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

(a)

120

(b)

240

(c)

720

(d)

6

If p(n):49ⁿ + 16ⁿ +\(\lambda \) is divisible by 64 for n \(\in \) N is true, then the least negative integral value of \(\lambda \) is _________

(a)

-3

(b)

-2

(c)

-1

(d)

-4

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 ways in which we can post 5 letters in 10 letter boxes is  _________

(a)

50

(b)

5¹⁰

(c)

10⁵

(d)

1