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!

The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is

(a)

⁵²C₅

(b)

⁴⁸C₅

(c)

⁵²C₅ + ⁴⁸C₅

(d)

⁵²C₅ - ⁴⁸C₅

The number of 10 digit number that can be written by using the digits 2 and 3 is

(a)

¹⁰C₂+⁹C₂

(b)

2¹⁰

(c)

2¹⁰-2

(d)

10!

The product of first n odd natural numbers equals

(a)

²ⁿC_n\(\times\)ⁿP_n

(b)

\({ \left( \frac { 1 }{ 2 } \right) }^{ n }\times\)²ⁿC_n\(\times\)ⁿP_n

(c)

\({ \left( \frac { 1 }{ 4 } \right) }^{ n }\times \)²ⁿC_n\(\times\)²ⁿP_n

(d)

ⁿC_n \(\times\)ⁿP_n

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

(a)

120

(b)

240

(c)

720

(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 7 points out of 12 are in the same straight line then the number of triangles formed is _________

(a)

35

(b)

21

(c)

220

(d)

185

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

If ⁿP_t = 720 nCr, then the value of r =  _________

(a)

6

(b)

5

(c)

4

(d)

7