A polygon has 44 diagonals. Find the number of sides.

• 8

• 10

• 11

• 13

In how many ways, words can be made from the letters of the word BHARAT in which B and H are never together ?

• 360

• 300

• 240

• 120

In how many ways can 5 keys be put in a ring ?

• 4!

• 5!

• $\frac{4!}{2}$

• $\frac{5!}{2}$

20 persons are invited for a party. The number of ways in which they and the host can be seated at a circular table, if two particular persons be seated on eitherside of the host is equal to

• 2 . (18)!

• 18! . 3!

• 19! . 2!

• None of these

The number of ways in which 5 boys and 4 girls sit around a circular tables. So, that no two girls sit together is

• 5! 4!

• 3! 3!

• 5!

• 4!

Using the digits 0, 2, 4, 6, 8 not more than once in any number, the number of 5 digited numbers that can be formed, is

• 16

• 24

• 96

• 120

The number of ways that 8 beads of different colours be strung as a necklace is

• 2520

• 2880

• 4320

• 5040

The number of 5-digited number which are not divisible by 5 and which consists of different odd digits is

• 24

• 32

• 96

• 120

49.

Let l₁ and l₂ be two lines intersecting at P. If A₁, B₁, C₁ are points on l₁, and A₂, B₂, C₂, D₂, E₂ are points on l₂ and if none of these coincides with P, then the number of triangles formed by these eight points, is :

• 56

• 55

• 46

• 45

Consider the fourteen lines in the plane given by y = x + r, y = - x + r,where r $\in$ {0, 1, 2, 3, 4, 5, 6}. The number of squares formed by these lines, whose sides are of length $\sqrt{2}$, is

• 9

• 16

• 25

• 36