about to only mathematics

Five books on english and three books on mathematics are placed at random on a bookshelf . Find the probability that the books on mathematics are placed side by side.

Among the examinees in an examination, 25%, 30% and 45% failed in statistics, in mathematics and in at least one of statistics and mathematics respectively. An examincee is selected at random. Find the probability that he failed in statistics only.

Among the examinees in an examination, 25%,30% and 45% failed in statistics, in mathematics and in at least one of statistics and mathematics respectively. An examinee is selected at random. Find the probabilities that (i) he failed in statistics only (ii) he passed in statistics if it is known that he failed in mathematics.

A bag contains a total of 20 books on physics and mathematics. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 2 books on mathematics.

A bag contains a total of 20 books on physics and mathematics, Any possible combination of books is equally likely. Ten books are chosen from the bag and it is found that it contains 6 books of mathematics. Find out the probability that the remaining books in the bag contains 3 books on mathematics.

20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching only physics is

In a survey of 35 students of a class it was found that 17 students like mathematics and 10 like Mathematics but not Biology. Find the number of students who like (i) Biology, (ii) Biology but not Mathematics, it being given that each student takes at least one of the two subjects.

Establish the mathematical expression of de Broglie wavelength about dual nature of electrons .

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics. How many teach physics ?

State the mathematical definition of enthalpy.