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 product of r consecutive positive integers is divisible by

(a)

r!

(b)

(r-1)!

(c)

(r+1)!

(d)

r^r

If ^a2-a \(C_2 = ^{a^2-a}\) C₄ then the value of 'a' is

(a)

2

(b)

3

(c)

4

(d)

5

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

(a)

45

(b)

40

(c)

39

(d)

38

The number of different signals which can be give from 6 flags of different colours taking one or more at a time is _________

(a)

1958

(b)

1956

(c)

16

(d)

64

The number of ways to average the letters of the word CHEESE are _________

(a)

120

(b)

240

(c)

720

(d)

6

Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is _________

(a)

24

(b)

30

(c)

125

(d)

100

The product of r consecutive positive integers is divisible by _________

(a)

r!

(b)

r!+1

(c)

(r+1)

(d)

none of these

If 15C_3r = 15 C_r+3 , then r is equal to _________

(a)

5

(b)

4

(c)

3

(d)

2