A forecast is to be made of the results of five cricket matches, each of which can be a win or a draw or a loss for Indian team. Let `p=` number of forecasts with exactly 1 error `q=` number of forecasts with exactly 3 error `r=` number of forecasts with all five error Then the correct statement(s) is/are a. `2q=5r` b. `8p=q` c. `8p=r` d. `2(p+r)> q`

The results of 6 cricket test mathes (win loss or draw are to be predicted . How many different forecasts can contain exactly 2 correct results ?

Total number of relations that can be defined on set X={p,q,r}is

Two teams are to play a series of five matches between them. A match ends in a win, loss, or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain n people, where n is a. 81 b. 243 c. 486 d. none of these

The Indian Cricket XI is to play 5 test matches against M.C.C Cricket XI in the next winter . The results of these 5 matches (win , loss or draw ) are to be predicted . How many different forecasts can contain all the 5 correct results ?

Let a, b , c, p , q , r be positive real numbers such that a , b , c are in G.P. and a^p = b^q = c^r . Then

Let p,q,r be the altitudes of a triangle with area s and perimeter 2t. Then the value of 1/p+1/q+1/r is

Let P Q and R S be tangent at the extremities of the diameter P R of a circle of radius r . If P S and R Q intersect at a point X on the circumference of the circle, then prove that 2r=sqrt(P Q xx R S) .

If r,s,t are prime numbers and p,q are the positive integers such that LCM of p,q is r^2t^4s^2 , then find the number of ordered pair (p,q).

Let P\ a n d\ Q be any two points. Find the coordinates of the point R\ which divides P Q externally in the ratio 2:1 and verify that Q is the mid point of P R .

If vec r_1, vec r_2, vec r_3 are the position vectors of the collinear points and scalar p a n d q exist such that vec r_1=p vec r_2+q vec r_3, then show that p+q=1.