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)` ?