Q.12 Show that each of the relation R in the set A of all triangles as R = Q.13 Let R

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1 CLASS XII RELATION,FUNCTION & BINARY OPERATION Q Write the name of function Q If,,, find the value of and Q Let A {-, 0,, }, B {-, -, 0, } and f, g : A B be functions defined b f(), A and g(), A are f and g equal Justif our answer Q Given that the ordered pairs ( a, 7 ) and ( -,b) belongs to relation, : 8 Find the value of a and b {( ) } Q5 Let relation {(, ) w w: } R If ( a, - ) and (, b ) belong to relation R, find the value of a and b Q6 7 If f : R R be defined as f ( ), then find f ( ) 9 Q7 A relation R is defined on the set Z of integer as follows : Epress R and R as the set of ordered pairs and hence find R AGYAT GUPTA (TARGET MATHEMATICS) Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph: 0685,6060(O)Mobile : ; PREMIER INSTITUTE for X, XI & XII 5 their respective domains and range Q8 Let R be the relation on the set N of natural number defined b R {(, ) : &, N (i) Write R in the roster form (ii) Find domain of R (ii) Find range of R Q9 Find the total number of function from set A to set B if A {,, }& set B { a, b } Q0 Find the total number of relation from set A to A if A {,, } Q If f ( ) and g( ) 5 find fog & gof Q Show that each of the relation R in the set A of all triangles as R {( T, T ) : T ~ T } is an equivalence relation Consider three right triangles T with sides,, 5 ; T with sides 6, 8, 0 & T with sides, 5,, Which triangle among T, T & T are similar Q Let R be the set of all non-negative real numbers Let f : R [, ): ( ) f Show that f is invertible and find f Q Let A {,,, 5, 6, 7, 8, 9 } Let R be the relation on A defined b {(, ) : A & divides )} Find (i) R (ii)domain of R (iii) Range of R (iv) R state whether or not R, is (a) Refleive (b) smmetric (c) transitive Q5 Show that each of the relation R in the set A { : 0 },given b (i)r {(a,b): a b is a multiple of } (ii)r {(a,b):a b} is an equivalence relation Find the set of all elements to in each cases Q6 Is sine function onto in the set of real numbers? Give reasons Q7 Let N N be the set of ordered pairs of natural numbers Also let R be the relation in N N, defined b ( a, b) R( c, d) a d b c Show that R is an equivalence relation f : R 5 given b f ( ) Show that f is invertible Q8 Consider [ ) with, 6 f ( ) Q9 Discuss whether the relation defined b R { (, ) : is father of } is Refleive, smmetric & transitive are not Q0 Show that the signum function f : R R defined b, if > 0 f ( n) 0, if 0 is neither one-one nor onto, if < 0 Q Let N N be the set of ordered pairs of natural numbers Also let R be the relation in N N, defined b ( a, b) R( c, d) ad bc Show that R is an equivalence relation Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

2 Q Prove that the function f : R { } R { } given b f ( ) is bijection Q Discuss whether the relation defined b R { (, ) : is wife of } is Refleive, smmetric & transitive are not Q Prove that the greatest Integer function f : R R given b f ( ) is neither one one nor on to Q5 Show that the relation R in the set R of real no defined as R {( a, b) : ab > 0, a, b R} is Refleive & smmetric but not transitive Q6 Prove that the greatest Integer function f : R R given b f ( ) [ ] is neither one one nor on to where [] denotes the greatest integer Q7 Let N denote the set of all natural number and R be a relation on N N defined b ( a, b) R( c, d) ad( b c) bc( a d) Cheque whether R is an equlivance relation Q8 Show that the relation R in the set R of real no defined as R{( a, b) : a b } is neither Refleive, nor smmetric nor transitive Q9 Find the total number of bijective function from set A to A if A {,,, } Q0 Show that the relation R in the set R of real no defined as R{( a, b) : a b } is neither Refleive, nor smmetric nor transitive Q n, if n is odd Let f : N N be defined b f ( n) for all n N Find whether the function f is bijective n, if n is even Q Consider the set A { a, b, c} give an eample of a relation R on A which is (i) Refleive & smmetric but not transitive (ii) transitive & smmetric but not Refleive (iii) Refleive & transitive but not smmetric Q Show that f :{,} R; given b f ( ), is one one Find the inverse of the function f :{,} R Q Consider : R [ 5 ) with f given b f ( ) 5 Show that f is