All Courses
Get the App Signup / Login
Sign in Open App
JEE Exam  >  JEE Tests  >  Mathematics (Maths) Class 12  >  Test: Relations and Functions- Case Based Type Questions- 2 - JEE MCQ

Test: Relations and Functions- Case Based Type Questions- 2 - JEE MCQ


Test Description

15 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Relations and Functions- Case Based Type Questions- 2

Test: Relations and Functions- Case Based Type Questions- 2 for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Relations and Functions- Case Based Type Questions- 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Relations and Functions- Case Based Type Questions- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Relations and Functions- Case Based Type Questions- 2 below.
Solutions of Test: Relations and Functions- Case Based Type Questions- 2 questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Relations and Functions- Case Based Type Questions- 2 solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Relations and Functions- Case Based Type Questions- 2 | 15 questions in 30 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Relations and Functions- Case Based Type Questions- 2 - Question 1
Save

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 = {b1, b2, b3} G = {g1, g2} 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
Given

B = {b1, b2, b3} G = {g1, g2}

Numbers of Relation from B to G

= 2Numbers of elements of B x Number of elements of G

= 23 x 2

= 26

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

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 = {b1, b2, b3} G = {g1, g2} 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 = {(b1, g1), (b2, g2), (b3, g1)}, then R is__________

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 2
R : B → G be defined by R = {(b1, g1), (b2, g2), (b3, g1)}

R is surjective, since, every element of G is the image of some element of B under R, i.e., For g1, g2 ∈ G, there exists an elements b1, b2, b3 ∈ B, (b1 g1) (b2, g2), (b3, g1) ∈ R.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Relations and Functions- Case Based Type Questions- 2 - Question 3
Save

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 = {(L1, L2) : L1 || L2 where L1, L2 ∈ L} then R is______ relation

Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 3
Let relation R be defined by

R = {(L1, L2) : L1 || L2 where L1, L2 ∈ L}.

R is reflexive, since every line is parallel to itself.

Further, (L1, L2) ∈ R

⇒ L1 is parallel to L2

⇒ L2 is parallel to L1

⇒ (L2, L1) ∈ R

Hence, R is symmetric.

Moreover, (L1, L2), (L2, L3) ∈ R

⇒ L1 is parallel to L2 and L2 is parallel to L3

⇒ L1 is parallel to L3

⇒ (L1, L3) ∈ R

Therefore, R is an equivalence relation

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

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
Range of f(x) is R
Test: Relations and Functions- Case Based Type Questions- 2 - Question 5
Save

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 = x2.

Let f : R → R be defined by f(x) = x2 is_________
Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 5
f : R ® R be defined by f(x) = x2

∵ f(–1) = f(1) = 1, but –1 ≠ 1

∴ f is not injective

Now, –2 ∈ R. But, there does not exist any element x ∈ R such that f(x) = –2 or x2 = –2

∴ f is not surjective.

Hence, function f is neither injective nor surjective.

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

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 = x2.

Let f : {1, 2, 3, ….} → {1, 4, 9, ….} be defined by f(x) = x2 is _________
Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 6
f : {1, 2, 3, ....} → {1, 4, 9, ...} be defined by f(x) = x2

x1 ∈ {1, 2, 3, ...} and x2 ∈ {1, 2, 9, ....}

f(x1) = f(x2)

⇒ x12 = x22

⇒ x1 = x2

∴ f is injective

Now, 4 ∈ {1, 4, 9...}, there exist 2 in {1, 2, 3 ...} such that f(x) = 22 = 4, Hence, f is surjective Therefore f is bijective.

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

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 = x2.

The function f : Z → Z defined by f(x) = x2 is ______
Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 7
f : z → z defined by f(x) = x2

So, f(–1) = f(1), but 1 ≠ –1

∴ f is not injective

Now, –2 ∈ Z, but, there does not exist any element x ∈ z such that

f(x) = –2

or x2 = –2

∴ f is not surjective

Hence, f is neither injective nor surjective.

