Binary Operations, Class 12 Mathematics NCERT Solutions

1. There will be total 10 MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

1. Number of binary sets on the set {p, q,r} is:

 3⁹

 16

 18

 3⁶

Question 1 of 10

2. * is a binary operation on Z such that: a * b = a + b + ab. The solution of
(3* 4) *x = – 1 is

 1

 -1

  4

  3

Question 2 of 10

3. Given below is the table corresponding to some binary operation a * b on a set {0,1,2,3,4,5}. How many elements of this operation have an inverse?.

 1

 0

 6

 4

Question 3 of 10

4. If * and ^O are two binary operations defined by a * b = a + b and a ^O b = ab, then

  (a * b) ^O c = ab + ac

 ^O is distributive on *.

 * is distributive on ^O.

 a ^O (b * c) = ac + bc

Question 4 of 10

5. The law a + b = b + a is called

 Associative law

 Distributive law

 Closure law

 Commutative law

Question 5 of 10

6. The number of binary operations which can be defined on the set P= { p, q}is

  6

 0

  1

  16

Question 6 of 10

7. Given below is binary composition table
a* b = LCM of a and b on S = { 1,2,3,4}. Then, from the table determine which one of these options is correct.

  a* b is a distributive binary operation

 a* b is an associative binary operation

  a* b is not a binary operation

  a* b is a commutative binary operation

Question 7 of 10

8. Let * be any binary operation on the set R defined by a * b = a + b – ab, then the binary operation * is

  Associative

 Commutative but not associative

 Commutative and associative

 Commutative

Question 8 of 10

9. Given below is the table corresponding to some binary operation a * b on a set {0, 1,2,3,4,5}. Identify the identity element of this operation.

 4

 0

 1

 6

Question 9 of 10

10. The identity element for the binary operation * defined by a * b = , where a, b are the elements of a set of non-zero rational numbers, is

 1

  1/2

 0

  2

Question 10 of 10

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