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

• 4!

• 5!

• $\frac{4!}{2}$

• $\frac{5!}{2}$

42.

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

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

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

S₁, S₃, ...... ,S₁₀ are the speakers in a conference. If S₁ addresses only after S₂,then the number of ways the speakers address iS

• 10!

• 9!

• $10! \times 8!$

• $\frac{10!}{2}$

A three digit numbern is such that the last twodigits of it are equal and differ from the first. The number of such n's is

• 64

• 72

• 81

• 900

Eight different letters of an alphabet are given. Words of four letters from these are formed.The number of such words with at least one letter repeated is :

• $\left(\begin{array}{c}8\\ 4\end{array}\right) - {}^8\mathrm{P}_4$

• $8^4 + \left(\begin{array}{c}8\\ 4\end{array}\right)$

• $8^4 - {}^8\mathrm{P}_4$

• $8^4 - \left(\begin{array}{c}8\\ 4\end{array}\right)$

The number of natural numbers less than 1000, in which no two digits are repeated, is :

• 738

• 792

• 837

• 720

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

• 18720

• 18270

• 17280

• 12780