Download Maths-XI

DELHI PUBLIC SCHOOL
BOKARO STEEL CITY
ASSIGNMENT FOR THE SESSION 2009-2010
Subject : Mathematics
Class : XI
1.
2.
Assign. No. 1
Write the following sets in the Roster form :
a.
A = { x/x is an integer , -3/2 < x < 11/2 }
b.
B = { x/x > x }
c.
C = { x/x is a prime number and divisor of 60 }
d.
D= { x/x = n/(n +1) , where n  W }
e.
E= { x/x is a letter of word ‘ BANANA’}
Write the following sets in set builder form:
a. A = {1, 2, 3, 6, 9, 18}
b. B = {-4,-3,-2,-1, 0, 1, 2, 3, 4}
c. C = {0}
d. D = { }
3.
(a)
How many subsets are there in case of a set having n elements? Write all possible
subsets of (i) A = { 1,2,3} (ii) B = { -1,0,1,2 }.
(b)
Find the number of proper subsets of a set having 8 elements.
4.
Find the smallest set A such that A  {1,2 } = { 1,2,3,5,9 }.
5.
If U = { a,b,c,d,e,f,g } , A = { a,b,c,d } and B = { b,d,f,g }
Verify that: (i) (AU B)’ = ( A’ C B’) (ii)( A  B)’ = ( A’ U B’)
(iii) A  ( B U C ) = (A  B) U (A  C )
6.
Draw appropriate Venn diagram for (AUB) ∩ C. If U= {x/x is a natural number less than 10},
A= {x/x is an odd natural number less than 10}, B= {x/x is an even natural number less than 10}
and
C= {x/x is a first five natural number}.
7.
If X and Y are two sets such that n(X U Y) = 60%, n(X) = 40%,
if n(X U Y) = 300.
8.
Without using the Venn diagram find the number of people who read at least one newspaper in a
group of 600 people , it was found that 250 people read X, 260 read Y and 260 read Z , 90 read X
and Z ,110 read X and Y , 80 read Y and Z and 30 read all.
9.
In a school there are 320 students. Out of these 90 play hockey, 50 play cricket and 65 play
football. It is also known that 11 play both football and cricket, 8 plays both cricket and hockey
and 10 play both football and hockey. If 7 students play all the three games, find the number of
students who do not play any of these three games.
10.
IF A = {1, 2}, B = {1, 2, 3, 4} and C = {5, 6} then
Verify that Ax (B – C) = (AxB) – (A x C).
11.
(a)
(b)
n(Y)
= 30% then find n(X/Y)
Give an example to show that (BxA)  ( A x B).
All equal sets are equivalent but the converse is not necessarily true. Give an example to
justify the statement.
1
12.
If X and Y are two sets such that n(X U Y) = 70%, n(X) = 50%, n(Y) = 30% then find n(X/Y) if
n(X U Y) = 420.
13.
IF A = {1, 2}, B = {1, 2} and C = {3, 4, 5, 6} then
Verify that Ax (B – C) = (AxB) – (A x C).
14.
The Cartesian product of AxA has 9 elements among which are found (-1, 0) and
the set A and the remaining elements of AxA.
15.
If A = {2, 3, 4, 5, 6, 7, 8}. Let R be a relation on A defined as
{(a, b): a, b  A and b
exactly divisible by a}
(i) Write R in roster form
(ii) Find the domain and range of R
16.
(a) Let f = {(1,1), (2,3),(0,-1 ),(-1,-3)}be a linear function from Z to Z. Find f(x).
x2
(b) Let f = {(x,
): x εR} be a function from R to R. Determine the range of f.
1 x2
17.
If A = {1} then write A x A x A.
18.
N is the set of natural numbers. f is a function as f : N → N and
f (x) = 3x2 – 4x +1. If f(x) = 0 then find the value of x.
19.
If f(x) = x3, find
20.
Find the domain of f(x) =
21.
(a) Find the domain and range of the function f(x) =
f (1.1)  f (1)
.
(1.1  1)
1 x2
(b) If f(x) = 
2
1 x
1
.
x  7x  6


3
x4
x4
.

 Show that f (tanθ) = sec4θ.

22.
If x = cosec (- 14100) then find x.
23.
Evaluate: cot 150.
24.
If cosx + cos2x = 1 then find the value of (sin2x + sin4x).
25.
The radian measure of 37030’30’’.
26.
If sinA = (3/5), find cosA and tanA where (∏/2 <A<∏).
27.
If tanB = (-3/4), find cosA and sinA where (3∏/2 <B<2∏).
28.
If sinA = (5/12), find (cosA + tanA) where (∏/2 <A<∏).
29.
If sinx + sin2x = 1, evaluate cos12x + 3cos10x + 3 cos8x + cos6x.
30.
Evaluate: (i) sin 11200 (ii) cos7500 (iii) tan21300 (iv) tan (-21150).
--------------x--------------
2
(0, 1). Find
is