How many 4-digit numbers are there, when a digit may be repeated any number of times?

2

(a)

How many 3 digit numbers more than 600 can be formed by using the digit 2, 3, 4, 6 and 7.

2

(a)

How many words can be formed out of the letters of the word 'ORIENTAL' so that the vowels occupy the odd places?

2

(a)

How many different words can be formed with the letters of the word SUNDAY? How many of these begin with N? How many begin N and end in Y?

2

(a)

A man wants to select a shirt and trousers from a showroom. If there are 20 shirts and 50 trousers in variety, in how many ways can he choose one shirt and one trousers?

2

(a)

How many three digit odd numbers can be formed by using the digits 1,2,3,4,5 and 6 if (i) the repetition of digits is not allowed. (ii) the repetition of digits is allowed.

2

(a)

In how many ways can 5 letters be posted in 4 letter boxes?

2

(a)

If \(\frac { (n-1)! }{ (n-4)! } :\frac { n! }{ (n-4)! } \) = 1:9, find the value of n

2

(a)

Evaluate:\(\frac { 15! }{ 9!5! } \)

2

(a)

\(\text{If } \frac { (n-1)! }{ n-4)! } :\frac { n! }{ (n-4)! } =1:9\) find the value of n

2

(a)

If ⁿC _r-1=36, ⁿC_r = 84 and ⁿC_r+1 = 126 then find ^rC₂

2

(a)

If ⁿC₅ and ⁿC₄ are in A.P. then find n.

2

(a)

Find r if ⁵⁴P_r+3 : ⁵⁴P_r+3 = 30800 : 1

2

(a)

If ²ⁿC₃ : ⁿC₂ = 44 : 3, find n

2

(a)

In how many ways 9 pictures can be hung from 6 pictures nail on a wall?

2

(a)