CBSE X Summative Assessment: 2011
Subject – Mathematics
SECTION: A Question number 1 to 10 contains1 mark each. For each of the
questions 1- 10 four alternative choices have been given of which only one is
correct. You have to select the correct choice
1. The sum of first seven multiples of 5 is :
2. which of the following quadratic equations has the product of its roots as
(a) 2x square -3x +6 = 0
(b) x square – 3x + 6 = 0
(c) Root 2x square – 3/root 2 x + 1 = 0
(d) 3x square – 3x +3 = 0
3. From a point Q, the length of the tangent to a circle is 24 cm and the
distance of Q from the centre is 25 cm. Then the radius of the circle is :
(a) 12 cm
(b) 10 cm
(c) 9 cm
(d) 7 cm
4. Two concentric circles are of radii 5 cm. The length of the chord of the
larger circle which touches the smaller circle is :
(a) 4 cm
(b) 8 cm
(c) 6 cm
5. A hollow sphere of external and internal and internal diameters 8cm and 4
cm respectively, is melted into a cone of base radius 4 cm. Then height of the
circular cone is :
(a) 15 cm
(b) 10 cm
(c) 14 cm
(d) 16 cm
6. A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the
bag at random. the probability that the drawn ball is red, is :
7. If the ratio of the circumferences of two circles is 3 : 1 , then the radio
of their areas is :
(a) 1: 9
(b) 9 : 1
(c) 3 : 1
(d) 1 : 3
8. The volume of the largest right circular cone that can be cut our from a
cube of edge 21cm is :
(a) 1155 cm cub
(b) 577.5 cm square
(d) 2425.5 cm cub
(d) 2400 cm cub
9. If angle between two radii of a circle is 125 degree, the angle between
the tangents at the ends of the radii is :
(a) 90 degree
(b) 50 degree
(c) 55 degree
(d) 40 degree
10. IF P (E) = 0.07, then the probability of ‘ not E’ is:
SECTION – B
11. A poorv throws two die once and computed the product of the numbers
appearing on the dice. Peeehu throws one die and squares the number that appears
on it. Who has the better chance of getting the number 36 ?
18 cards, numbered 1,2,3,………… , 18 are put in a box and mixed th0roughly. A card
is drawn at random from the box. Find the probability that the card drawn bears
(i) an even number
(ii) a number divisible by 2 or 3.
12. Find the roots of the following quadratic equation z square – 11/4 z
+ 15/8 =0
13. Find the area of a ring shaped region enclosed between two concentric
circles of radii 20 cm and 15 cm.
14. The seventh term of an A.P. is 34 and 15th term is 74. Determine its
15. Prove that the tangent at any point of a circle is perpendicular to
the radius through the point of contact.
16. The volume of a cylinder is 448 PI cm cub and height 7cm. Find its
lateral surface area.
17. The center O of a circle has the coordinates (4, 5) and one point on
the circumference is (8, 10). Find the coordinates of the other end of the
diameter of the circle through this point.
18. Show that the point P (1, 2) lies on the line segment joining the
points A ( -2, 3 ) and B ( 7, 0)
19. Prove that opposite sides of a quadrilateral circumscribing a circle
subtends supplementary angles at the center of the circle.
20. Draw a line segment AB of length 8 cm. Taking A as center, drawn a
circle of radius 4 cm and taking B as centre, draw another another circle of
radius 3 cm. Construct tangents to each circle from the center of the other
21. Find the roots of the equation : a/ax-1 + b/bx – 1 = – (a+b) ; x does
not equal 1/a, 1/b
22. A hemispherical bowl of internal radius 9 cm is full of liquid. The
liquid is to be filed into cylindrical shaped bottles each of radius 1.5 cm and
height 4 cm. How many bottles are needed to empty the bowl ?
23. A man on the deck of a ship is 12 m above the water level. He
observes that the angle of elevation of the top of a cliff is 45 degree and the
angle of depression of the base is 30 degree Calculate the distance of the cliff
from the ship and the height of the cliff.
24. If A (1, 2), B (4, 3) and C (6,6) are the three vertices of a
parallelogram ABCD , find the coordinates of the fourth vertex D.
25. Point P divides the line segment joining the points A (2 ,1) and (5 ,
8), such that AP : AB = 1 : 3 If P lies on the line 2x – y + k = 0, find the
value of k.
26. Cards bearing numbers 1, 3, 5, ……35 are kept in a bag. A card is
drawn at random from the bag . Find the probability of getting a card bearing :
(i) a prime number less than 15
(ii) a number divisible by 3 and 5
27. Find the 31st tern of an A.P. whose 11th term is 38 and the 16th term
28. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and angle
=90 degree . BD is the perpendicular from B on AC. The circle through B,C,D, is
drawn. Construct the tangents from A to this circle.
29. Find two consecutive odd positive integers sum of whose square is
30. A train traveling at a uniform speed for 360 km/h would have taken 48
minutes less to travel the same distance if its speed were 5 km/h more. Find the
original speed of the train.
31. Solve the equation :- 4 + ( -1) + 2 + …..+ x = 437
32. A bucket is in the form of frustum of cone. Its depth is 24 cm and
the diameters of the top and the bottom ends are 30 cm 10 cm respectively. Find
the capacity of bucket.
33. In a right triangle ABC, right angled at B, a circle is drawn with AB
as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the
circle at P bisects BC.
34. An aero plane left 30minutes later than its schedule time, and in
order to reach its destination 1500 km aways in time, it has to increase its
speed by 250 km/h from its usual speed. Determine its usual speed.