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Test: Relations and Functions- Case Based Type Questions- 2 - Question 1

Direction: Read the following text and answer the following questions on the basis of the same:

An organization conducted bike race under 2 different categories–boys and girls. Totally there were 250 participants. Among all of them finally three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project.

Let B = {b_{1}, b_{2}, b_{3}} G = {g_{1}, g_{2}} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions

Ravi wishes to form all the relations possible from B to G. How many such relations are possible?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 1

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

Direction: Read the following text and answer the following questions on the basis of the same:

An organization conducted bike race under 2 different categories–boys and girls. Totally there were 250 participants. Among all of them finally three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project.

Let B = {b_{1}, b_{2}, b_{3}} G = {g_{1}, g_{2}} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions

Let R : B → G be defined by R = {(b_{1}, g_{1}), (b_{2}, g_{2}), (b_{3}, g_{1})}, then R is__________

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

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Test: Relations and Functions- Case Based Type Questions- 2 - Question 3

Direction: Read the following text and answer the following questions on the basis of the same:

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Let relation R be defined by R = {(L_{1}, L_{2}) : L_{1} || L_{2 }where L_{1,} L_{2} ∈ L} then R is______ relation

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 3

Test: Relations and Functions- Case Based Type Questions- 2 - Question 4

Direction: Read the following text and answer the following questions on the basis of the same:

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

Let f : R → R be defined by f(x) = x − 4. Then the range of f(x) is _______

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 4

Test: Relations and Functions- Case Based Type Questions- 2 - Question 5

Direction: Read the following text and answer the following questions n the basis of the same:

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x^{2}.

Let f : R → R be defined by f(x) = x^{2} is_________

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 5

Test: Relations and Functions- Case Based Type Questions- 2 - Question 6

Direction: Read the following text and answer the following questions n the basis of the same:

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x^{2}.

Let f : {1, 2, 3, ….} → {1, 4, 9, ….} be defined by f(x) = x^{2} is _________

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 6

Test: Relations and Functions- Case Based Type Questions- 2 - Question 7

Direction: Read the following text and answer the following questions n the basis of the same:

Raji visited the Exhibition along with her family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y = x^{2}.

The function f : Z → Z defined by f(x) = x^{2} is ______

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 7

Test: Relations and Functions- Case Based Type Questions- 2 - Question 8

Direction: Read the following text and answer the following questions on the basis of the same:

An organization conducted bike race under 2 different categories–boys and girls. Totally there were 250 participants. Among all of them finally three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project.

Let B = {b_{1}, b_{2}, b_{3}} G = {g_{1}, g_{2}} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions

Ravi wants to know among those relations, how many functions can be formed from B to G?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 8

Test: Relations and Functions- Case Based Type Questions- 2 - Question 9

Direction: Read the following text and answer the following questions on the basis of the same:

Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.

The function f : R → R defined by f(x) = x − 4 is______

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 9

Test: Relations and Functions- Case Based Type Questions- 2 - Question 10

Direction: Read the following text and answer the following questions on the basis of the same:

_{1}, b_{2}, b_{3}} G = {g_{1}, g_{2}} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions

Let R : B → B be defined by R = {(x, y) : x and y are students of same sex}, Then this relation R is_______

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 10

Test: Relations and Functions- Case Based Type Questions- 2 - Question 11

Direction: Read the following text and answer the following questions on the basis of the same:

Let R = {(L_{1}, L_{2}) : L_{1} ⊥ L_{2} where L_{1}, L_{2} ∈ L} which of the following is true?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 11

Test: Relations and Functions- Case Based Type Questions- 2 - Question 12

Direction: Read the following text and answer the following questions n the basis of the same:

^{2}.

Let : N → R be defined by f(x) = x^{2}. Range of the function among the following is _______

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 12

Test: Relations and Functions- Case Based Type Questions- 2 - Question 13

Direction: Read the following text and answer the following questions on the basis of the same:

_{1}, b_{2}, b_{3}} G = {g_{1}, g_{2}} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions

Ravi wants to find the number of injective functions from B to G. How many numbers of injective functions are possible?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 13

Test: Relations and Functions- Case Based Type Questions- 2 - Question 14

Direction: Read the following text and answer the following questions on the basis of the same:

Let R = {(L_{1}, L_{2}) : L_{1} || L_{2} and L_{1} : y = x – 4} then which of the following can be taken as L_{2}?

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 14

Test: Relations and Functions- Case Based Type Questions- 2 - Question 15

Direction: Read the following text and answer the following questions n the basis of the same:

^{2}.

Let f : N → N be defined by f(x) = x^{2} is ________

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 15

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