invertible, 6 f ( ) Q5 Let * be a binar operation on N given b a*b HCF (a, b), a, b ε N Write the value of * Q6 Let * be a binar operation on R If a * b a b ab ; a, b R Find such that ( * ) * 7 Q7 Prove that the function f : R { } R { } given b f ( ) is bijection Q8 Q9 Find the total number of one one function from set A to A if A { a, b, c } Q0 If the binar operation *, defined on Q, is defined as a * b a b ab, for all a, b Q, find the value of * Q Let X be non empt set P(X) be its power set let * be an binar operation defined on elements of P(X) b, A * B A B A, B P( X ) then (i) Prove that * is a binar operation in P(X) (ii) Is * commutative? (iii)is associative (iv) Find the identit element of in P(X) wrt * (v) Find all the invertible of P( ) (vi) If is another binar operation defined on P(X) as A B A B then verif that distributive over * Q Let f ( ) [ ] and g( ) Find (i) ( gof ) ( fog) (ii) 5 5 ( gof ) ( fog) (iii) ( f g)( ) (iv) (gof )( 5) Q Prove that a relation on a set A is smmetric if and onl if R R Q If R is an equivalence relation on a set A, then R is also equivalence relation on A Q5 5 5 Let f ( ) and g ( ) [ ] Evaluate ( fog ) ( gof ) Q6 Let f : R R & g : R R be defined b f ( ) & g ( ) 7 then f g find the value of such that { ( )} 5 Q7 Let relation {(, ) w w: } R If ( a, - ) and (, b ) belong to relation R, find the value of a and b Q8 If f ( ), Prove that fof What is the inverse of f 6 Q9 If 7 f : R R be defined as 7 f ( ) & g : R R be defined as g( ) Prove that gof I A & ( fog) I B where 7 B R & A R Find Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

3 also &, f ( gof ) g Q50 Let X be non empt set P(X) be its power set let * be an binar operation defined on elements of P(X) b, A * B A B A, B P( X ) then (i) Prove that * is a binar operation in P(X) (ii) Is * commutative? (iii)is associative (iv) Find the identit element of in P(X) wrt * (v) Find all the invertible of P( ) (vi) If is another binar operation defined on P(X) as A B A B then verif that distributive over * Q5 let A N N and * be an binar operation defined b ( a, b) *( c, d ) ( ac, bd ) a, b, c, d N on the set R, then (i) Prove that * is a binar operation on N (ii) Is * commutative? (iii)is associative (iv) Find the identit element for * on N N if an Q5 If f( ) and g () be two invertible function defined as f ( ) be defined as 5 g( ) Prove that ( gof ) f og 7 Q5 let * be an binar operation defined a * b a b ab on the set R {-}, then (i) Prove that * is a binar operation R {-} (ii) Is * commutative? (iii)is associative (iv) Find the identit element R {-} wrt * and also prove that ever element of R {-}is invertible Q5 If * be the binar operation on the set Q of rational numbers defined b a * b ab For binar operation eamine the commutative and associative propert Also find identit element and inverse Q55 If f, g : Q Q be two invertible function defined as f ( ) be defined as g( ) Prove that ( gof ) f og Q56 Let A {,,,} B {, 5, 7, 9 } C { 7,, 7, 79 } and f : A B, g : B C be defined as f() and g() Epress ( ) gof & f og as the set of ordered pair and verif that ( ) f og gof Q57 Let f :{,,, 5} {,, 5, 9} and g :{,, 5,9} { 7,,5} be functions defined as f(),f(),f() 5, f(5) 5 and g() g() 7 and g(5) g(9) Find gof Also find the domain and the range of gof Q58 Let f :{,, } {,,5 }& g :{,,5 } {, } be given b f {(,),(,5),(,) } {(,)(,)( 5,) } g write down of gof Q59 Let * be a binar operation defined b a * b a b Find * Q60 Find the inverse element of the binar relation a b a b Q6 Let f : R R be defined b ( ) f, then (i) f (7 ) (ii) f ( 5) (iii) f (0,7 ) Q6 Define a binar operation * one the set {0,,,,,5} as a * b a b, a b< 6 Show that zero is the identit for this operation and each element a a b6, a b 6 of the set is invertible with 6 a being the inverse of a Q6 let A N N and * be an binar operation defined b ( a, b) *( c, d ) ( a c, b d ) a, b, c, d N on the set R, then (i) Prove that * is a binar operation on N (ii) Is * commutative? (iii)is associative (iv) Find the identit element for * on N N if an Q6 Determine the nature of the following functions for even and odd: (i) a f ( ) (ii) f ( ) log( ) a Q65 Let * be a binar operation on N If a * b lcm of a & b ; a, b N Find ( * ) * 6 Q66 Let * be a binar operation on Z If a * b a b ; a, b Z Find the identit element with respect