If `A_1,\ A_2a n d\ A_3` denote the areas of three adjacent faces of a cuboid, then its volume is ` (a) A_1A_2\ A_3` (b) `2A_1A_2A_3` ` (c) sqrt(A_1\ A_2A_3)` (d) `A_1A_2A_3`

If A,A_1,A_2 and A_3 are the areas of the inscribed and escribed circles of a triangle, prove that 1/sqrtA=1/sqrt(A_1)+1/sqrt(A_2)+1/sqrt(A_3)

If A,A_1,A_2 and A_3 are the areas of the inscribed and escribed circles of a triangle, prove that 1/sqrtA=1/sqrt(A_1)+1/sqrt(A_2)+1/sqrt(A_3)

If A_1 , A_2 , A_3 are areas of excircles, A is the area of incircle of a triangle then (1 ) /( sqrt(A_1)) + (1)/( sqrt(A_2)) + ( 1)/( sqrt(A_3))=

Three rectangles A_1, A_2 and A_3 have the same area. Their lengths a_1, a_2 and a_3 respectively are such that a_1

If A_1 , A_2 , A_3 are mutually exclusive, mutually independent and exhaustive, then the probability that A_1 , A_2 , A_3 occur simultaneously is

The equation A/(x-a_1)+A_2/(x-a_2)+A_3/(x-a_3)=0 ,where A_1,A_2,A_3gt0 and a_1lta_2lta_3 has two real roots lying in the invervals. (A) (a_1,a_2) and (a_2,a_3) (B) (-oo,a_1) and (a_3,oo) (C) (A_1,A_3) and (A_2,A_3) (D) none of these

The equation A/(x-a_1)+A_2/(x-a_2)+A_3/(x-a_3)=0 where A_1,A_2,A_3gt0 and a_1lta_2lta_3 has two real roots lying in the invervals. (A) (a_1,a_2) and (a_2,a_3) (B) (-oo,a_1) and (a_3,oo) (C) (A_1,A_3) and (A_2,A_3) (D) none of these

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : (1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1)) =n.