-
Prove that there exist two infinite sequences (an)n≥1 and (bn)n≥1 of positive integers such that the following conditions hold simultaneously: (i) 1 < a1 < a2 < a3 .... (ii) an<bn<a2n, for all n ≥1 ( ...
-
Suppose a and b are real numbers such that the roots of the cubic equation ax3-x2+bx-1 = 0 are all positive real numbers. Prove that : (i) 0 < 3ab ≤1 (ii) b≥ 3 P.S. I can't believe I missed this ... this one i ...
-
Three non-zero real numbers a,b,c are said to be in H.P. if 1/a + 1/c = 2/b. Find all three-term H.P. a,b,c of strictly increasing positive integers in which a = 20 and b divides c. ...
-
Find the number of all integer-sided isosceles obtuse-angled triangles with perimeter 2008. ...
-
Find the number of all 6-digit natural numbers such that the sum of their digits is 10 and each of the digits 0,1,2,3 occurs at least once in them. ...
-
It gains heat, so its enthalpy increases. ...
