The number of points of intersection of diagonals which lie within the decagon: `^10 C_2` b. `^10 C_4^` c. `^10 C_6+1` d. `10+^(10)C_2`

Evaluate .^10C_4+^10C_5

The coordinates of the point of intersection of the lines (x-1)/1=(y+2)/3=(z-2)/(-2) with the plane 3x+4y+5z-25=0 is (A) (5,6,-10) (B) (5,10,-6) (C) (-6,5,10) (D) (-6,10,5)

The number of positive numbers of not more than 10 digits formed by using 0,1,2 and 3 is (A) 18 (B) 24 (C) 4^10, 3^10 (D) 4^10-1

Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, 10 passengers enter the train during the journey with 10 different ticket of two class. The number of different sets of tickets they may have is a. ^15 C_(10) b. ^20 C_(10) c. ^30 C_(10) d. none of these

A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to a. ^20 C_(10)xx2^(10) b. ^20 C_(10)xx3^(20) c. ^20 C_(10)xx3^(10) d. ^20 C_(10)xx2^(20)

In a polygon the number of diagonals is 54. The number of sides of the polygon, is A. 10 B. 12 C. 9 D. None of these

Find the sum .^(10)C_1+^(10)C_3+^(10)C_5+^(10)C_7+^(10)C_9

A contest consists of pedicting the results (win, draw or defeat) of 10 foot ball matches. Then the number of ways n which one entry contains at least 6 icorrect results is (A) 3^10 - sum_(r=0) ^5 .^10C_r 2^r (B) 30^10-sum_(r=1)^5 .^10C_r 2^r (C) sum_(r=0)^5 .^10C_r (D) sum_(r=6)^5 .^10C_r 3^r

Find the point of intersection of AB and A( 6,-7,0),B(16,-19,-4,) , C(0,3,-6) and D(2,-5,10).

Among 10 persons, A, B, C are to speak at a function. The number of ways in which it can be done if A wants to speak before B and B wants to speak before C is a. 10 !//24 b. 9!//6 c. 10 !//6 d. none of these