Question

There are three papers of 100 marks each in an examination. Then the no. of ways can a student get 150 marks such that he gets atleast 60% in two papers

Solution

Correct option is

3C2 × 32C2

Therefore,

         Sum of marks obtained = 150

         

The required number of ways

        = No, of integral solutions of (i)

        = Coefficient of x150 in {x60 x61 + …+x100)2 (1+ x + x2+  …+ x30)}         

        = Coefficient of x30 in {(1 + x + … + x40)(1 + x + … + x30)}

        

        = Coefficient of x30 in (1 – x)-3

        = 30 + 3 – C3 – 1 32C2.

Thus, the student gets atleast 60% marks in first two papers to get 150 marks as total in 32C2 ways. But the two papers, of atleast

60% marks, can be chosen out of three papers in 3C2 ways.

Hence the required number of ways = 3C2 × 32C2.

SIMILAR QUESTIONS

Q1

Find the sum of all four-digit numbers that can be formed using digits 0, 1, 2, 3, 4, no digits being repeated in any number.

Q2

If m parallel lines in plane are intersected by a family of n parallel lines. Find the number of parallelograms formed.

Q3

There are n concurrent lines and another line parallel to one of them. The number of different triangles that will be formed by the (n + 1) lines, is

Q4

Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them, is

Q5

The sides AB, BC and CA of a triangle ABC have a, b and c interior points on them respectively, then find the number of triangles that can be constructed using these interior points as vertices.

Q6

Let is a set containing n elements. A subset P of set X is chosen at random. The set X is then reconstructed by replacing the elements of set Pand another set Q is chosen at random then find the number of ways to form sets such that 

Q7

Let is a set containing n elements. A subset P of set X is chosen at random. The set X is then reconstructed by replacing the elements of set Pand another set Q is chosen at random. Find  number of ways to  chosenand Q such that ∪ Q contains exactly r elements.

Q8

In how many ways can 12 books be equally distributed among 3 students?

Q9

10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys so that exactly 2 children do not get any toy, is equal to:

Q10

There are 20 persons among whom are two brothers. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers.