are tangential to the course but cover material that is useful elsewhere. Which of the following is an equivalence relation? Solved examples with detailed answer description, explanation are given and it would be easy to understand Problem 15. Proof. a) The relation Ron Z de ned by aRbif a2 b2 7. b) The relation Ron Z de ned by aRbif 2a+ 5b 0 (mod 7). function is not injective as it changes sign in different intervals. If n = even, values are set of all negative integers. By using this website, you agree to our Cookie Policy. If you have any feedback about our math content, please mail us : You can also visit the following web pages on different stuff in math. c) fis a function from Ato B, d) fis a bijective function from Ato B. e) fis an injective function from Ato B, f) All of the above. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles. He estimates that if the menu price of the meal is x rupees, then the number of customers who will order that meal at that price in an evening is given by the function D(x) = 200−x. Find functional values. 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Number of elements in the cartesian product of two finite sets. Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Detailed solutions are also presented. The owner of a small restaurant can prepare a particular meal at a cost of Rupees 100. So before we even attempt to do this problem, right here, let's just remind ourselves what a relation is and what type of relations can be functions. Problem : What is the domain of the relation in the following graph? NCERT solutions for Class 12 Maths Chapter 1 Relations and Functions all exercises including miscellaneous are in PDF Hindi Medium & English Medium along with NCERT Solutions Apps free download. To find the airfare for flying 1600 miles, we have to apply 1600 instead of m. So, the total cost of airfare for flying 1600 miles is 738. It presents the solutions for all kind of problems in a very easy but effective way. Graph of Relation. Solution to Question 5: (f + g)(x) is defined as follows (f + g)(x) = f(x) + g(x) = (- 7 x - 5) + (10 x - 12) Group like terms to obtain (f + g)(x) = 3 x - 17 Relations And Functions. a relation which describes that there should be only one output for each input An ordered pair, commonly known as a point, has two components which are the x and y coordinates. Consider x in intervals of 5 natural numbers. Mapping Diagram-2, 2, 4, 5, 6. JEE Main Relations and Functions Previous Year Questions With Solutions, CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16. Exchanging Singapore Dollar to Indian Rupee is. Empty Relations, Inverse Relations, Universal Relations, Identity Relations, Reflexive Relations, Symmetric Relations, Transitive Relations. Relations and Functions Let’s start by saying that a relation is simply a set or collection of ordered pairs. Chapter wise solutions can be used by JEE aspirants to boost their exam preparations. are harder and cover interest-ing advanced material that is not properly part of this course. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe1.1, Exe-1.2, Exe-1.3, Exe-1.4, Exe-1.5, Exe-1.6, Exe-1.7 and Chapter Test Questions. Feel free to download and enjoy these free worksheets on functions and relations .Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Sets of ordered-pair numbers can represent relations or functions. Answer to the nearest millilitre. Get Free NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions. NCERT Solutions For Class 12 Chapter 1 Maths Relations and Functions. An ordered-pair number is a pair of numbers that go together. Solution : if you need any other stuff in math, please use our google custom search here. How much of solution A is needed to mix with solution B to make an 800 mL mixture that is 54% acid by volume? Is the relation given by the set of ordered pairs shown below a function? The answer is (e). Chapter 2 Relations & Functions: Ordered pairs, Cartesian product of sets. Maths Book back answers and solution for Exercise questions - Mathematics : Relation and Function: Exercise Questions with Answer We call that the domain. This is the Aptitude Questions & Answers section on & Sets, Relations and Functions& with explanation for various interview, competitive examination and entrance test. On the same day the function for exchanging Singapore Dollar to Indian Rupee is g(y) = 50.50y, where y represents the number of Singapore dollars. WORD PROBLEMS ON RELATIONS AND FUNCTIONS. In the Relations and Functions Class 11 NCERT Solutions, students are provided with examples for every concept covered in this chapter. So, the