If `a,b lt 0 and 0 lt p lt 1` , then prove that `(a+b)^p lt a^p + b^p` .

If a,b,c are real numbers such that 0 lt a lt 1, 0 lt b lt 1, 0 lt c lt 1, a + b + c = 2 , then prove that (a)/(1 - a) (b)/(1 - b) (c )/(1 - c) ge 8 .

If x=Sigma_(n=0)^(oo) a^n,y=Sigma_(n=0)^(oo) b^n,z=Sigma_(n=0)^(oo) c^n where a, b,and c are in A.P and |a|lt 1 ,|b|lt 1 and |c|1 then prove that x,y and z are in H.P

If x=Sigma_(n=0)^(oo) a^n,y=Sigma_(n=0)^(oo) b^n,z=Sigma_(n=0)^(oo) c^n where a, b,and c are in A.P and |a|lt 1 ,|b|lt 1 and |c|1 then prove that x,y and z are in H.P

If a lt 0, b gt 0 and c lt 0 , then the point P(a, b, -c) lies in the octant

Statement-1 : For 0 le p lt 1 and for any positive a and b the intequality (a+b)^p lt a^p+b^p is valid Staement - 2: For 0 le ple 1 the function f(x)=1 +x^p -(1+x)^p decreases on [0,oo)

Statement-1 : For 0 le p lt 1 and for any positive a and b the intequality (a+b)^p lt a^p+b^p is valid Staement - 2: For 0 le ple 1 the function f(x)=1 +x^p -(1+x)^p decreases on [0,oo)

If A and B are independent events such that 0 lt P (A) lt 1 and 0 lt P(B) lt 1 , then which of the following is not correct ?

Let A and B be two events such that P (A uu B) = P (A) + P (B) - P (A) P (B).If 0 lt P (A) lt 1 and 0 lt P (B) lt1, then P (A uuB)' is equal to

If A and B are independent events such that 0 lt P (A) lt 1 and 0 lt P (B) lt 1 then which of the followingis not correct ?