Sets, Relations & Functions · JEE Main previous year questions

2017 4 questions

1. Q12017 · 9 Apr 2017 · Shift 1

   The function $f:\mathbf{N}\to \mathbf{N}$ defined by $f(x)=x-5\left[\frac{x}{5}\right]$, Where $\mathbf{N}$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to x, is :

   1. A.one-one and onto
   2. B.one-one but not onto.
   3. C.onto but not one-one.
   4. D.neither one-one nor onto.
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   Answer: D

2. Q102017 · 9 Apr 2017 · Shift 1

   The function f defined by $f(x)=x^3-3x^2+5x+7$ , is :

   1. A.increasing in $\mathbf{R}$.
   2. B.decreasing in $\mathbf{R}$.
   3. C.decreasing in $(0,\infty )$ and increasing in $(-\infty ,0)$
   4. D.increasing in $(0,\infty )$ and decreasing in $(-\infty ,0)$
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   Answer: A

3. Q112017 · 9 Apr 2017 · Shift 1

   Let f be a polynomial function such that $f(3x)=f{}^{\prime }(x)\cdot f{}^{\prime \prime }(x)$, for all $x\in \mathbf{R}$. Then :

   1. A.$f(2)+f{}^{\prime }(2)=28$
   2. B.$f{}^{\prime \prime }(2)-f{}^{\prime }(2)=0$
   3. C.$f{}^{\prime \prime }(2)-f(2)=4$
   4. D.$f(2)-f{}^{\prime }(2)+f{}^{\prime \prime }(2)=10$
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   Answer: B

4. Q12017 · 8 Apr 2017 · Shift 1

   Let $f(x)=2^{10}\cdot x+1$ and $g(x)=3^{10}\cdot x-1$. If $(f\circ g)(x)=x$, then $x$ is equal to :

   1. A.$\frac{3^{10}-1}{3^{10}-2^{-10}}$
   2. B.$\frac{2^{10}-1}{2^{10}-3^{-10}}$
   3. C.$\frac{1-3^{-10}}{2^{10}-3^{-10}}$
   4. D.$\frac{1-2^{-10}}{3^{10}-2^{-10}}$
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   Answer: D