Meidan of a data , arranged in ascending order 7,10,15,x,y,27,30 is 17 and when one more observation 50 is added to the data, the median has become 18 . Find x and y.

If the median of the observations arranged in the ascending order as 6, 7, x-2, x, is 10 then the value of x is .....

Some observations are arranged in the ascending order as 9, a +3, a +7, 20, 23 and 26. If the median of the data is 18.5, find the value of a. Also find the mean of the data.

If the median of the observations arranged in the ascending order as 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5, then x = . . . .

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x. 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Find the orthocentre of the triangle formed by the lines 4x-7y+10=0,x+y=5 and 7x+4y=15 .

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data . {:("Number of cars ",0-10,10-20,20-30,30-40,40-50,50-60,60-70,70-80),("Frequency "," "7," "14," "13," "12," "20," "11," "15," "8):}

Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A, coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

(Allocation problem) A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Rs. 10,500 and Rs. 9000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 litres and 10 litres per hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to to maximise the total profit of the society ?