to operation * on Z Q67 Let f : R R be defined b f ( ) 5 9, Find f (9) Q68 Let f, g be the function f { (, 5 ), (, 6 ), (, )} ; g {(, 7 ) (5,8), ( 6, 9)}What is the range of f & g Find gof Q69 Let * be a binar operation on N N If (a,b) * (c,d) ( ad bc, bd ) ; (a,b),(c,d) N N Prove that (i) * is closed to binar operation on N N (ii) * is commutative on N N (iii) * is associative on N N (iii) Find the identit element with respect to operation * on N N if an Q70 Let * be the binar operation such that Q Q Q defined b a * b a b - ab; a,b Q {} Show that * is (i) associative, (ii) commutative Q7 Eamine which of the following is a binar operation a b a b (i) a b a, b N (ii) a b a, b Q Q7 Consider f :{,,} { a, b, c} and g :{ a, b, c} { apple, ball, cat} defined as Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

4 f ( ) a; f () b, f () c; g( a) apple; g( b) ball; g( c) cat Show that f, g and gof are invertible Find out f, g and( gof ) f og Q7 5 If f ( ), show that f () 5 Q7 Let * be a binar operation defined b a * ba b - Find * 5 Q75 Let * be a binar operation on Z Find * (-) if a * b ab; a, b Z DIFFERENTIAL EQUATION Q Solve the differential equation (log log ) Q Show that the differential equation e e 0 is homogeneous and find its particular solution given that 0, when Q From the differential equation of the famil of curves e (A cos B sin ), where A and B are arbitrar constants Q Find the particular solution of the differential equation ( ) sin ( ) cos, given that π when Q5 Solve the differential equation ( )( log ) 0 given that when, Q6 Solve : ( ) 0 Q7 Solve the initial value problems: (sin ), (0) 0 ( ) Q8 Solve : ( ) 5 Q9 Solve : e e Q0 Show that A B is a solution of the differential Q equation d Solve the differential equation: ( ) Q Solve the differential equation: d sin Q Solve the differential equation 0; () Q Show that ae be is a solution of the differential d equation 0 Q5 Show that ae be is a solution of the differential d equation 0 Q6 Show that the function ( A B) e is a solution of the d equation Q7 Solve the following differential equation: 0 Q8 Solve the following differential equation :( ) ( ) 0, where 0 when Q9 Prove that a ( b ) is a solution of differential equation d 0 Q0 The slope of the tangent to a curve at an point (, )on it is given b cot cos, ( 0, 0) and the curve passes through the point (, π / ) Find the equation of the curve Q Solve: ( ) 0 subject to the initial condition (0) 0 Q Find the particular solution of the differential equation π cot cot, 0, given that 0, when Q Obtain the differential equation of the famil of ellipse of the famil of ellipse having foci on -ais and centre at the origin Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

5 Q d Solve the differential equation : given that, 0, when Q5 Solve the differential equation (log log ) Q6 Solve the differential equation : ( ) Q7 Solve the differential equation : ( ) Q8 Solve the differential equation, sec tan sec ; (0) Q9 Form the differential equation of the famil of curve ae be ce ; where a, b, c are some arbitrar constants Q0 Solve the differential equation: ( ) ( tan ), (0) 0 Q Solve the following differential equation: Given that, when Q Solve : ( ) ( ) Q Q Q5 Q6 Solve the differential equation: log log, 0 Write the order and degree of the differential equation, a e tan Write the IF of the differential equation ( ) d Write down the general sol of the differential equation 0 0 Q7 Write the IF of the differential equation ( ) 0 Q8 Write the order and degree of the differential equation, Q9 Find the particular solution of the differential equation d Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) cot cot, 0, π given that 0, when Q0 Find the particular solution of the differential equation ( ) sin ( ) cos, given that π when Q Find the differential equation of all the lines in the -plane Q Find the order and degree of the differential equation ρ d Q The general solution of the differential equation ( ) ( ) 0 Q Q5 Q6 Q7 Q8 d Order and degree of the differential equation The order and degree of the differential equation 0 Solve the differential equation: d Degree of the given differential equation d sin d The order and degree of the differential equation Q9 Solve : co ( cos ) sin ( sin ) 0 Q50 Q5 / / d Integrating factor of the linear diff eq ( ) d / Solve the differential equation: given that, 0, when / 5

