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Simplified form of (p+(1)/(q))^((p-q))(p-(1)/(q))^((p+q))(q+(1)/(p))^((p-q))(q-(1)/(p))^((p+q))

((p+1/q)^p.(p-1/q)^q)/((q+1/p)^p.(q-1/p)^q)=(p/q)^x then x=

If a,b and c are the sides of a /_ABC, then a^(1/p)+b^(1/p)-c^(1/p), where p>1, is

Let p_(1),p_(2),...,p_(n) and x be distinct real number such that (sum_(r=1)^(n-1)p_(r)^(2))x^(2)+2(sum_(r=1)^(n-1)p_(r)p_(r+1))x+sum_(r=2)^(n)p_(r)^(2)<=0 then p_(1),p_(2),...,p_(n) are in G.P.and when Statement 2: If (p_(2))/(p_(1))=(p_(3))/(p_(2))=...=(p_(n))/(p_(n-1)), then p_(1),p_(2),...,p_(n) are in G.P.

Let A, B be any two events P(A)=P_(1), P(B)=P_(2) and P(A nn B)=P_(3) .Then which of the following are true P(bar(A uu B))=1-(P_(1)+P_(2)) P[A uu(bar(A)nn B)]=P_(1)+P_(2)-P_(3) P(bar(A)/bar(B))=(1-P_(1)-P_(2)+P_(3))/(1-P_(2)) P[bar(A)nn(A uu B)]=P_(2)-P_(3)

If p_1,p_2,p_3 are altitudes of a triangle ABC from the vertices A,B,C respectively and Delta is the area of the triangle and s is semi perimeter of the triangle. If 1/p_1+1/p_2+1/p_3=1/2, then the least value of p_1p_2p_3 is

If p_1p_2,p_3 are the lengths of altitudes of a triangle from the vertices A, B, C and Delta the area fo the triangle the 1/p_1 + 1/p_2 - 1/p_3 =