Limits, Continuity & Differentiability · JEE Main previous year questions

2017 3 questions

1. Q82017 · 9 Apr 2017 · Shift 1

   The value of k for which the function $$f(x)=\{\begin{array}{ll}{\left(\frac{4}{5}\right)}^{\frac{\tan 4x}{\tan 5x}},& 0<x<\frac{\pi }{2}\\ k+\frac{2}{5},& x=\frac{\pi }{2}\end{array}$$ is continuous at $x=\frac{\pi }{2}$, is :

   1. A.$\frac{17}{20}$
   2. B.$\frac{2}{5}$
   3. C.$\frac{3}{5}$
   4. D.$-\frac{2}{5}$
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   Answer: C

2. Q252017 · 9 Apr 2017 · Shift 1

   If ${\lim }_{n\to \infty }\frac{1^a+2^a+\dots \cdots +n^a}{(n+1{)}^{a-1}[(na+1)+(na+2)+\dots \cdots +(na+n)]}=\frac{1}{60}$ for some positive real number a, then a is equal to :

   1. A.$7$
   2. B.$8$
   3. C.$\frac{15}{2}$
   4. D.$\frac{17}{2}$
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   Answer: A

3. Q92017 · 8 Apr 2017 · Shift 1

   ${\lim }_{x\to 3}\frac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt{2}}$ is equal to :

   1. A.$\sqrt{3}$
   2. B.$\frac{1}{\sqrt{2}}$
   3. C.$\frac{\sqrt{3}}{2}$
   4. D.$\frac{1}{2\sqrt{2}}$
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   Answer: B