Mathematics - Set Theory Relations and Mappings
Exam Duration: 45 Mins Total Questions : 30
If X and Y are two sets, then \((X\sim Y)\cup (Y\sim X)\)equals
- (a)
\(X\cup Y\)
- (b)
\(X\cap Y\)
- (c)
\((X\cup Y)\sim (X\cap Y)\)
- (d)
none of these
Which of the following is empty set?
- (a)
\(\{ \varphi \} \)
- (b)
{0}
- (c)
\(\{ x:x>0\wedge x<0\} \)
- (d)
\(\{ x:x>0\vee x<0\} \)
,A2,A3,.........,A with three elements.Furthereachre n sets a thirty sets each with five elements and Bare1,B2,B3,......Bn 30\(\overset { 30 }{ \underset { i=1 }{ \cup } } { A }_{ i }=\overset { n }{ \underset { j=1 }{ \cup } } B_{ j }=s\) and each element of S belongs to exactly ten Ai' s and exactly 9 of Bj's.Then value of n is
Suppose A1- (a)
30
- (b)
40
- (c)
45
- (d)
none of these
If \(X=\left\{ { 8 }^{ n }-7n-1:n\epsilon N \right\} \) and \(Y=\left\{ 49\left( n-1 \right) :n\epsilon N \right\} \) , then
- (a)
X C Y
- (b)
Y C X
- (c)
X = Y
- (d)
None of these
Which of the following cannot be the number of elements in the power set of any finite set?
- (a)
26
- (b)
32
- (c)
64
- (d)
128
If R and S are two symmetric relations. Then,
- (a)
RoS is a symmetric relation
- (b)
SoR-1 is a symmetric relation
- (c)
RoS-1 is a symmetric relation
- (d)
RoS is a symmetric relation iff RoS = SoR
If (x+3, 4-y)=(1,7), then (x-3, 4+y) is equal to
- (a)
(-2,-3)
- (b)
(-5,1)
- (c)
(3,4)
- (d)
(1,5)
If A={1,2,4}, B={2,4,5}, C={2,5}, then (A-C)x(B-C) is equal to
- (a)
{(1,4)}
- (b)
{(1,4),(4,4)}
- (c)
{(4,1),(4,4)}
- (d)
{(1,2)(2,5)}
Which of the following sets is a finite set?
- (a)
A = {x:x ∈ Z and x2-5x+6=0}
- (b)
B={x:x ∈Z and x2 is even}
- (c)
D = {x:x ∈ Z and x > -10}
- (d)
All of these
Which of the following sets are equal?
(i) A = {1,2,3}
(ii) B = {x ∈ R : x2-2x+1=0}
(iii) ={1,2,2,3}
(iv) D={x∈R : x3-6x2+11x-6=0}
- (a)
A=B=C
- (b)
A=C=D
- (c)
A=B=D
- (d)
B=C=D
Ax(B∩C)=
- (a)
{(1,3), (1,4), (1,5), (2,5), (2,4), (3,3), 93,6), (3,4)}
- (b)
{(1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6)}
- (c)
{(2,4), (3,3), (3,4), (3,5), (3,6)}
- (d)
None of these
If number of elements in sets A and B are m and n respectively, then the number of relations from A to B is
- (a)
2m+n
- (b)
2mn
- (c)
m+n
- (d)
mn
Which of the following is a universal set?
