If a and b are whole number such that `a^(b)=512` where a `gt` b and 1 `lt` b `lt` 4 then `bsqrt(a)`=

If a, b and c are three real numbers such that a - b+c lt 1, a + b + c gt -1 and 9a + 3b + c lt -4 , then what is the sign of 'a' ?

If a and b are positive numbers such that a gt b , then the minimum value of a sec theta- b tan theta (0 lt theta lt pi/2) is a) 1/sqrt(a^2-b^2) b) 1/sqrt(a^2+b^2) c) sqrt(a^2+b^2) d) sqrt(a^2-b^2)

If a and b are two negative integers such that a lt b " then " (1)/(a) gt (1)/(b) .

Suppose a,b and c are real numbers such that a/b gt 1 and a/c lt 0 . What one of the following is true ?

If a and b are nonzero numbers such that a lt b , which of the following must be true ? I. 1/a gt 1/b II. a^2 lt b^2 III. b^2 ge 1

If two integers a and b be such that -2 lt a lt 0 and 0 lt b lt 2 , then show that (i) (a +b) belongs to the set of whole numbers W : (ii) (b-a) belongs to the set of natural numbers N : (iii) (a-b) belongs to the set of integers Z .

If A and B are independent events such that 0 lt P(A) lt 1 and 0 lt P(B) lt 1 , then -