CBSE SAMPLE PAPER FOR Maths class10
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December 31, 2015 |
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SECTION A
1. Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is
(A) 0 only (B) 4
(C) 8 only (D) 0, 8
2. The list of numbers – 10, – 6, – 2, 2,... is
(A) an AP with d = – 16 (B) an AP with d = 4
(C) an AP with d = – 4 (D) not an AP
3. If the first term of an AP is –5 and the common difference is 2, then the sum of the first
6 terms is
(A) 0 (B) 5
(C) 6 (D) 15
4. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
(A) 4 cm (B) 5 cm
(C) 6 cm (D) 8 cm
5. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11: 14
6. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a
(A) square (B) rectangle
(C) rhombus (D) trapezium
7. A shuttle cock used for playing badminton has the shape of the combination of
(A) a cylinder and a sphere (B) a cylinder and a hemisphere
(C) a sphere and a cone (D) frustum of a cone and a hemisphere
8. A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called
(A) a frustum of a cone (B) cone
(C) cylinder (D) sphere
9. A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30 ° to the ground, where as for the elder children she wants to have a steep side at a height of 3 m, and inclined at an angle of 60 ° to the ground. What should be the length of the slide in each case?
10. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out
(i) an orange flavoured candy? (ii) a lemon flavoured candy?
11. John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.
12. Which term of the A.P. 3, 8, 13, 18, … is 78?
13. Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding side of ΔABC. Give the justification of the construction.
14. Find the area of a quadrant of a circle whose circumference is 22 cm.
15. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboids.
16. Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.
17. Check whether (5, − 2), (6, 4) and (7, − 2) are the vertices of an isosceles triangle.
18. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) She will buy it? (ii) She will not buy it?
19. Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(I) 2x2 + kx + 3 = 0 (II) kx (x − 2) + 6 = 0
20. Show that a1, a2 … , an , … form an AP where an is defined as below
(i) an = 3 + 4n (ii) an = 9 − 5n
Also find the sum of the first 15 terms in each case.
21. A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that AB + CD = AD + BC
23. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
24. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle. Give the justification of the construction.
25. A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
26. Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of ΔABC.
(i) The median from A meets BC at D. Find the coordinates of point D.
(ii) Find the coordinates of the point P on AD such that AP: PD = 2:1
(iii) Find the coordinates of point Q and R on medians BE and CF respectively such that BQ: QE = 2:1 and CR: RF = 2:1.
(iv) What do you observe?
(v) If A(x1, y1), B(x2, y2), and C(x3, y3) are the vertices of ΔABC, find the coordinates of the centroid of the triangle.
27. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
28. Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on
(i) the same day? (ii) consecutive days? (iii) different days?
29. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
30. Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
31. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
32. A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)
33. A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.
34. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m. from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.
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