Solved papers for JEE Main & Advanced JEE Main Paper (Held On 12 April 2014)

done JEE Main Paper (Held On 12 April 2014) Total Questions - 2

• question_answer1) Let \[f,g:R\to R\]be two functions defined by \[f(x)=\left\{ \begin{align}   & x\sin \left( \frac{1}{x} \right),x\ne 0 \\  & 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x=0 \\ \end{align} \right.,\]and \[g(x)=xf(x)\] Statement I: f is a continuous function at x = 0. Statement II: g is a differentiable function at x = 0.   [JEE Main Online Paper ( Held On 12 Apirl  2014 )
  A)
  Both statement I and II are false.
  done clear
  B)
  Both statement I and II are true.
  done clear
  C)
  Statement I is true, statement II is false.
  done clear
  D)
  Statement I is false, statement II is true.
  done clear
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• question_answer2) Let f and g be two differentiable functions on R such that f'(x) > 0 and g'(x) < 0 for all \[x\in R\]. Then for all x:   [JEE Main Online Paper ( Held On 12 Apirl  2014 )
  A)
  f (g (x)) > f (g (x - 1))
  done clear
  B)
  f (g (x)) > f (g (x + 1))
  done clear
  C)
  g(f (x)) > g (f (x - 1))
  done clear
  D)
  g(f (x)) < g (f (x + 1))
  done clear
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