Chap No.3 Groups mcqs with solution
Chap No.3 Groups
1)
The set N of natural numbers is
closed with respect to
A) Addition
B) Multiplication
C) Both
A & B
D) Subtraction
2)
The set Z of integers is closed
with respect to
A) Addition
B) Multiplication
C) Subtraction
D) A, B
and C are correct
3) The set R – {0} of real numbers is closed
with respect to
A) Addition
B) Multiplication
C) Division
D) A,B & C are correct
4)
In the set S = {0, 1} the binary
operation defined is
A) –
B) +
C) ´
D) ¸
5) The set S = {- 1, 1, - i, i} is a group
with respect to the binary operation
A) ¸
B) ´
C) +
D) –
6) The set S = {1, w, w2} is a group with
respect to the binary operation
A) ´
B) ¸
C) +
D) –
7) If set is a group with respect to
addition then the number of identity elements in S is
A) Unique
B) Two
C) Three
D) None
8) If set S is a group with respect to
addition then each element of S has _____ inverse.
A) Unique
B) Two
C) Three
D) None
9)
R – {0} is a group w.r.t the
binary operation
A) +
B) ´
C) ¸
D) –
10)
Q – {0} is a group w.r.t the binary
operation
A) +
B) ´
C) ¸
D) –
11)
R is a group w.r.t the binary
operation.
A) +
B) ´
C) ¸
D) –
12)
Q is a group w.r.t the binary
operation.
A) +
B) ´
C) ¸
D) –
13)
S = {1, - 1} is a group w.r.t the
binary operation.
A) +
B) ´
C) -
D) none
of these
14)
S = {0} is a trivial group under
A) +
B) ´
C) ¸
D) –
15)
S = {1} is trivial group under
A) +
B) ´
C) –
D) division
16) A non empty set S which is closed with a
binary operation ‘*’ is called group if
A) The
binary operation is associative
B) There
exists identity element with respect to the binary operation.
C) There
exist a unique inverse of each element of S with respect to the binary
operation.
D) All
A, B & C hold.
17) In a proposition if p→
q then q → p is called
A)
inverse of p→ q
B)
converse of p→ q
C)
contrapasitive p→ q
D)
none
18) Truth table containing all false values
is called
A) Tautology
B) Selfcontridiction
C) Equivallent
D) None
19) Truth table containing all true values
is called
A) Tautology
B) Selfcontridiction
C) Equivallent
D) None
20)
In a proposition if p→ q then
contrapasitive of this proposition is denoted by
A)
q
→ p
B)
~ q
→ p
C)
~ q
→ ~ p
D)
None
21)
In a proposition if p→ q then inverse of
this proposition is denoted by
A)
q
→ p
B)
~ q
→ p
C)
~ p
→ ~ q
D)
None
22)
In a proposition if p→ q then converse
of this proposition is denoted by
A)
q
→ p
B)
~ q
→ p
C)
~ q
→ ~ p
D)
None
Groups
1)
C
2)
D
3) D
4)
C
5) B
6) A
7) A
8) A
9)
B
10)
B
11)
A
12)
A
13)
B
14)
A
15)
B
16) D
17) B
18) Answer B
19) A
20) C
21) C
22) A
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