If two loaded dice each have the property that 2 or 4 is three times as likely to appears as `1,3,5,or6` on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is p, then value of `[1//p]` is, where `[x]` represents the greatest integer less than or euqal to x.

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 _______.

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these

Consider P(x) to be a polynomial of degree 5 having extremum at x=-1,1, and ("lim")_((xvec) 0) ((p(x))/(x^3)-2)=4 . Then the value of [P(1)] is (where [.] represents greatest integer function)___

2P and P are two vectors inclined to each other at such an angle that if the 1 st vector is doubled , the value of the resultant becomes three times. What is the angle between the two vectors ?

If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real number for which 2xtan^(-1)x is greater than or equal to ln(1+x^2), then the number of maximum possible values of alpha (where [.] represents the greatest integer function) is_____

Let f(x)=3x^2-7x+c , where c is a variable coefficient and x >7/6 . Then the value of [c] such that f(x) touches f^(-1)(x) is (where [.] represents greatest integer function)_________

Let f(x)=3x^2-7x+c , where c is a variable coefficient and x >7/6 . Then the value of [c] such that f(x) touches f^(-1)(x) is (where [.] represents greatest integer function)_________

The value of int_(0)^(x)[cost]dt, x epsilon[(4n+1)(pi)/2,(4n+3)(pi)/2] and n epsilonN is equal to (where [.] represents greatest integer function.

A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that the sum of two numbers thrown is even is 1//12 b. 1//6 c. 1//3 d. 5//9