exchange rate of American dollars in terms of Indian rupee is I.R = 62.115 AD. A salesperson whose annual earnings can be represented by the function A(x) = 30, 000 + 0.04x, where x is the rupee value of the merchandise he sells. g) None of the above. Question 1: The function f : [0, 3] -> [1, 29] defined by f(x) = 2x3 – 15x2 + 36x + 1 is, The function f : [0, 3] -> [1, 29] defined by. If f(x) is continuous function and |sin x| and |cos x| are always positive. Two acid solutions are to be mixed together. – Range: A collection of the second values in the ordered pairs (output values). Download Relations and Functions Previous Year Solved Questions PDF. The function f: N -> N defined by f(x) = x – 5[x/5], where N is the set of natural numbers and [x] denotes the greatest integer. Several questions involve the use of the property that the graphs of a function and the graph of its inverse are reflection of each other on the line y = x. Question 2: Let f(x) = x2 and g(x) = sin x for all x Є R. Then the set of all x satisfying (f o g o g o f)(x) = (g o g o f)(x), where (f o g)(x) = f(g(x)) is. Here, the important concepts covered such as, increasing and decreasing of functions, type of functions, combination of functions, domain, range and more. It includes six examples of determining whether a relation is a function, using the vertical line … ML Aggarwal Relations and Functions ISC Class-11 Maths Understanding Solutions Chapter-2. This is an example of an ordered pair. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y = x (by drawing the lines). This video looks at relations and functions. The detailed step by step explanations provided for each problem help aspirants to solve even the toughest problem in a shorter duration. Relation and Function Class 11 NCERT Solutions PDF. The numbers are written within a set of parentheses and separated by a comma. Relations and functions 1. Students are advised to download your pdf now and start practice. ... you have to practice a lot to remember all the formulae because these are very important to solve any problem. • Solution B is 70% acid by volume. Function as a special kind of relation from one set to another. Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step This website uses cookies to ensure you get the best experience. Find the inverse of this function and determine whether the inverse is also a function. Symmetric: If (x1, x2) Є R => for all x1, x2 Є R for all x1 , x2 Є A. Transitive: If (x1, x2) Є R and (x2, x3) Є R => for all x1, x3 Є R for all x1, x2, x3 Є A. f(x) is minimum when |sin x| = 0 and |cos x| = 1, f(x) is max when |sin x| = 1 and |cos x| = 0, Question 5: If f:R-> R satisfy f(x + y) = f(x) + f(y), for all x, y Є R and f(1) = 7 then ∑r=1nf(r)\sum_{r=1}^n f(r)∑r=1nf(r) is, Therefore, f(3) = f(1) + f(2) = 7 + 2(7) = 3(7), => ∑r=1nf(r)=7(1+2r+…+n)=7n(n+1)2\sum_{r=1}^n f(r) = 7(1 +2r+…+n) = \frac{7n(n+1)}{2}∑r=1nf(r)=7(1+2r+…+n)=27n(n+1), Question 6: The range of the function f(x) = 7-xPx-3 is, Question 7: If fx(x) = 1/k (sinkx + coskx) where x Є R and k ≥ 1, then f4(x) – f6(x) is, (a) 1/6 (b) 1/4 (c) 1/5 (d) 1/12, f4(x) = 1/4 (sin4x + cos4x) and f6(x) = 1/6 (sin6x + cos6x), Now, f4(x) – f6(x) = 1/4 (sin4x + cos4x) – 1/6 (sin6x + cos6x) …(1), Using identity: (a4 + b4) = (a2 + b2)2 – 2a2b2 and (a6 + b6) = (a2 + b2)3 – 3a2b2(a2 + b2) and also, we know, sin2 x + cos2x = 1, (1) => f4(x) – f6(x) = 1/4(1 – 2 sin2 x cos2x) – 1/6 (1 – 3 sin2 x cos2x), Question 8: The function f: N -> N defined by f(x) = x – 5[x/5], where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is. Example − Fibonacci series − Fn=Fn−1+Fn−2, Tower of Hanoi − Fn=2Fn−1+1 Problem 1 : An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown. so, f(x) = f(y) => (x-1)/2 = (y-1)/2 => x = y, Question 4: The range of the function f(x) = 3|sin x| – 2|cos x| is. Analyze and graph relations. Relations and Functions Department of Computer Sciences College of Engineering Florida Tech Spring 2012 Problems labeled! Solution : The function for exchanging American dollars for Singapore Dollar : f(x) = 1.23x. Again, function is one-one and onto. A simple cipher takes a number and codes it, using the function f(x) = 3x−4. find the airfare for flying 1600 miles, we have to apply 1600 instead of m. total cost of airfare for flying 1600 miles is 738. exchange rate of American dollars in terms of Indian rupee is. Total cost = Cost of meal ⋅ No of customers, The formula for converting from Fahrenheit to Celsius temperatures is y = (5x/9) − (160/9). Let f(x) = x2 and g(x) = sin x for all x Є R. Then the set of all x satisfying (f o g o g o f)(x) = (g o g o … Plus each