in the ratio 2:3 lies in the quadrant _______.
2. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by ____.
3. In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to
4. The roots of the equation${x}^{2}$+ x − p (p + 1) = 0, where p is a constant, are ______.
5. Which of the following can not be the probability of an event?
6. The mid-point of segment AB is the point P(0, 4). If the coordinates of B are (−2, 3) then the coordinates of A are
7. In figure 2, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is _______.
8. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 45°. The height of the tower (in metres) is _______.
9. In an A.P., if a =−10, n = 6 and${a}_{n}$= 10, then the value of d is _________.
10. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is __________.
11. In figure 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi-circles of diameter 14 cm each. Find the perimeter of the shaded region.[ Use π = $\frac{22}{7}$]
OR
Find the area of a quadrant of a circle, where the circumference of circle is 44 cm. [ Use π = $\frac{22}{7}$]
12. Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger circle, of length 48 cm, touches the smaller circle. Find the value of r.
13. Find the values(s) of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.
14. Find whether − 150 is a term of the A.P. 17, 12, 7, 2,…?
15. Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
16. Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3:4.
17. Find the value of k so that the quadratic equation kx (3x − 10) + 25 = 0, has two equal roots.
18. A coin is tossed two times. Find the probability of getting not more than one head.
19. In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21${\mathrm{cm}}^{2}$, then find the lengths of sides AB and AC.
20. Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.
OR
A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
21. If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex.
OR
Find the value of k, if the points P(5, 4), Q(7, k) and R (9, −2) are collinear.
22. Find the roots of the following quadratic equation:
2$\sqrt{3}{x}^{2}$−5x +$\sqrt{3}$= 0
23. Find the value of the middle term of the following A.P.:
−6, −2, 2, …, 58.
OR
Determine the A.P. whose fourth term is 18 and the differences of the ninth term from the fifteenth term is 30.
24. Find the area of the major segment APB, in Fig 5, of a circle of radius 35 cm and ∠AOB = 90°. [Use π = $\frac{22}{7}$]
25. From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the cars. [Use $\sqrt{3}$= 1.73]
26. The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm ( r < 14 cm). If the volume of the bucket is 5390 ${\mathrm{cm}}^{3}$, then find the value of r. [ Use π = $\frac{22}{7}$]
27. Draw a triangle ABC with side BC = 7 cm,∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are $\frac{3}{5}$ times the corresponding sides of △ABC.
28. If P(2, 4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance PQ.
29. Prove that the lengths of tangents drawn from an external point to a circle are equal.
30. A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.
OR
Find the roots of the equation $\frac{1}{x+4}$-$\frac{1}{x-7}$= $\frac{11}{30}$, x ≠ − 4 , 7.
31. If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.
OR
Find the sum of the first 30 positive integers divisible by 6.
32. From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 10 m high building are 30° and 60° respectively. Find the height of the tower.
33. Find the area of the shaded region in Fig. 6, where arcs drawn with 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 ABCD, where the length of each side of square is 14 cm. [ Use π = $\frac{22}{7}$]
34. A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 21 cm and 40 cm respectively, and the height of cone is 15 cm, then find the total surface area of the toy. [π = 3.14, be taken]