A salesman has the following record of sales during three months for three items `A, B and C` which have different rates of commission Month, Sale of units, Total commissiondrawn (in Rs) Find out the rates of commission on items `A, B and C` by using deter-minant method.

The given bar graph shows the number of identical articles sold by 5 different stores A, B, C, D and E during a particular month. Study the bar graph and answer the following questions : (i) Which store sold the largest number of articles ? (ii) By what per cent is the sale of store D more than that of store B ? (iii) Find the ratio of the total sale of the two highest selling stores to the total sale of the two least selling stores. (iv) By how much must store E increase its sale to catch up with its nearest rival store ?

The prices of three commodities P ,\ Q ,\ a n d\ R are Rs x ,\ y\ a n d\ z per unit respectively. A purchases 4 units of R and sells 3 unit of P and 5 units of Qdot B purchases 3 units of Q and sells 2 units of P and 1 unit of Rdot C purchases 1 unit of P and sells 4 units of Q and 6 units of Rdot In the process A ,\ B\ a n d\ C earn Rs 6000, 5000 and 13000 respectively. If selling the units is positive earning and buying the units is negative earnings, find the price per unit of three commodities by using matrix method.

Three colonies of insects were each treated with a different pesticide over an 8-week period to test the effectiveness of the three pesticides. Colonies A, B, and C were treated with Pesticides A, B, and C, respectively. Each pesticide was applied every 2 weeks to one of the three colonies over the 8-week period. The bar graph above shows the insect counts for each of the three colonies 0, 2, 4, 6, and 8 weeks after the initial treatment. Of the following, which is closest to the ratio of the total number of insects in all three colonies in week 8 to the total number of insects at the time of initial treatment?

A rubber company is engaged in producing three types of tyres A, B and C. each type requires processing in two plants, Plant I and Plant II. The capacities of the two plants, in number of tyres per day, are as follows: Plants A B C I 50 100 100 II 60 60 200 The monthly demand for tyre A, B and C is 2500, 3000 and 7000 respectively. If plant I costs Rs. 2500 per day, and plant II costs R. 2500 per day to operate , how many days should each be run per month to minimize cost while meeting the demand? Formulate the problem as LPP.

krishna has an apple orchard which has a 10 m xx 10 m sized kitchen garden attached to it . She divides it into a 10 xx 10 grid and puts soil and manure into it She growns a lemon plants at . A a coriander plants at B , an onion plants at C and a tamato plants at D. Her bushand Ram prasied her kitchen graden and points out that on joining A, B, C, and D they may form a paralleleogram Look at the below. figure carefully and answer the following question. (i) Write the coordinates of the points A,B, C and D using the 10 xx 10 grid as coordinate axes. (ii) Find whether ABCD is a paralleogram or not .

Krishna has an apple orchard which has a 10 m xx 10 m sized kitchen garden attached to it. she divides it into a 10 xx 10 grid and puts soil and manure into it. she grows a lemon plant at A, a coriander plant at B, an onion plant at C and a tomato plant at D. Her husband Ram praised her kitchen garden and points out that on joining A,B,C and D they may form a parallelogram. look at the below figure carefully and answer the following questions: (i) write the coordinates of the points A,B,C and D using the 10xx10 grid as coordinate axes. (ii) find whether ABCD is a parallelogram or not.

The reaction 2AX(g)+2B_(2)(g)rarr A_(2)(g)+2B_(2)X(g) has been studied kinetically and on the baiss of the rate law following mechanism has been proposed. I. 2A X hArr A_(2)X_(2) " " ("fast and reverse") II. A_(2)X_(2)+B_(2)rarrA_(2)X+B_(2)X III. A_(2)X+B_(2)rarrA_(2)+B_(2)X where all the reaction intermediates are gases under ordinary condition. form the above mechanism in which the steps (elementary) differ conisderably in their rates, the rate law is derived uisng the principle that the slowest step is the rate-determining step (RDS) and the rate of any step varies as the Product of the molar concentrations of each reacting speacting species raised to the power equal to their respective stoichiometric coefficients (law of mass action). If a reacting species is solid or pure liquid, its active mass, i.e., molar concentration is taken to be unity, the standard state. In qrder to find out the final rate law of the reaction, the concentration of any intermediate appearing in the rate law of the RDS is substituted in terms of the concentration of the reactant(s) by means of the law of mass action applied on equilibrium step. Let the equilibrium constant of Step I be 2xx10^(-3) mol^(-1) L and the rate constants for the formation of A_(2)X and A_(2) in Step II and III are 3.0xx10^(-2) mol^(-1) L min^(-1) and 1xx10^(3) mol^(-1) L min^(-1) (all data at 25^(@)C) , then what is the overall rate constant (mol^(-2) L^(2) min^(-1)) of the consumption of B_(2) ?

The figure below depicts life-histroy strategies for three plant species (a,b and c) along 3 axes : strength of competition with other organisms, level of distrubance in the habitat, and level of environmental stress in the habitat. Species a grows in habitats where competition among species b grown in habitats with and stress are low. Species b grows in habitats with high environmental stress but with low interspecies competition. Species c grows in highly disturbed habitats with low enviornmental stress. Which of the statements below is/are correct ? I. Characteristics of "a-type" plants are faster growth rate and short-lived leaves. II. Desert annual plants are "b-type" species. they have rapid growth and produce large amount of seeds in a short time after rains. III. Most plants belonging to "c-type" species would be herbaceous while "a-type" and "b-types" species are likely to be trees or shrubs.

The reaction 2AX(g)+2B_(2)(g)rarr A_(2)(g)+2B_(2)X(g) has been studied kinetically and on the baiss of the rate law following mechanism has been proposed. I. 2A X hArr A_(2)X_(2) " " ("fast and reverse") II. A_(2)X_(2)+B_(2)rarrA_(2)X+B_(2)X III. A_(2)X+B_(2)rarrA_(2)+B_(2)X where all the reaction intermediates are gases under ordinary condition. form the above mechanism in which the steps (elementary) differ conisderably in their rates, the rate law is derived uisng the principle that the slowest step is the rate-determining step (RDS) and the rate of any step varies as the Product of the molar concentrations of each reacting speacting species raised to the power equal to their respective stoichiometric coefficients (law of mass action). If a reacting species is solid or pure liquid, its active mass, i.e., molar concentration is taken to be unity, the standard state. In qrder to find out the final rate law of the reaction, the concentration of any intermediate appearing in the rate law of the RDS is substituted in terms of the concentration of the reactant(s) by means of the law of mass action applied on equilibrium step. How many times the rate of formation of A_(2) will increase if concentrations of AX is doubled and that of B_(2) is increased theee fold?