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`

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

If each of the statements p to ~q , ~ r to q and p are true then which of the following is NOT true ?

If p+q+r=0=a+b+c =0, then the value of the determnalnt |p a q b r c q c r a p b r b p c q a|i s a 0 b. p a+q b+r c c. 1 d. none of these

Given that P(3,1),Q(6. 5), and R(x , y) are three points such that the angle P Q R is a right angle and the area of R Q P is 7, find the number of such points Rdot

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) .

Find the coordinates of the circumcentre of PQR if P(2,7), Q(-5,8) and R(-6,1).

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_3=p vec r_1+q vec r_2, then show that p+q=1.

If the sum of the coefficients in the expansion of (q+r)^(20)(1+(p-2)x)^(20) is equal to square of the sum of the coefficients in the expansion of [2rqx-(r+q)*y]^(10) , where p , r , q are positive constants, then

Let z be a complex number satisfying equation z^p=z^(-q),w h e r ep ,q in N ,t h e n (A) if p=q , then number of solutions of equation will be infinite. (B) if p=q , then number of solutions of equation will be finite. (C) if p!=q , then number of solutions of equation will be p+q+1. (D) if p!=q , then number of solutions of equation will be p+qdot

A man having the genotype EEFfGgHH can produce P number of genetically different sperms, and a woman of genotype liLLMmNn can generate Q number of genetically different eggs. Determine the values P and Q. a. P = 4, Q = 4 b. P = 4,Q = 8 c. P = 8, Q = 4 d. P = 8,Q = 8