Find the differential equation representing the family A of curves Ï… = A/r + B, where A and B are arbitrary r constants.
Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctually. The school P wants to award Rs x each, y each and Rs z each for the three respective values to its 3,2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4,1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value. Apart from the above three values, suggest one more value for awards.
Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < Ï€, is strictly increasing or strictly decreasing.
Find the particular solution of the differential equation (1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.
Three Schools A, B and C organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand made fans, mats and plates from recycled material at a cost of Rs 25, Rs 100 and Rs 50 each. The number of articles sold are given below:
Find the fund collected by each school separately by selling the above articles. Also find the total funds collected for the purpose. Write one value generated by the above situation.
Let/: N -> N be a function defined as/(x) = 9x2 + 6x-5. Show that: N—>S, where S is the range off, is invertible. Find the inverse of f and hence find f-1 (43) and f-1(163).
Using integration find the area of the region {(x, y): x2 +y2 ≤2ax, y2 ≥ ax, x,y≥ 0}
Find the coordinate of the point P where the line through A(3, -4,-5) and B (2, – 3,1) crosses the plane passing through three points L (2,2,1), M (3,0,1) and N (4, -1,0). Also, find the ratio in which P divides the line segment AB.
A manufacturer produces two products A and 6. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs 7 profit and B at a profit of Rs 4. Find the production level per day for maximum profit graphically.