- (a)
Set of all points in xy-plane
- (b)
Set R of real numbers
- (c)
Set N of natural numbers
- (d)
All of these
If R is the relation 'less than' from A={1,2,3,4,5} to B={1,4,5}, then the set of ordered pairs corresponding to R is
- (a)
{(1,4), (1,5), (2,5), (3,5), (4,5)}
- (b)
{(1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (4,5)}
- (c)
{(5,2), (4,5), (5,3), (5,2), (5,1)}
- (d)
None of these
Let A={x,y,z} and B={1,2}. The number of relations from A to B is
- (a)
64
- (b)
32
- (c)
16
- (d)
28
If A and B are two sets, then A∩(A-B) is equal
- (a)
A
- (b)
B
- (c)
Φ
- (d)
None of these
The set (AUBUC) ∩ (A∩B'∩C')∩C' is equal to
- (a)
B∩C'
- (b)
A∩C
- (c)
B'∩C'
- (d)
none of these
If f(x)=x2-x-2, x∈R-{0}, then \(f(\frac{1}{x})\) is equal to
- (a)
f(x)
- (b)
-f(x)
- (c)
\(\frac{1}{f(x)}\)
- (d)
(f(x))2
From 50 student taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 21 Physics and 43Chemistr. At most 29 passed Mathematics and Chemistry and at most 20 passed Physics and Chemistry. The largest possible number that could have passed three examinations is
- (a)
11
- (b)
12
- (c)
13
- (d)
14
In a certain town, 25% families own a cell phone and 15% own a scooter and 65% families own neither a cell phone nor a scooter. If 2000 families own both a cell phone and a scooter, then the total number of families in the town is
- (a)
10,000
- (b)
20,000
- (c)
30,000
- (d)
40,000
Fill in the blanks.
(i) The P of an element x under a relation R is given by, where (x,y)∈R.
(ii) The Q of R is the set of all first elements of the ordered pairs in a relation R.
(iii) The R of the relation R is the set of all second elements of the ordered pairs in a relation R.
(iv) An S is a visual representation of a relation.
- (a)
P Q R S domain range domain arrow diagram - (b)
P Q R S range domain image arrow diagram - (c)
P Q R S image domain range arrow diagram - (d)
P Q R S image range domain arrow diagram
If f(x)=ax+b, where a and b are integers, f(-1)=-5 and f(3)=3, then a and b are equal to
- (a)
a=-3, b=-1
- (b)
a=2, b=-3
- (c)
a=0, b=2
- (d)
a=2, b=3
Statement I: If the set A has 5 elments and set B={1,2,3}, then number of elements in AxB=15.
Statement II: Number of elements in AxB=3n2 , where n is the sum of number of elements in A and B.
- (a)
If both Statement I and Statement II are true and Statement II is the correct explanation of Statement I
- (b)
If both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I.
- (c)
If Statement I is true but Statement II is false
- (d)
If Statement I is false and Statement II is true.
Statement I: Let f and g be two real functions given by f={(0,1), (2,0), (3,-4), (4,2), (5,1)} and g={(1,0), (2,2), (3,-1), (4,4), (5,3)}. Then domain of f.g is given by {2,3,4,5}
Statement II: Let f and g be two real functions. Then, (f.g)(x)=f{(g(x)}.
- (a)
If both Statement I and Statement II are true and Statement II is the correct explanation of Statement I
- (b)
If both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I.
- (c)
If Statement I is true but Statement II is false
- (d)
If Statement I is false and Statement II is true.
If there are three athletic teams in a school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 15 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is
- (a)
42
- (b)
43
- (c)
45
- (d)
32
Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science, 6 in English and Mathematics, 7 in Mathematics and Science, 4 in English and Science; 4 in all the three passed. Then
(i) The number of students passed in English and Mathematics but not in Science is
(ii) The number of students only passed in Mathematics is
(iii) The number of students passed in more than one subject is
- (a)
(i) (ii) (iii) 1 3 2 - (b)
(i) (ii) (iii) 2 3 9 - (c)
(i) (ii) (iii) 3 2 9 - (d)
(i) (ii) (iii) 2 9 3
Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in the plane. Then F1 may be equal to
- (a)
F2∩F3
- (b)
F3∩F4
- (c)
F2UF5
- (d)
F1UF2UF3UF4
If X={8n-7n-1|n∈N} and Y={49n-49|n∈N}. Then
- (a)
X⊂Y
- (b)
Y⊂X
- (c)
X=Y
- (d)
X∩Y=ф