Total number of words formed by 3 vowels and 5 consonants taken from 4 vowels and 7 consonants is equal to ______.

1

(a)

75360

(b)

60480

(c)

54230

(d)

none of these

The number of ways to arrange the letters of the word HAPPY are ______.

1

(a)

120

(b)

90

(c)

40

(d)

60

The number of ways in which 8 men can be arranged in a row so that three particular men are seated consecutively is ______.

1

(a)

6! \(\times\)3!

(b)

5!

(c)

9! \(\times\) 3!

(d)

none of these

The number of arrangements of the letters of the word BHARAT taking 3 at a time is ______.

1

(a)

54

(b)

120

(c)

62

(d)

72

If ⁴⁰C_r+2 = ⁴⁰C_r-2 then r is equal to ______.

1

(a)

20

(b)

18

(c)

14

(d)

28

If ^mC₂ = ⁿC₁ then ______.

1

(a)

m = 2n

(b)

m(m-1) = 2n

(c)

m = 2n(n+1)

(d)

none of these

If ⁿC_r+ⁿC_r+1=ⁿ⁺¹C_x then x is equal to ______.

1

(a)

r-2

(b)

r-1

(c)

n+1

(d)

r+1

⁶C₁ + ⁶C₂+⁶C₃+⁶C₄+⁶C₅+⁶C₆ is equal to ______.

1

(a)

63

(b)

43

(c)

83

(d)

none of these

If C₀ + C₁ + C₂ +...+C_n = 256 then ²ⁿC₂ is equal to ______.

1

(a)

45

(b)

105

(c)

120

(d)

130

If ⁿ⁺¹C₃ = 2.ⁿC₂ then n is equal to ______.

1

(a)

2

(b)

3

(c)

4

(d)

5