There are `n` locks and `n` matching keys. If all the locks and keys are to be perfectly matched, find the maximum number of trails required to open a lock.

If characteristic of three numbers a, b and c and 5, -3 and 2, respectively, then find the maximum number of digits in N = abc.

Explain lock and key mechanism.

The "lock and key", model of enzyme action illustrates that a particular enzyme molecule

A bag contain n white and n black balls, all of equal size. Balls are drawn at random. Find the probability that there are both white and black balls in the draw and that the number of white balls is greater than that of black balls by 1.

There are n points in a plane in which no large no three are in a straight line except m which are all i straight line. Find the number of (i) different straight lines, (ii) different triangles, (iii) different quadrilaterals that can be formed with the given points as vertices.

Two teams are to play a series of five matches between them. A match ends in a win, loss, or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain n people, where n is a. 81 b. 243 c. 486 d. none of these

Let C_1, C_2, ,C_n be a sequence of concentric circle. The nth circle has the radius n and it has n openings. A points P starts travelling on the smallest circle C_1 and leaves it at an opening along the normal at the point of opening to reach the next circle C_2 . Then it moves on the second circle C_2 and leaves it likewise to reach the third circle C_3 and so on. Find the total number of different path in which the point can come out of nth circle.

Two friends Aa n dB have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of Aa n dB . The probability that all the tickets go to the daughters of A is 1/20. Find the number of daughters each of them have.

In a conference 10 speakers are present. If S_1 wants to speak before S_2a n dS_2 wants to speak after S_3, then find the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number.