There are 10 professors and 20 lecturers, Out of whom a committee of 2 professors and 3 lecturers is to be formed, find

In a group at 100 men 5 persons are good lecturers and from 1000 women 5 are good lecturers. Here numbers of men and women are equal. One good lecturer is selected from the group. Find the probability of an event that selected lecturer is man.

There are 10 points in a plane, out of these 6 are collinear. The number of triangles formed by joining these points, is

There are 10 persons named ""P_1,P_2,P_3,....,P_10' Out of 10 persons, 5 persons are to be arrangement P_1 must occur where as P_4 and P_5 do not occur. Find the number of such possible arrangements.

Find the equation of sphere whose centre is (5, 2, 3) and radius is 2 in cartesian form .

A committee of 4 students is selected from a group of 8 boys and 4 girls. Given that there is at least one girl in the committee. Find probability of an event that there are exactly 2 girls in the committee.

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

A committee of 6 is to be chosen from 10 men and 7 women. So as to contain atleast 3 man and 2 women. In how many different ways can this be done, if two particular women refuse to serve on the same committee ?

A block of mass 1 kg falls freely on a spring form a height of 20 cm as shown in figure . Find the compression in the spring if its force constant is 10^(3) N/m . ( Take g = 10.0 m//s^(2) )

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?