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

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 = {b1, b2, b3} G = {g1, g2} 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
Given

B = {b1, b2, b3} G = {g1, g2}

So, B hase 3 elements, G has 2 elements

Numbers of functions from B to G = 2 x 2 x 2

= 23

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

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
The function f is one-one,

for f(x1) = f(x2)

⇒ x1 – 4 = x2 – 4

⇒ x1 = x2

Also, given any real number y in R, there exists y + 4 in R

Such that f(y + 4) = y + 4 – 4 = y

Hence, f is onto

Hence, function is both one-one and onto, i.e., bijective.

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

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 = {b1, b2, b3} G = {g1, g2} 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
R : B → B be defined by R = {(x, y) : x and y are students of same sex}

R is reflexive, since, (x, x) ∈ R

R is symmetric, since, (x, y) ∈ R and (y, x) ∈ R

R is transitive. For a, b, c ∈ B

∃ (a, b) (b, c) ∈ R

and (a, c) ∈ R.

Therefore R is equivalence relation.

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

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 R = {(L1, L2) : L1 ⊥ L2 where L1, L2 ∈ L} which of the following is true?
Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 11
R is not reflexive, as a line L1 can not be perpendicular to itself, i.e., (L1, L1) ∉ R.

R is symmetric as (L1, L2) ∈ R

As, L1 is perpendicular to L2

and L2 is perpendicular to L1

(L2, L1) ∈ R

R is not transitive. Indeed, it L1 is perpendicular to L2 and L2 is perpendicular to L3, then L1 can never be perpendicular to L3.

In fact L1 is parallel to L3,

i.e., (L1, L2) ∈ R, (L2, L3) ∈ R but (L1, L3) ∉ R

i.e., symmetric but neither reflexive nor transitive.

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

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 = x2.

Let : N → R be defined by f(x) = x2. Range of the function among the following is _______
Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 12
Range of f = {1, 4, 9, 16, ...}

∵ N = {1, 2, 3, ....}

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

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 = {b1, b2, b3} G = {g1, g2} 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
In a function,

Every element of set B will have an image.

Every element of set B will only one image in set

For injective functions

All elements of set G should have a unique pre-image

Which is not possible

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

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 R = {(L1, L2) : L1 || L2 and L1 : y = x – 4} then which of the following can be taken as L2?
Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 14
Since, L1 || L2 then slope of both the lines should be same.

Slope of L1 = 1

⇒ Slope of L2 = 1

And 2x – 2y + 5 = 0

–2y = –2x – 5

y = x + (5/2)

Slope of 2x – 2y + 5 = 0 is 1

So, 2x – 2y + 5 = 0 can be taken as L2.

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

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 = x2.

Let f : N → N be defined by f(x) = x2 is ________
Detailed Solution for Test: Relations and Functions- Case Based Type Questions- 2 - Question 15
f : N → N be defined by f(x) = x2 for x, y ∈ N, f(x) = f(y)

⇒ x2 = y2

⇒ x = y

∴ f is injective

Now; 2 ∈ N, But, there does not exist any x in n such that f(x) = x2 = 2

∴ f is not surjective

Hence, function is injective but not surjective.

204 videos|290 docs|139 tests
Join Course
Information about Test: Relations and Functions- Case Based Type Questions- 2 Page
In this test you can find the Exam questions for Test: Relations and Functions- Case Based Type Questions- 2 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Relations and Functions- Case Based Type Questions- 2, EduRev gives you an ample number of Online tests for practice

Top Courses for JEE

204 videos|290 docs|139 tests
Join Course
Download as PDF

Top Courses for JEE

Important Questions for Relations and Functions- Case Based Type Questions- 2

Find all the important questions for Relations and Functions- Case Based Type Questions- 2 at EduRev.Get fully prepared for Relations and Functions- Case Based Type Questions- 2 with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Relations and Functions- Case Based Type Questions- 2 syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Relations and Functions- Case Based Type Questions- 2 resources.

Relations and Functions- Case Based Type Questions- 2 MCQs with Answers

Prepare for the Relations and Functions- Case Based Type Questions- 2 within the JEE exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Relations and Functions- Case Based Type Questions- 2 Mathematics (Maths) Class 12

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Relations and Functions- Case Based Type Questions- 2 with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup