Class -12: Mathematics

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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

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.

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Query KaroQK#001

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

Show that if x2 – 5x + 6 = 0, then x = 3 or x = 2.

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Query KaroQK#001

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

Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

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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

Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric.

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Query KaroQK#001

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

Prove that the function f : R → R defined by f (x) = 2x + 5 is one-one.

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Query KaroQK#001

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

Show that the relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

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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

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

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Class -12: Mathematics

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