Q1 Let A = Set of boys of XII Class in some school. Let a R b, if and only if a and b use unfair means in the exam, a,b A
(i) Is R a transitive relation?
(ii) Should a student use such means? If not why Q2 There are two families P and Q . There are 3 men, 3 women and 12 children in family P and 2men, 2 women and 4 children in family Q. The recommended daily allowance for calories is :
Man : 2400, woman : 2000, child : 1400 and man : 60g for proteins is : woman : 40g and child : 35g.
(i) Represent the above information by matrices. Using matrix multiplication, calculate the total requirement of calories and proteins of each of the two families. (ii) Which family is an ideal family and why ? Q3 Represent the following problem by a system of linear equations : Rs 154500 is the Cost of 3 cycles, 2 motorbikes and one car, the cost of one cycle, one motorbike and 2 cars is Rs 226500. The cost of 4 cycles and 3 motorbikes is Rs 81000. Use matrix to Find the cost of each . Which mode of conveyance preferred the most and why? Q4 Two firms P and Q decided to award prizes to their employees for three values Punctuality (x), Honesty (y) and obedience (z). Firm P decided to award a total of Rs 22000 for the three values to 10,8 and 6 employees respectively, while firm Q decided to award Rs 21400 for the three values to 8,6 and 10 employees respectively. If all the three prizes together amount to Rs 2700, then (i) Represent the above situation by a matrix equation and form linear equations using matrix multiplication.
(ii) Is it possible to solve the system of linear equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why? Q5 Two schools A and B decided to award prizes to their students for the three values Truth (x), patriotism (y) and Non - violence (z). School A decided to award a total of Rs 11000 For the three values to 5,4 and 3 students respectively. While school B decided to award Rs 10700 for the three values to 4,3 and 5 students respectively . If all the three prizes together amount to Rs 2700, then (i) Represent the above situation by a matrix equation and form linear equations using matrix multiplication.
(ii) Is it possible to solve the system of equations so obtained using matrices? (iii) Which value you prefer to be awarded most and why?
Q6 A sum of saving amount of Rs 10000 is put into three investments at the rate of 10%, 12% and 15% p.a. The combined income of first and second investment is Rs 190 less of the income of third investment. If the combined income is Rs 1310, then find the Investment in each using matrices. Keeping nation’s growth in mind, justify the value of saving in individual life. Q7 A window is in the form of rectangle surmounted by a semicircular opening. The total perimeter of the window is 10m. Find the dimensions of the window to admit maximum sunlight through the whole opening. Explain the importance of sunlight. Q8 A manufacturer can sell bio gas operated x items at a price of Rs each. The cost price of bio gas operated x items is Rs . Find the number of items he should sell to earn maximum profit. Explain the importance of use of renewable resources of energy. Q9 Anil wants to invest at most Rs 12000 in Saving Certificates and National Saving Bonds. According to rules, he has to invest at least Rs 2000 in Saving Certificates and at least Rs 4000 in National Saving Bonds. If the rate Of interest on Saving Certificate is 8% Per annum and the rate of interest on National Saving Bonds is 10% per annum, how much money should he invest to earn maximum yearly income? Find also his maximum yearly income....
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