The sum of the digits at the 10^th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

(a)

432

(b)

108

(c)

36

(d)

18

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

(a)

30⁴\(\times\) 29²

(b)

30³\(\times\) 29³

(c)

30²\(\times\) 29⁴

(d)

30\(\times\)29⁵

The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is

(a)

2 \(\times\) ¹¹ C₇+¹⁰C₈

(b)

¹¹C₇+¹⁰C₈

(c)

¹²C₈-¹⁰C₆

(d)

¹⁰C₆+2!

Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is

(a)

11

(b)

12

(c)

10

(d)

6

The product of r consecutive positive integers is divisible by _________

(a)

r!

(b)

r!+1

(c)

(r+1)

(d)

none of these

If mC₁ = nC₂, then _________

(a)

2m = n

(b)

2m = n(n+1)

(c)

2m = n(n-1)

(d)

2n=m(m-1)

The number of ways of selecting of 3 poets and 4 scientists such that poets are in even places _________

(a)

12

(b)

36

(c)

72

(d)

144

The number of ways of disturbing 7 identical balls in 3 distinct boxes, so that no box is empty is  _________

(a)

7

(b)

6

(c)

35

(d)

15

The number of integers greater than 6000 that can be formed, using the digits 3, 5, 6, 7 and 8 without repetition  _________

(a)

216

(b)

192

(c)

120

(d)

72

Each of five questions is a multiple-choice test has 4 possible answers. The number of different sets of possible answers is  _________

(a)

4⁵-4

(b)

5⁴-5

(c)

1024

(d)

1023