Questions asked by Abhi N.

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• If #a#, #b#, #c#, #d# and #e# are real numbers, prove that the roots of #x^5 + ax^4 + bx^3 + cx^2 + DX + e=0#, cannot be all real if #2a^2<5b#?
  
• A solution of protein (extracted from crab) was prepared by dissolving 0.75g in 125ml of a solution. At 4°C an osmotic pressure rise of 2.6 mm of the solution was observed. Then molecular mass of protein is (assume density of solution is 1gm/ml) ?
  
• #2tan^-1(x)+sin^-1((2x)/(1+x^2))# is independent of #x#, then?
  
• Prove that?
  
• Given that #arccos(x/a) + arccos(y/b)=alpha#. Then prove that?
  
• If #g(x)= 1+(x)^(1/3)# and #f(g(x))=3-(x)^(1/3)+x#, then find #f(x)#?
  
• Identify ‘Y’?
  
• Find #lim_{x to infinity} {pi/2 - arctan (x)}^1/x# ?
  
• Find #lim_{x to oo} {pi/2 - arctan(x)}^(1/x)# ?