Mathematics

Sample Paper - 2


GENERAL INSTRUCTIONS


All questions are compulsory.
The question paper consist of 30 questions divided into four sections A, B, C and D. Section A comprises of 6 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 of 8 questions of 4 marks each.
There is no overall choice.
Use of calculator is not allowed.




SECTION-A

(1 mark each)
1. What will be perimeter of a regular pentagon of side 3 cm?
Simplify :  ab  c   2abc
2
2.
3. Show that 500 is not a perfect square.
4. Factorise: lx  my  mx  ly
5. Express each of the following in standard form :
(a) The mass of a proton in gram is
1673
1000000000000000000000000000

(b) A Helium atom has a diameter of 0.000000022 cm.
6. If the division N  5 leaves a remainder of 4, what might be the one's digit of N? Suppose that the division N  5
leaves a remainder of 4 and the division N  2 leaves a remainder of 1. What must be the one's digit of N?



SECTION-B

(2 marks each)
7. Find the volume of a cube whose surface area is 150 m . 2

8. The population of a place increased to 54,000 in 2003 at a rate of 5% per annum
(a) Find the population in 2001.
(b) What would be its population in 2005?
9. Find the multiplicative inverse of the following:
13
(a) 13 (b)
19
1 5 3
(c) (d) 
5 8 7

, 1 1
10. If x   7, then find the value x 2  2 .
x x
11. Simplify:
(a)  pcr p 2
 q2  r 2 
(b) ( px  qy)(ax  by)
12. The area of a rectangular field is 48 m2 and one of its sides is 6 m. How long will a lady take to cross the field
diagonally at the rate of 20 m/minute?



SECTION-C


(2  x)(7  x)
13. Solve for x : 1
(5  x)(4  x)
14. (a) Construct a quadrilateral BLUE in which BL = 5.3 cm, BE = 2.9 cm, B  70, L  95 and U  85.
(b) A student attempted to draw a quadrilateral PLAY, where PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm,
LY = 6 cm, but could not draw it. What is the reason?
15. (a) In a lottery, there are 10 prizes and 20 blanks. A ticket is chosen at random, what is the probability of getting a
prize?
(b) Study the following pictograph and answer the questions given below it.




(i) How many cars were produced in the month of July?
(ii) In which month were maximum number of cars produced?
16. A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. How long will it take when the car
travels at the speed of 80 km/h ?
35 105 125
17. (a) (9)3  (9)8 (b)
57  65
18. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. find the quantity of milk in litres that
can be stored in the tank?




19. The ratio of radii of two cylinders 1: 2 and heights are in ratio 2: 3. The ratio of their volumes is?
20. Factorise
(a) x2  xy  8x  8 y

, (b) 15xy  6 x  5 y  2


(c) ax  bx  ay – by
21. Three numbers in the ratio 2:3: 4. The sum of their cubes is 0.334125. Find the numbers.
22. Find the following square by using the identities
(a) (b  7)2 (b) ( xy  3z )2
2
2 3 
(c) (6 x 2  5 y)2 (d)  m  n 
3 2 
(e) (0.4 p  0.5q)2 (f) (2 xy  5 y)2


SECTION-D

(4 marks each)
23. (a) Water is poured into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3,
find the number of hours it will take to fill the reservoir.
(b) If the radius and height of the cylindrical tank are 7 m and 10 m, find the capacity of the tank.
24. In a hypothetical sample of 20 people, the amount of money (in thousands of rupees) with each was found to be as
follows :
114,108,100,98,101,109,117,119,126,131,136,143,156,169,182,195, 207, 219,235,118.
Draw a histogram of the frequency distribution, taking one of the class interval as 50  100.
25. Find using distributivity.
 7  3    7 5 
(a)         
 5  12    5 12 


 9 4   9 3 
(b)       
16 12  16 9 
26. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs. 50 per metre and trouser
material that costs him Rs. 90 per metre. For every 3 metres of the shirt material he buys 2 metres of the trouser
material. He sells the materials at 12% and 10%, respectively. His total sale is Rs. 36,600. How much trouser material
did he buy?
27. Using identities evaluate :
(a) 712 (b) 992 (c) 1022 (d) 9982 (e) 5.22

(f) 297  303 (g) 78  82 (h) 8.92
28. Diagram of the adjacent picture frame has outer dimensions = 24 cm  28 cm and inner dimensions 16 cm  20
cm. Find the area of each section of the frame, if the width of each section is same.