6 Q5 Show the differential equation representing one parameter famil of curves ( ) c( ) is ( ) ( ) Q5 Solve the differential equation: log log, 0 Q5 From the differential equation corresponding to (-a) ( -b) r b eliminating a and b Q55 Show that the differential equation whose solution is ( ) Ce is Q56 Solve the differential equation, sec tan sec ; (0) Q57 Solve : e e Q58 Solve : ( )( ) ( )( ) 0 Q59 The normal lines to a given curve at each point pass through (,0 ) The curve passes through (, ) Formulate the differential equation and hence find out the equation of the curve Q60 cos Solve : sin Q6 Solve : cos tan Q6 π Solve the initial value problem: sin sin 0, () Q6 Solve : cos( ) sin( ) Q6 Solve e e e e Q65 Solve the differential equation ( ) 0, given that when Q66 The slope of the tangent to a curve at a point (, ) which passes through origin on it, is given b Find the equation of curve CONTINIUTY Q Find the value of a and b such that the function f defined b f() 5 if a b if < < 0 if 0 Q < Discuss the continuit and differentiabilit of f() ( )( ) at > & Q a If Determine the values of a and b so that f () is continuous f ( ) a b b at Q Find all the points of discontinuit of the function f () [ ] on [, )where [ ]denotes the greatest integer function Q5 a b,0 The function f () is defined as follows: f ( ), If is a 5b,, 8 continuous on [ 0,8], find the values of a and b Q6 Determine the values of a, b, c for which the function Q7 sin( a ) sin, for 0 is continuous at 0 f ( ) c, for 0 b, for 0 / b Find all the point of discontinuit of the function f defined b f ( ) 0 Q8 Show that the functions f ( ) is a continuous at ever R but fails to be Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

7 differentiable at - Q9 e Show that the function f ( ) if 0 is discontinuous at 0 e 0 if 0 Q0 a b, < Find the values of a and b if f() 9, is continuous at a b, > Q π sin if The function f is given b cos π ( ) a f if b( sin ) π ( π ) if Q Find all point of discontinuit of f, where f is defined as following : if f ( ) < < 6 if continuous and differentiable at, Q Is f () Q Show that f(), R, is continuous but not differentiable at Q5 Q6 Q7 Eamine the continuit of the function f defined b f() sin, 0 at 0 0, 0 If f () Let a b, if a, if 5 b, if cos, if 0 f ( ) a, if 0, if 0 6 at 0 5 < 5 is a continuous functions Find a, b Determine the value of a so that f () is continuous Q8 Q9 Q0 Q Show that lim does not eist If find the value of if is continuous at log( a) log( b),, if 0 If the function f () defined b f ( ), if 0 is k continuous at 0, find k Let π sin if cos π f ( ) a if b( sin ) π ( π ) if If f() is continuous at π LINEAR PROGRAMMING, find a and b Q Minimize and maimize of Z subject to 00 ; 0; 00 ;, 0 Q There is a factor located at each of the two places P & Q From these locations, a certain commodit is delivered to each of the three depots situated at A, B & C The weekl requirements of the depots 5, 5 & units of commodit while the production capacit of the factories at P & Q are respectivel 8 & 6 units The cost of transportation per unit is given below Formulate the above LPP mathematicall to determine how man units should be transported from each factor to each depot in order that the transportation cost is minimum T O C O S T ( i n R s ) A B C P Q Q Solve the following linear programming problem graphicall: Minimise Z subject to the constraints: 0 ; ; 0, 0 0 Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

8 Q Solve the following problem graphicall:minimise and Maimise Z 9 subject to the constraints: 60 ; 0 ; ; 0, 0 Q5 A cooperative societ of farmers has 50 hectare of land to grow two crops X and Y The profit from crops X and Y per hectare are estimated as Rs 0,500 and Rs 9,000 respectivel To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 0 litres and 0 litres per hectare Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land How much land should be allocated to each crop so as to maimise the total profit of the societ?; Q6 A to compan manufactures two tpes of dolls, A & B Market tests and available recourses have indicated that the combined production level should not eceeds 00 dolls per week and the demand for dolls of tpe B is at most half of that for doll of tpe