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Find the largest positive integer, m such that 2m-1 divides 33!. ...
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'a' and 'b' are integers. Solve 2(a2-b)=b2-a ...
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Why do distant hills covered with trees appear blue? ...
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Hi guys. How was RMO? I did 3 correct and attempted one more. ...
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Given that the equation x^4+px^3+qx^2+rx+s=0 has four real, positive roots, prove that- (a)pr-16s\geq 0 (a)q^2-36s\geq 0 Is there any proof without using Cauchy-Schwarz? ...
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Is there any proof to (n!)2≥nn without using induction? ...
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ABC is a triangle. The tangent to the circumcircle at A meets the line BC at D. The perpendicular to BC at B meets the perpendicular bisector of AB at E, and the perpendicular to BC at C meets the perpendicular bisector of AC ...
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Find the value of- \left( 2+\sqrt{1+\sqrt{2+\sqrt{1+\sqrt{2+...}}}}\right)-\left(1+\sqrt{2+\sqrt{1+\sqrt{2+\sqrt{1+...}}}} \right) ...
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Is there any non-geometrical proof of sin(A+B)=sinAcosB+cosAsinB ...
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ABCD is a rhombus.'N' is a point on AB .NP and NQ are two perpendiculars to AC and BD respectively.Find the length of PQ if AC=16 cm, BD=30 cm. ...
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In wolfram i read that 1 is a special case: It is neither prime nor composite. The fundamental theorem of arithmetic fails if we consider 1 to be a prime. But somewhere else i read that 1 is a prime. So, what's the truth? PS- ...
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List all solutions of the system of equations with positive real numbers: x2+y4=16 x2+z2=4+xz y2+z2=4+yz√3 Please give a legitimate solution. ...
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A lighthouse, facing north, sends out a fan-shaped beam of light extending fron north-east to north-west. An observer on a steamer, sailing due west, first sees the light when he is 5 km awayfrom the lighthouse, and continues ...
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A lighthouse, facing north, sends out a fan-shaped beam of light extending fron north-east to north-west. An observer on a steamer, sailing due west, first sees the light when he is 5 km awayfrom the lighthouse, and continues ...
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IF cos(a-b), cos(a) and cos(a+b) are in HP find cos(a)sec(b/2) ...
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If sinx+tanx=5/6 find sinx*tanx. By converting everything to sinx we get a quartic equation but how to solve that? ...
