VIDYA BHARATI SCHOOL

ASSIGNMENT (2017-18) MAY

CLASS-XI MATHS

Chapter 1 Sets

1. Which of the following collection of objects is a set?

a) A collection of popular leaders of the country.

b) Student of class XI of a particular school.

c) All days of a week beginning with T.

d) A collection of most dangerous animals of the world.

2. Write the following set in Roster form

a) Set of letters of the word TRIGONOMETRY.

b) Set of prime factor of 60.

c) {x: x N and 2x-3≤15}

d) {x: x>x and x R}

e) *

+

3. Write the following set in set Builder form

a) A ={1,5,10,15………..}

b) B={14,21,28,35,……….98}

c) *

+

d) *

+

e) Z = {-1,1}

4. If A B then find AB and A B.

5. Show that n{ P[P ( P() )]} =4

6. If A and B are two sets such that n(A) = 3 and n(B)=6. Find:

i. Minimum value of n(AB) ii. Find maximum value of n(AB)

7. Describe the set {0} in set builder form.

8. Write the set *

+ in set builder form.

9. If n(U)=40 , n(A B)= 31. Find n(A’ B’)

10. Let A = {2,4,6}, B ={3,5} and C={1,2,4,7} and U={1,2,3,4,5,6,7}. Verify

a) A-(B C) = (A-B) (A-C)

b) A (B-C) = (A B) - (A C)

c) (A-B) (B-A) = (AB) – (AB)

d) (AB)’ = A ‘ B’

e) (A B)’ = A’ B’

f) A – (B-C) = (A-B) (A C)

11. In a group of 950 persons, 750 can speak Hindi and 480 can speak English. Find:

i. How many can speak both Hindi and English?

ii. How many can speak Hindi only?

iii. How many can speak English only?

12. In a group of 84 persons each play at least one game out of three viz tennis, badminton and

cricket, 28 of them play cricket, 40 play tennis and 48 play badminton. If 6 play both cricket

and badminton and four play tennis and badminton and no one play all the three games. Find

the number of persons who play cricket but not tennis.

13. In a survey of 25 students it was found that 15 had taken Mathematics, 12 had taken Physics

and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken

Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three

subjects. Find the number of students that had:

i. Only Chemistry v. Only mathematics

ii. Only Physics vi. At least one of the three subject

iii. Physics and Chemistry vii. Mathematics and Physics but not

but not Mathematics Chemistry

iv. Only one of the subject viii. None of the subjects

14. In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy

newspaper B, 10% families buy newspaper C. 5% buy newspapers A and B, 3% buy newspaper

B and C, 4% buy newspaper A and C. If 2% buy all the three newspapers, find the number of

families which buy:

i. A only

ii. B only

iii. None

15. In an examination 80% students passed in mathematics, 72% passed in Science and 13% failed

in both the subjects. If 325 students passed in both subjects , find the total number of students

who appeared in the examination.

16. In a group of 40 students, 26 take samosa, 18 take burger and 8 take neither of the two. How

many take both samosa and burger? Is taking samosa and burger good for health?

17. 35 children of a class draw a world map. 26 use blue colour and some use green colour. If 19

use both the colours and each student uses at least one colour, find the number of children

who use the green colour. In a map, blue colour represents water and green colour represents

the trees. Why should we preserve water and trees?

18. In a town of 10000 families, it was found that 40% families buy newspaper X, 20% families buy

newspaper Y and 10% families buy newspaper Z, 5% families buy X and Y , 3% buy Y and Z and

4% buy X and Z. if 2% families buy all the three papers, find the number of families which buy

(i) X only (ii) Y only (iii) none of X, Y, and Z

19. Two finite sets have m and n elements. The number of elements in the power set of first set is

48 more than the total number of elements in the power set of the second set then the value

of m and n are?

20. A and B are two sets such that ( ) ( ) and ( ) . Draw

venn diagram to illustrate this information. If ( ) ( ) find (i)the value of x (ii) ( ).

VIDYA BHARATI SCHOOL

ASSIGNMENT (2017 – 18) MAY

CLASS-XI MATHS

CHAPTER 3

TRIGONOMETRIC FUNCTIONS

1. Prove that sin (-420) cos (390) + cos (-660) sin (330) = -1.

2. Prove that ( ) ( ) ( )

( ) ( ) ( ) .

3. Prove that tan 70° = 2 tan 50° + tan 20°

4. Prove that : tan 30° + tan 15° + tan 30°.tan 15° = 1.

5. Find the value of sin 150° + cos 300°. 6. A horse is tied to a post by a rope. If the horse moves along a circular path, always

keeping the rope tight and describes 88 meters when it has traced out 72 at the centre. Find the length of the rope.

7. Show that √ √ √ = 2 cos.

8. Solve the equation sin2 + sin4 + sin6 = 0.

9. Solve the equation tan+tan2+3tan tan2 = 3.

10. Solve 7 cos2 + 3 sin2

= 4.

11. Solve the equation 3 sin x – cos x = 2.

12. Prove that

13. A wheel makes 500 revolutions per minute. How many radians it turns in one second.

14. Prove that

15. Find the angle between the minute hand and the hour hand of a clock when the time is 5:20.

16. If tan(+)=n tan (-), show that (n+1) sin 2 = (n-1) sin 2.

17. Prove that Cos5A= 16cos5A – 20cos3A + 5cosA

18. Find the value of sin18, cos18, sin36, cos36. 19. Prove that

(

) (

) (

) (

)

20. Prove that

( ) ( )

21. Prove that

22. Prove that

(

) (

) (

) (

)

23. Prove that cos20 cos40 cos60 cos80=

.

24. Prove that sin10 sin30 sin50 sin70 =

.

25. IF and , show that,

(i) ( )

(ii) ( )

26. Find the maximum and minimum values of the following expressions:

(i) (

) (ii) 4

27. If

√

, prove that

.

28. If

, prove that one value of

.

29. Find the value of .

30. Prove that:

.