A Further the production level of dolls of tpe A can eceeds three times the production of dolls of other tpe b at most 600 units If the compan makes profit of and 6 per doll respectivel on doll A and B,how man each should be produce weekl in order to maimum profit? Q7 An aero plane can carr a maimum of 00 passengers A profit of Rs 000 is made on each first class ticket and a profit of Rs 600 on each econom class ticket The air line reserves at least 0 sets for first class However, at least times as man passengers prefer to travel in econom class ticket Form a L P P to determine how man tickets of each class must be sold to maimize profit for the air lines Q8 David wants to invest at most Rs,000 in Bonds A and B According to the rule, he has to invest at least Rs,000 in Bond A and at least Rs,000 in Bond B If the rate of interest in bonds A and B respectivel are 8% and 0% per annum, formulate the problem as LPP and solve it graphicall for maimum interest Also determine the maimum interest received in a ear Q9 A dealer wishes to purchase a number of fans and sewing machines He has onl Rs5,760 to invest and has space for at most 0 items A fan and sewing machine cost Rs60 and Rs0 respectivel He can sell a fan at a profit of Rs and sewing machine at a profit of Rs8 Assuming that he can sell whatever he bus, how should he invest his mone in order to maimize his profit? Translate the problem into LPP and solve it graphicall Q0 A farmer has a suppl of chemical fertilizer of tpe A which contains 0% of nitrogen and 6% of phosphoric acid and of tpe B which contains 5% of nitrogen and 0% of phosphoric acid After soil testing it is found that at least 7 kg of nitrogen and the same quantit of phosphoric acid is required for a good crop The fertilizer of tpe A costs Rs500 per kg and the tpe B costs Rs800 per kg Using linear programming find how man kgs of each tpe of the fertilizer should be bought to meet the requirement and the cost be minimum Solve the problem graphicall Q A manufacturer produces two tpes of steel trunks He has two machines, A and B The first tpe of trunk requires hours on machine A and hours on machine B The second tpe requires hours on machine A and two hours on machine B Machines A and B can work at most for 8 hours and 5 hours per da respectivel He earns a profit of Rs0 per trunk on the first tpe of trunk and Rs5 per trunk on the second tpe Formulate a Linear Programming Problem to find out how man trunks of each tpe he must make each da to maimize his profit Q A dietician wishes to mi two tpes of foods in such a wa that vitamin contents of the miture contain at least 8 units of vitamin A and 0 units of vitamin C Food I contains units/kg of vitamin A and unit/kg of vitamin C Food II contains unit/kg of vitamin A and units/kg of vitamin C It costs Rs50 per kg to purchase Food I and Rs70 per kg to purchase Food II Formulate this problem as a linear programming problem to minimize the cost of such a miture Q Two tailors A and B are paid Rs50 and Rs00 per da respectivel A can stich 6 shirts and paints while B can stich 0 shirts and paints per da Form a linear programming problem to minimize the labour cost to produce at least 60 shirts and paints Solve the problem graphicall [ Q Kellogg is a new cereal formed of a miture of bran and rice that contains at least 88 grams of protein and at least 6 milligrams of iron Knowing that bran contains 80 grams of protein and 0 milligrams of iron per kilogram, and that rice contains 00 grams of protein and 0 milligrams of iron per kilogram, find the minimum cost of producing this new cereal if bran costs Rs5 per kilogram and rice costs Rs per kilogram Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

