Sets, Relations & Functions · JEE Main previous year questions

2014 3 questions

1. Q92014 · 6 Apr 2014 · Shift 1

   If $g$ is the inverse of a function $f$ and $f^{\prime }(x)=\frac{1}{1+x^5}$, then $g^{\prime }(x)$ is equal to:

   1. A.$\frac{1}{1+\{g(x){\}}^5}$
   2. B.$1+\{g(x){\}}^5$
   3. C.$1+x^5$
   4. D.$5x^4$
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   Answer: B

2. Q212014 · 6 Apr 2014 · Shift 1

   If $X=\{4^n-3n-1:n\in N\}$ and $Y=\{9(n-1):n\in N\}$, where $N$ is the set of natural numbers, then $X\cup Y$ is equal to:

   1. A.$X$
   2. B.$Y$
   3. C.$N$
   4. D.$Y-X$
   Show answer

   Answer: B

3. Q272014 · 6 Apr 2014 · Shift 1

   If $f$ and $g$ are differentiable functions in $[0,1]$ satisfying $f(0)=2=g(1),g(0)=0$ and $f(1)=6$, then for some $c\in ]0,1[$

   1. A.$f^{\prime }(c)=g^{\prime }(c)$
   2. B.$f^{\prime }(c)=2g^{\prime }(c)$
   3. C.$2f^{\prime }(c)=g^{\prime }(c)$
   4. D.$2f^{\prime }(c)=3g^{\prime }(c)$
   Show answer

   Answer: B