MCQ Binary Operations ISC Class-12 Ch-3 Maths for Semester-1 . These MCQ / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Physics.
MCQ Binary Operations Chapter-3 for ISC Class-12 Maths of Semester-1
Board | ISC |
Class | 12th (XII) |
Subject | Maths |
Chapter-3 | Binary Operations |
Syllabus | on bifurcated syllabus (after reduction) |
bifurcated pattern |
Semester-1 |
Session | 2021-22 |
Topic | MCQ / Objective Type Question |
ISC Maths Class-12 of Semester-1 MCQ Binary Operations Chapter-3
Question 1
If a*b = a2 + b2, then the value of (4*5) * 3 is
(a) (42+ 52) + 32
(b) (4 + 5)2+ 32
(c) 412+ 32
(d) (4 + 5 + 3)2
Solution :- option (c ) 412+ 32
Question 2
If a * b denote the bigger among a and b and if a ⋅ b = (a * b) + 3, then 4.7 = __________ .
(a) 14
(b) 31
(c) 10
(d) 8
Solution :- option (c) 10
Hint :- 4.7 = (4 * 7) + 3
= 7 + 3
= 10
Question 3
On the power set P of a non-empty set A, we define an operation ∆ by
X∆Y=(X―∩Y)∪(X∩Y―)
Then which are of the following statements is true about ∆.
(a) commutative and associative without an identity
(b) associative but not commutative without an identity
(c) commutative but not associative with an identity
(d) associative and commutative with an identity
Solution :- option (d) associative and commutative with an identity
Hint:-
Question-4
If the binary operation * on Z is defined by a * b = a2 − b2 + ab + 4, then value of (2 * 3) * 4 is ____________ .
(a) 233
(b) 33
(c) 55
(d) -55
Solution option (c) 33
Question-5
Mark the correct alternative in the following question:-
For the binary operation * on Z defined by a * b = a + b + 1, the identity element is
(a) 0
(b) -1
(c) 1
(d) 2
Solution option (b) -1
Question-6
If a binary operation * is defined on the set Z of integers as a * b = 3a − b, then the value of (2 * 3) * 4 is ___________ .
(a) 2
(b) 3
(c)4
(d) 5
Solution :- option (d) 5
Question-7
Q+ denote the set of all positive rational numbers. If the binary operation a ⊙ on Q+ is defined as a⊙=ab/2 ,then the inverse of 3 is __________
(a)4/3
(b) 2
(c) 1/3
(d) 2/3
Solution :- option (b) 2
Question-9
Q+ is the set of all positive rational numbers with the binary operation * defined by a∗b=ab/2 for all a, b ∈ Q+. The inverse of an element a ∈ Q+ is ______________ .
(a) a
(b) 1/a
(c) 2/a
(d) 4/a
Solution :- option (d) 4/a
Question-10
If the binary operation ⊙ is defined on the set Q+ of all positive rational numbers by Then a⊙b=ab/4. Then ,3⊙(1/5⊙1/2) is equal to __________
(a) 3/160
(b)5/160
(c) 3/10
(d) 3/40
Solution :- option (a) 3/160
Question-11
Let * be a binary operation defined on set Q − {1} by the rule a * b = a + b − ab. Then, the identify element for * is ____________ .
(a) 1
(b) a-1 /a
(c) a /a-1
(d) 0
Solution :- option (d) 0
Question-12
Which of the following is true ?.
(a) * defined by a∗b=a+b /2 is a binary operation on Z .
(b) * defined by a∗b=a+b /2 is a binary operation on Q .
(c) all binary commutative operations are associative.
(d) subtraction is a binary operation on N
Solution :- option (b) * defined by a∗b=a+b /2 is a binary operation on Q .
Question-13
The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is ________________
(a) commutative only
(b) associative only
(c) commutative and associative both
(d) none of these
Solution :- option (c) commutative and associative both
Question-14
The binary operation * is defined by a * b = a2 + b2 + ab + 1, then (2 * 3) * 2 is equal to ______________ .
(a) 20
(b) 40
(c) 400
(d) 455
Solution :- option (d) 455
Question-15
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is _________________ .
(a) commutative but not associative
(b) associative but not commutative
(c) neither commutative nor associative
(d) both commutative and associative
Solution :- option (a) commutative but not associative
Question-16
Subtraction of integers is ____________
(a) commutative but not associative
(b) associative and commutative
(c) associative but not commutative
(d) neither commutative nor associative
Solution :- option (d) neither commutative nor associative
Question-17
The law a + b = b + a is called ______
(a) closure law
(b) associative law
(c) commutative law
(d) distributive law
Solution :- option (c) commutative law
Question-18
An operation * is defined on the set Z of non-zero integers by a∗b=ab for all a, b ∈ Z. Then the property satisfied is ________
(a) closure
(b) associative
(c) commutative
(d) none of these
Solution :- option (d) none of these
Question-19
On Z an operation * is defined by a * b = a2 + b2 for all a, b ∈ Z. The operation * on Z is _______________ .
(a) commutative and associative
(b) associative but not commutative
(c) not associative
(d) not a binary operation
Solution :- option (c) not associative
Question-20
A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is _________
(a) commutative
(b) associative
(c) not commutative
(d) commutative and associative
Solution :- option (c) not commutative
Question-21
Let * be a binary operation on Q+ defined by a∗b=ab/100 for all a, b ∈Q+ The inverse of 0.1 is _________________ .
(a) 105
(b)104
(c)106
(d) none of these
Solution :- option (a) 105
Question-22
Let * be a binary operation on N defined by a * b = a + b + 10 for all a, b ∈ N. The identity element for * in N is __________
(a) -10
(b) 0
(c)10
(d) non existence
Solution :- option (d) non existence
Question-23
Consider the binary operation * defined on Q − {1} by the rule
a * b = a + b − ab for all a, b ∈ Q − {1}
The identity element in Q − {1} is ____________
(a) 0
(b) 1
(c) 1/2
(d) -1
Solution :- option (a) 0
Question-24
For the binary operation * defined on R − {1} by the rule a * b = a + b + ab for all a, b ∈ R − {1}, the inverse of a is ________________
(a) -a
(b) -a / (a+1)
(c) 1/a
(d) a2
Solution :- option (b) -a / (a+1)
Question-26
On the set Q+ of all positive rational numbers a binary operation * is defined by, a∗b = ab / 2 for all, a, b ∈Q+. The inverse of 8 is _________ .
(a) 1/8
(b) 1/2
(c) 2
(d) 4
Solution :- option (b) 1/2
Question-27
Let * be a binary operation defined on Q+ by the rule
a∗b=ab/3 for all a, b ∈Q+ The inverse of 4 * 6 is ________
___ .
(a) 9/8
(b)2/3
(c) 3/2
(d) none of these
Solution :- option (a) 9/8
Question-28
The number of binary operation that can be defined on a set of 2 elements is _________ .
(a) 8
(b) 4
(c) 16
(d) 64
Solution :- option (c) 16
Question-29
The number of commutative binary operations that can be defined on a set of 2 elements is ____________ ..
(a) 8
(b) 6
(c) 4
(d) 2
Solution :- option (d) 2
-: End of MCQ Binary Operations ISC Class-12 Ch-3 Solutions :-
-: also visit :-
- ISC Class-12 Text book Solutions, Notes , Syllabus, Paper
- MCQ Type Questions ISC Class-12 Semester-1 Session 2021-22
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