9 Q5 Ehibit graphicall the solution set of the linear in equations P, Q, R The monthl requirements of the schools are respectivel 0,0 and 50 food 5; ; 5 5; ; packets A packets contains lunch for 000 students Preparing capacit of kitchens Q6 Solve the following LPP b graphical method : Minimize ; Z 0 0 Subject A and B are 60 and 70 packets per month respectivel The transportation cost per to 0 ; 0 : 60 &, 0 packet from the kitchen to schools is given below : Q7 A compan makes three different products A, B and C b combining steel and Transportation cost per packet (in rupees) rubber Product A requires units of steel and units of rubber and can be sold at a To From profit of Rs 0 per unit Product B requires unit of steel and unit of rubber and A B can be sold at a profit of Rs 5 per unit Product C requires unit of steel unit of rubber and can be sold at a profit of Rs per unit There are 00 units of steel and P 5 0 units of rubber available per da, what should be dail production of each of the Q products, so that the combined profit is maimum Formulate it as a linear R 5 programming problem mathematicall How man packets from each kitchen should be transported to school so that Q8 A farmer decides to plant up to 0 hectares with cabbages and potatoes He decides the cost of transportation is minimum? Also find the minimum cost to grow at least but not more than 8 hectares of cabbages and at least but not Q Two godowns A and B have a grain capacit of 00 quintals and 50 quintals more than 6 hectares of potatoes If he can make a profit of Rs 500 per hectare on respectivel The suppl to three shops D, E and F, whose requirements are 60, 50 cabbages and Rs 000 per hectare on potatoes, how should he plan his farming so as and 0 quintals respectivel The cost of transportation per quintal from godowns to to get the maimum profit? From an LPP and solve it graphicall Q9 A compan manufactures two tpes of tos A and B Tpe A requires 5 minute each for cutting and 0 minute each for assembling Tpe B requires 8 minute for cutting and 8 minutes each for assembling These are hours available for cutting and hours available for assembling in a da The profit is Rs 50 each for tpe A and Rs 60 each for tpe B How man tos of each tpe should the compan manufacture in the shops are given below : How should the a da to maimize the profit? supplies be transported in order that transportation cost is minimum? Q0 Suppose ever gram of wheat provides 0 gm of proteins and 05 gm of Q An oil compan requires,000; 0,000 and 5,000 barrels of high grade, medium carbohdrates and the corresponding values for rice are 005 gm and 05 gm grade and low grade oil respectivel Refiner A produces 00, 00 and 00 barrels respectivel Wheat costs Rs 5 per kg and rice Rs 0 The minimum dail per da of high, medium and low grade oil respectivel whereas the Refiner B requirements of proteins and carbohdrates for an average child are 50 gm and 00 gm respectivel In what quantities should wheat and rice be mied in the dail diet produces 00, 00 and 00 barrels per da respectivel If A costs 00 per da to provide the minimum dail requirements of proteins and carbohdrates, if both the and B costs 00 per da to operate,how man das shoud each be run to items are to be taken up in each diet? minimize cost while satisfing requirements Q A small firm manufactures gold rings and chains The total number of rings and chains manufactured per da is at most It takes hour to make a ring and 0 Q5 A firm deals with two kinds of fruit juices -pineapple and the orange juice These are minutes to make a chain The maimum number of hours available per da is 6 If mied and two tpes of mitures are obtained which are sold as soft drinks A and B the profit on a ring is 00 and that on a chain is 90, find the number of rings One tin of A needs liters of pineapple juice and liter of orange juice One tin of and chains that should be manufactured per da, so as to earn the maimum profit B needs liters pineapple and liters of orange juice The firm has onl 6 liters of Make it as an LPP and solve it graphicall pineapple juice and liters of orange juice Each tin of A and B is sold at a profit of Q A categor agenc has two kitchens to prepare food at two places A and B From Rs/- and Rs/- respectivel How man tins of A and B should the firm produce to these places Mid-da Meal is to be supplied to three different schools situated at maimize profit? Formulate the linear programming problem and solve it Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)