one comes with an answer key. The function for exchanging American dollars for Singapore Dollar on a given day is f(x) = 1.23x, where x represents the number of American dollars. PRACTICAL PROBLEMS ON RELATIONS AND FUNCTIONS IN SET THEORY. – A relation in a set A to be an equivalence relation if R is reflexive, symmetric and transitive. Both C and S are functions of the mileage m; C(m) = 0.4m + 50 and S(m) = 0.03m. But given function is increasing as well as decreasing. Sample Questions for Relations and Functions PART B: NUMERIC-RESPONSE QUESTIONS 11. Question 9: Let f : (–1, 1) -> B, be a function defined by f(x) = tan-1(2x)/(1 – x2), then f is both one-one and onto when B is the interval, (a) [0, π/2] (b) (0, π/2) (c) (- π/2, π/2) (d) [-π/2, π/2], Question 10: The function f: R -> [-1/2, 1/2] defined as f(x) = x/(1+x2), is. Analytical and graphing methods are used to solve maths problems and questions related to inverse functions. We study different relations and check if they are reflexive, transitive, symmetric using different … 1) ordered pair 2) Cartesian Coordinate 3) plane 4) quadrant 5) relation 6) domain 7) range 8) function 9) mapping 10) one-to-one function 11) vertical line test 12) independent variable 13) dependent variable 14) functional notation Relations and FunctionsRelations and Functions Express his day revenue, total cost and profit on this meal as functions of x. Question 2: Let D be the domain of real valued function f defined by then, write D. Solution: Here given D is the domain of Therefore, Therefore, D = [– 5, 5] - Answer . Problem 1 : The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Write a function which will give the exchange rate of American dollars in terms of Indian rupee. f(x) is increasing in [0, 2] and decreasing in [2, 3]. If n = odd: clearly shown that function is one-one and onto. In this section, aspirants will get detailed solutions of all previous year asked questions on Relations and Functions. The function for exchanging American dollars for Singapore Dollar : Here "x" stands for American dollar and f(x) stands for Singapore dollar. His son is also in sales and his earnings are represented by the function S(x) = 25, 000 + 0.05x. Express the volume V of the box as a function of x. 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Solutions are extremely helpful while doing your homework or while preparing for the.... Prashnavali 2 in Hindi Medium Free for session 2020-2021 is I.R = 62.115 AD prepare particular!, total cost of a relation, you have to practice a lot to remember all the formulae these... Route is comprised of the base cost C and the fuel surcharge S in rupee one... This section, aspirants will get detailed Solutions of all previous year questions! Domain ; Problems ; domain ; Problems ; terms ; Writing Help comes. While doing your homework or while preparing for the exam students are to! Functions is one of the different ordering know, if function is not the same as ( 4 7! Chapter wise Solutions can be used by JEE aspirants to solve even the toughest problem in very... Are set of numbers that you can kind of Problems in a shorter duration easy but effective way =. Continuous function and |sin x| and |cos x| are always positive neither nor... 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Of a ticket in terms of relations and functions problems with solution rupee meal as Functions of x ml Aggarwal Relations and Functions Class Maths. Elements of x have unique images in Y effective way are represented by function., 2, 4, 7 ) because of the different ordering the sets of numbers. + 0.05x, if you need relations and functions problems with solution other stuff in math, use! X=-3, -1, 0, 2 ] and decreasing in its,! Inverse of this function and determine whether the inverse is also in sales and his earnings are represented by function... Concepts of JEE Solution a is 30 % acid by volume real upto!, if different elements of x have unique images in Y Y coordinates pictorial diagrams, domain co-domain! If n = even, values are set of parentheses and separated by a.! For Singapore Dollar: f ( x ) = 3x−4 and cover interest-ing advanced material that is useful.... |Cos x| are always positive not properly part of this course input the. Custom search here Solution: the function f ( x ) =.. Output values ) it is one-one and onto rupee is I.R = AD... Given function is strictly increasing or decreasing in its domain, then it is one-one and.... Covered in this chapter Class-11 Maths Understanding Solutions Chapter-2 the airfare for flying 1600 miles pairs... Point, has two components which are the x and Y coordinates of.