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Test: Relations & Functions- Case Based Type Questions - Commerce MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Relations & Functions- Case Based Type Questions

Test: Relations & Functions- Case Based Type Questions for Commerce 2025 is part of Mathematics (Maths) Class 11 preparation. The Test: Relations & Functions- Case Based Type Questions questions and answers have been prepared according to the Commerce exam syllabus.The Test: Relations & Functions- Case Based Type Questions MCQs are made for Commerce 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Relations & Functions- Case Based Type Questions below.
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Test: Relations & Functions- Case Based Type Questions - Question 1

A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.


The relation defined in the above arrow diagram from set P to set Q is

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 1

When x = 9, y = ±3

When x = 4, y = ±2

When x = 25, y = ±5

∴ x is a square of y.

Test: Relations & Functions- Case Based Type Questions - Question 2

A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.


Which among the above figures shows a Relation between the two non - empty sets?

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 2

Solution:

A relation R from set A to set B is defined as a subset of the Cartesian product A × B. It can be represented pictorially by drawing two disjoint circles representing sets A and B, and an arrow from an element in A to an element in B whenever the ordered pair belongs to the relation.

Let's analyze the three figures given:

  • Figure A: There are two sets with elements, and arrows from elements of the first set to multiple elements in the second set, representing pairs (a, b) that define the relation. Since multiple arrows can go from one element in the first set to one or more elements in the second set, this is a valid relation.
  • Figure B: Shows elements in set X connected by arrows to elements in set Y. Each arrow represents a pair (x,y) in the relation. Multiple elements in X can map to elements in Y, and elements in Y can have arrows from multiple elements in X. This is also a valid relation.
  • Figure C: This figure shows exactly one arrow originating from each element in the domain to an element in the codomain. This is the definition of a function (a special kind of relation with exactly one output for each input). Since every function is a relation, figure C also represents a relation.

Important note: Every function is a relation, but not every relation is a function.

Therefore, all three figures A, B, and C depict relations between the two non-empty sets.

Answer: D. A, B, C

Test: Relations & Functions- Case Based Type Questions - Question 3

A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.



The relation defined in the above arrow diagram from set A to set B is

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 3

1,2,4 and 8 are factors of 8.

Test: Relations & Functions- Case Based Type Questions - Question 4

A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.

If the number of elements in set A and set B are p and q, then the number of relations from A to B are

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 4
Number of relations from A to B is 2n(A)n(B) =2pq.
Test: Relations & Functions- Case Based Type Questions - Question 5

A Relation R from A to B can be depicted pictorially using arrow diagram. In arrow diagram, we write down the elements of two sets A and B in two disjoint circles. Then we draw arrow from set A to set B whenever (a, b) ∈ R. An example of information depicted through an arrow diagram is shown below. For example:

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M) and an Executive Officer (E). The company provides ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the people who work in the categories A, C, M and E respectively. Here A1, A2, A3, A4 and A5 are Assistants; C1, C2, C3, C4 are Clerks; M1, M2, M3 are Managers and E1, E2 are Executive Officers then the relation R is defined by xRy, where x is the salary given to person y.

If the number of elements in set A and set B are p and q then the number of functions from A to B are

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 5
Number of functions from A to B n(B)n(A) = qp
Test: Relations & Functions- Case Based Type Questions - Question 6

Consider the graphs of the functions f(x), h(x) and g(x).

The domain of f(x) is ..................

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 6

f(x) = |x|. The domain of f(x) is R.

Test: Relations & Functions- Case Based Type Questions - Question 7

Consider the graphs of the functions f(x), h(x) and g(x).

The range of g(x) is ................

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 7

g(x) is the signum function. Its range is {–1, 0, 1}.

Test: Relations & Functions- Case Based Type Questions - Question 8

Consider the graphs of the functions f(x), h(x) and g(x).

The range of h(x) is .......................

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 8

h(x) = [x] is the greatest integer function. Its range is Z (set of integers)

Test: Relations & Functions- Case Based Type Questions - Question 9

Consider the graphs of the functions f(x), h(x) and g(x).

The value of h(–2.3) is ...................

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 9

h(–2.3) = [–2.3] = –3

Test: Relations & Functions- Case Based Type Questions - Question 10

Consider the graphs of the functions f(x), h(x) and g(x).

The value of f(10) is ...................

Detailed Solution for Test: Relations & Functions- Case Based Type Questions - Question 10

Since 10 > 0, f(10) = 10.

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