10 graphicall using is profit line approach Q6 A firm makes two tpes of furniture: chairs and tables The contribution to profit for each product as calculated b the accounting department is Rs 0 per chair and 0 per table Both products are to be processed on three machines and The time required in hours b each product and total available in hours per week on each machine are as follows: Machine Chair Table Available Time M 6 M 5 50 M 6 60 How should the manufacture schedule their production in order to maimize profit? Q7 A fruit grower can use two tpes of fertilizer in his garden, brand P and brand Q The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table Tests indicate that the garden needs at least 0 kg of phosphoric acid, at least 70 kg of potash and at most 0 kg of chlorine If the grower wants to minimize the amount of nitrogen added to the garden, how man bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? Q8 An aero plane can carr a maimum of 50 passengers A profit of Rs 500 is made on each first class ticket and a profit of Rs 50 on each econom class ticket The air line reserves at least 5 sets for first class However, at least times as man passengers prefer to travel in econom class ticket Form a L P P to determine how man tickets of each class must be sold to maimize profit for the air lines Q9 If a oung man rides his motor ccle at 5 km per hour, he has to spend Rs per kilometer on petrol; if he rides at a faster speed of 0 km per hour, the petrol cost increases to Rs 5 per kilometer He has Rs 00 to spend on petrol and wishes to find the maimum distance he can travel within one hour Epress this as a linear programming problem and then solve it Q0 A factor owner wants to purchase two tpes of machines A and B, for his factor The machine A requires an area of 000 m and skilled men for running it and its dail output is 50 units, whereas the machine B requires 00 m area and 8 skilled man, and its dail output is 0 units If an area of 7600 m and 7 skilled men be available to operate the machines, how man machine of each tpe should be bought to maimize the dail output Q A producer has 0 and 7 units of labour and capital respectivel which he can use to produce two tpes of goods X and Y To produce one ulnit of X, units of capital and units of labour are required and to produce one unit of Y, units of labour and unit of capital is required If X and Y are priced at Rs 00 and Rs 0 respectivel, how should the producer use his resources to maimize the total revenue? From the LPP and solve it Q A farmer decides to plant upto 0 hectares with cabbages and potatoes He decides to grow at least but not more than 8 hectares of cabbages and at least but not more than 6 hectares of potatoes If he can make a profit of 500 per hectare on cabbages and 000 per hectare on potatoes, how should he plan his farming so as to get the maimum profit? From an LPP and solve it graphicall Q Kellogg is a new cereal formed of a miture of barn and rice that contain at least 88 gram of protein and 6 milligram of iron knowing that barn contain 80 gram of protein and 0 milligram of iron per kg and that rice contain 00 gram of protein and 0milligram of iron per kg, find the minimum cost of producing this new cereal if bran cost 5 per kg and rice cost per kg Q A to manufacturers produce two tpes of dolls ; a basic version doll A and delue version doll B Each doll of tpe B takes twice as long to produce as one doll of tpe A The compan have time to make a maimum of 000, dolls of tpe A per da, the suppl of plastic is sufficient to produce 500 dolls per da and each tpe requires equal amount of it The delue version ie tpe B requires a fanc dress of which there are onl 600 per da available If the compan makes profit of and 5 per doll respectivel on doll A and B, how man of each should be produced weekl in order to maimize the profit? Solve it b graphical method Q5 A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C Production of one chair requires hours on machine A, hour on machine B and hour on machine C Each table requires hour each on machine A and B and hours on machine C The profit obtained b selling one chair in 0 while b selling one table the profit is 60 The total time available per week on machine A is 70 hours, on machine B is 0 hours and on machine C is 90 hours How man chairs and tables should be made per week so as to maimize profit? Formulate the problem as LPP and solve it graphicall *************************** Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Target Mathematics b- AGYAT GUPTA ; Resi: D-79 Vasant Vihar ; Office : 89-Lami bai colon Ph :765; 00685, 6060(O) Mobile : ; ;95776(P) Ph :765; 00685, 6060(O) Mobile : ; ;95776(P)