# Central Board Secondary Examination(CBSE) – Maths Sample Paper (class 10) 2013-14

##### Time allowed : 3 hours            Maximum Marks :90

General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A,B,C and D . Section
A comprises of 8 questions of 1 mark each , section B comprises of 6 questions of 2 marks
each, section C comprises of 10 questions of 3 marks each and section D comprises 10
questions of 4 marks each.
(iii) Questions numbers 1 to 8 in section –A are multiple choice questions where you are to
select one correct option out of the given four.
(iv) There is no overall choice. However, internal choices have been provided in 2 questions of
three marks each. You have to attempt only one of the alternatives in all such questions.
(v) Use of calculation is not permitted.

SECTION –A

Note : Question numbers 1 to 8 carry one mark each. For each question, four alternative choices
have been provided of which only one is correct. You have to select the correct choice.

1. Value of K for which sum of the roots of the equation 3×2–(3x-2)x–(k-6)=0 is equal to the
product of its roots then
a) 1          b) -1          c) 0          d) 2

2. The perimeter of the triangle formed by the points (0,0) , (1,0) , (0,1) is
a) 1 +v2   b) v2 +1     c) 3     d) 2 +v2

3. The probability of guessing the correct answer to certain question is P/12 , if the probability of
not guessing the correct answer to the same question is ¾ then the value of P is
a) 4     b)2     c) 3     d) 1

4. If p( -1,1) is the midpoint of the line segment joining A (-3 , 6) and B (1, b+4) , then b is
a) 1     b) -1    c) 2    d) 0

5. The area of two circle are in the ratio 4 : 9 , the ratio of their circumference is
a) 2 :3 b) 3 :2 c) 4 :9 d) 9:4

6. The no. of two digits that are divisible by 6 is
a) 12 b) 16 c) 15 d) 18

7. The angle of depression of an object from a 60m high tower is 30O. The distance of the object
from the tower is
a) 20v3 m     b) 60v3m     c) 40v3m      d) 120m

8. A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical
balls of diameter 6 cm each. The no of balls formed is
a) 16     b) 24     c) 32      d) 28

SECTION – B (2 marks)

9. If the roots of the equation (a-b)x2+(b-c) x + (c-a)= 0 are equal , Prove that b+c = 2a.

10. For what value of P are (2P+1), 13,(5P-3) three consecutive terms of an A.P.

11. A quadrilateral ABCD is drawn to circum scribe a circle , Prove that AB + CD = AD + BC.

12. Find the distance between the points ( 5 sin60,0) and (0,5sin30).

13. If tangents AB and AC from a point A to a circle with centre O are inclined to each other at an
angle of 700,then Find ?AOB .

SECTION – C (3 marks)

15. Find two consecutive positive integers , the sum of whose squares is 25.

16. If 10 limes the 10th term of an A.P is equal to 15 times the 15th term , show that its 25th term is
zero.
(i) What is the relation between a and d.
(ii) Prateek declares that 25th term of the A.P is non zero , do you agree? Which
value of Prateek is depicted by his declaration.

17. A 1.5 m tall boy stands at a distance of 3m from a lamp post and cast a shadow of 4.5 m on the
ground. Find the height of the lamp post .

18. The curved surface area of a cylindrical pillar is 264 m2
and its volume is 924 m3, Find the height
of the pillar.

19. A person on tour has Rs.360 for his expenses . If he extends his tour for 4 days , he has to cut
down his daily expenses by Rs.3. Find the original duration of the tour.

20. Draw a circle of radius 4.2cm. Draw a pair of tangents to this circle inclined to each other at an
angle 50 o.

21. For what value of P for which the points (-5 ,1) , (1, P) and (4 ,-2) collinear .

OR

The line segment joining the points A(3,2) , B(5,1) is divided at the point P in the ratio of 1:2
and P lies on the line 3x – 18y + k =0 , Find the value of k ?

22. A bag contains 6 red balls and some blue balls. If the probability of drawing blue ball from the
bag is twice the probability of drawing a red ball, Find the no. of blue balls.23. If the radii of the ends of a buckets are 5cm and 15 cm and 24cm high , Find its surface area. (?
=3.14)

SECTION –D (4 marks)

25. The sum of the area of two squares is 640 m2
. If the difference in their perimeter is 64 m , Find
the sides of the two squares.

26. Find the sum of first 25 items of an A.P whose nth term is given by an =7 – 3n.

27. Prove that the tangents drawn from an external point of a circle are equal.

28. The angle of elevation of a jet fighter from a point A on the ground is 60. After a flight of 15
seconds, the angle of elevation changes to 30. If the jet is flying at a constant height of
1500v3m find
(i) The horizontal distance between the two positions of the jet plane .
(ii) The speed of the jet plane in km/h
(iii) Hari guesses that the speed of the jet plane is 720km/h ,how do you appreciate
his guess , What is the value you have learnt from his guess ?

29. A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel, partly filled with water.
The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water,
by how much will the level of water rise in the cylindrical vessel.

30. In what ratio in the line segment joining the points A (-6,3) and B (-2,-5) divided by the y axis .
Also find the co-ordinates of the point of division.

31. A bag contains 11 ,12,13,14 ………30 tickets. A ticket is taken out from the bag at random. Find the probability that number on the drawn ticket is
(a) Multiple of 7
(b) Greater than 15 and a multiple of 5.

32. The area of an equilateral triangle is 49v3 cm2 . Taking each angular point as centre , circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. ( v3 = 1.73 , ?= 22/7)33. A toy is the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm ,
(i) Find the slant height of the conical part.
(ii) Write the formulas used in this solution.
(iii) Find the total surface area of the toy.
(iv) David says that the height of the conical portion is an even number, is he true?
Which value is seen by his statement?