If two loaded dice each have the property that 2 or 4 is three times as likely to appear as 1, 3, 5, or 6 on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is `p ,` then the value of`[1//p]` is, where `[x]` represents the greatest integer less than or equal to `xdot`

The value of int_(1)^(2)[x]dx , where [x] is the greatest integer less than or equal to x is

let f(x)=(sin4pi[x])/(1+[x]^(2)) , where px] is the greatest integer less than or equal to x then

A die is thrown three times. The chance that the highest number shown on the die is 4 is p, then the value of [1//p] is where [.] represents greatest integer function is _________.

A dice is weighted such that the probability of rolling the face numbered n is proportional to n^(2) (n = 1, 2, 3, 4, 5, 6). The dice is rolled twice, yielding the number a and b. The probability that a gt b is p then the value of [2//p] (where [ . ] represents greatest integer function) is _______.

Two dice are rolled, find the probability that the sum is (i) equal to 1 (ii) equal to 4 (iii) less than 13

The plane denoted by P_(1) : 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane P_(2) : 5x+3y+ 10 z = 25 . If the plane in its new position is denoted by P , and the distance of this plane from the origin is d, then find the value of [k//2] (where [*] represents greatest integer less than or equal to k).

If the probability that the product of the outcomes of three rolls of a fair dice is a prime number is p , then the value of 1//(4p) is_____.

Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1, and ("lim")_(xvec0)((p(x))/(x^3)-2)=4 . Then the value of [P(1)] is (where [.] represents greatest integer function)___

Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively is p, then the value of [2//p] is, where [.] represents the greatest integer function,_____.