A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find:
(i) the production in the 1st yea
(ii) the production in the 10th year
(iii) the total production in first 7 years Solution :

Write the following sets in the roster form. (i) B is the set of all months in a year having 30 days. (ii) P is the set of all prime numbers smaller than 10. (iii) X is the set of colours of the rainbow.

A country has a food deficit of 10%. Its population ear. Its annual food production every year is 4% more than that of the last year Assuming that the average food requirement per person remains constant, prove that the country will become self-sufficient in food after n years, where n is the smallest integer bigger than or equal to (log_e 10-log_e 9)/((log_e 1.04)-0.03)

Which of the following are sets? Justify your answer (i) The collection of all the months of a year begimng with the letter "J". (ii) The collection of ten most talented writers of India. (iii) A team of eleven best cricket batsmen of the world. (iv) The collectionofall boys in your class. (v) The collection of all even integers.

In which of the following situations, does the list of numbers involved form an arithmetic progression, and why? (i) The taxi fare after each km fare is 15 for the first km Rs.8 for each additional km. (ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time. (iii) The cost of digging a well, after every metre of digging, when it costs 150 for the first metre and rises by 50 for each subsequent metre. (iv) The amount of money in the account every year, when 10000 is deposited at compound interest at 8 % per annum.

(i) A kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court? (ii) There are 15 persons in a party and if , each 2 of them shakes hands wit each with each other. How many handshakes happen in the party? (iii) How many chords can be drawn through 20 points on a circle? (iv) In a parking lot one hunderd, one year old cars are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars are possible? (v) How many ways can a team of 3 boys, 2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgender?

State whether the following sets are finite or infinite. (i) The set of months in a year. (ii) {1,2,3, ..., 99, 100) (iii) The set of prime numbers smaller than 99. (iv) The set of letters in the English alphabet. (v) The set of lines that can be drawn are parallel to the X-Axis (vi) The set of numbers which are muitiplies of 5. (vii) The set of circles passing through the origin (0,0).

In an ore containing uranium, the ratio of ""^(238)U to ""^(206)Pb nuclei is 3. Calculate the age of the ore assuming that all the lead present in the ore is the final stable product of ""^(238)U . Take half-life of ""^(238)U to be 4.5xx10^(9) years.

Read the statements regarding a stable community and choose the correct option.I. Must be resistant to occasional disturbances.II.Should show much variation in productivity from year to year.III. Must be resistant to invasions by alien species.

Which of the following sets are finite or infinite? i. The set of months of a year ii. {1,2,3,. . . .} iii. {1,2,3,. . . .99,100} The set of positive integers gt 100 v. The set of prime numbers lt 99