MCQ Binary Operations ISC Class-12 Maths Ch-3 for Semester-1

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 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 ab ∈ 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 ab for all a∈ 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 ab ∈ 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 ab ∈ 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

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