On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :

A tangent to the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is

An ellipse has OB as a semi – minor axis, F, F¢ are its foci and the angle FBF¢ is a right angle. Then the eccentricity of the ellipse is

The equation of the tangents drawn at the ends of the major axis of the ellipse 9x² + 5y² – 30y = 0 is

For the ellipse 3x² + 4y² – 6x + 8y – 5 = 0

If S’ and S are the foci of the ellipse and P (x, y) be a point on it, then the value of SP + S’P is

The eccentricity of the curve represented by the equation x² + 2y² – 2x + 3y + 2 = 0 is

The foci of the ellipse 25 (x + 1)² + 9 (y + 2)² = 225 are

The eccentricity of the ellipse 9x² + 5y² – 30y = 0 is

The sum of all possible numbers greater than 10,000 formed by using {1,3,5,7,9} is

Number of different permutations of the word 'BANANA' is

In this question, one might think that the total number of permutations for the word BANANA is 6!
This is wrong because in the word BANANA we have the letter A repeated thrice and the letter N repeated twice.

The number of one - one functions that can be defined from into is

Four dice are rolled then the number of possible out comes is

The number of ways in which 5 different coloured flowers be strung in the form of a garland is :

Number of ways to rearrange the letters of the word CHEESE is

The number of ways in which 17 billiard balls be arranged in a row if 7 of them are black, 6 are red, 4 are white is

We cannot arrange the billiards balls as follows:
There are 17 balls, so the total number of arrangements = 17!
This is incorrect because this method is applicable only when the balls are distinct, not identical. But, in our case, all the balls of the same color are identical.