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

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

^(n-1)C_r + ^(n-1)C_(r-1) is

(a)

⁽ⁿ⁺¹⁾C_r

(b)

^(n-1)C_r

(c)

ⁿC_r

(d)

ⁿC_r-1

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 rectangles that a chessboard has

(a)

81

(b)

9⁹

(c)

1296

(d)

6561

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!

If P_r stands for ^r P_r then the sum of the series 1+ P₁ + 2P₂ + 3P₃ +...+ nP_n is

(a)

P_n+1

(b)

P_n+1-1

(c)

P_n-1+1

(d)

⁽ⁿ⁺¹⁾P_(n-1)

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

If ⁿC₄,ⁿC₅,ⁿC₆ are in AP the value of n can be

(a)

14

(b)

11

(c)

9

(d)

5

1+3+5+7+........+17 is equal to

(a)

101

(b)

81

(c)

71

(d)

61