Class -12: Mathematics

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b}

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive.

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Let T be the set of all triangles in a plane with R a relation in T given by R = {(T1, T2) : T1 is congruent to T2}. Show that R is an equivalence relation.

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R′ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Let a tank contains 1000 litres of brine which contains 250 g of salt per litre. Brine containing 200 g of salt per litre flows into the tank at the rate of 25 litres per minute and the mixture flows out at the same rate. Assume that the mixture is kept uniform all the time by stirring. What would be the amount of salt in the tank at any time t?

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Suppose a company plans to produce a new product that incur some costs (fixed and variable) and let the company plans to sell the product at a fixed price. Prepare a mathematical model to examine the profitability.

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

A manufacturer of medicines is preparing a production plan of medicines M1 and M2. There are sufficient raw materials available to make 20000 bottles of M1 and 40000 bottles of M2, but there are only 45000 bottles into which either of the medicines can be put. Further, it takes 3 hours to prepare enough material to fill 1000 bottles of M1, it takes 1 hour to prepare enough material to fill 1000 bottles of M2 and there are 66 hours available for this operation. The profit is Rs 8 per bottle for M1 and Rs 7 per bottle for M2. How should the manufacturer schedule his/her production in order to maximise profit?

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Let a business firm produces three types of products P1, P2 and P3 that uses three types of raw materials R1, R2 and R3. Let the firm has purchase orders from two clients F1 and F2. Considering the situation that the firm has a limited quantity of R1, R2 and R3, respectively, prepare a model to determine the quantities of the raw material R1, R2 and R3 required to meet the purchase orders.

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Query KaroQK#001

Asked: February 23, 2024In: Class -12: Mathematics

Why Mathematical Modelling?

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Class -12: Mathematics

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