In a ` A B C ,ifA B=x , B C=x+1,/_C=pi/3` , then the least integer value of `x` is

If a^x=b, b^y=c,c^z=a then the value of xyz is

Let f(x)=Ax^2+Bx+C where A, B, C are three real constants, if f(x) is integer for integral values of x, then prove that each of 2A, (A+B) and C is an integer. Conversely, if each of 2A, (A+B) , C is an integer then f(x) will be integer for integral values of x.

In triangle A B C ,D is on A C such that A D=B C' and BD=D C ,/_D B C=2x ,a n d/_B A D=3x , all angles are in degrees, then find the value of x

If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and positive constant a such that int_b^(c+b)f(x)dx is independent of b , then find the least positive value of c

If a , b , c are the sides of triangle , then the least value of (a)/(c+a-b)+(b)/(a+b-c)+(c )/(b+c-a) is

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4

If a ,b ,a n dc be in G.P. and a+x ,b+x ,and c+x in H.P. then find the value of x(a ,b and c are distinct numbers) .

If a,b,c are in G. P. and x, y are A.M. of a, b and b, c respectively, then the value of ((a)/(x)+ (c )/(y)) is-

Let a = cos^(-1) cos 20, b = cos^(-1) cos 30 and c = sin^(-1) sin (a + b) then The largest integer x for which sin^(-1) (sin x) ge |x -(a + b + c)| is

A, B, C are mutually exclusive events such that P(A)=(3x+1)/(3),P(B)=(1-x)/(4) and P(C )=(1-2x)/(2) , then the set of possible values of x are in the interval -