Sets, Relations & Functions · JEE Main previous year questions

2006 5 questions

1. Q82006 · 29 Apr 2006 · Shift 1

   If the expansion in powers of $x$ of the function $\frac{1}{(1-ax)(1-bx)}$ is $a_0+a_{1}x+a_2{x}^2+a_3{x}^3\dots$. then $a_n$ is

   1. A.$\frac{b^n-a^n}{b-a}$
   2. B.$\frac{a^n-b^n}{b-a}$
   3. C.$\frac{a^{n+1}-b^{n+1}}{b-a}$
   4. D.$\frac{b^{n+1}-a^{n+1}}{b-a}$
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   Answer: D

2. Q172006 · 29 Apr 2006 · Shift 1

   The set of points where $f(x)=\frac{x}{1+|x|}$ is differentiable is

   1. A.$(-\infty ,0)\cup (0,\infty )$
   2. B.$(-\infty ,-1)\cup (-1,\infty )$
   3. C.$(-\infty ,\infty )$
   4. D.$(0,\infty )$
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   Answer: C

3. Q192006 · 29 Apr 2006 · Shift 1

   The function $f(x)=\frac{x}{2}+\frac{2}{x}$ has a local minimum at

   1. A.$x=2$
   2. B.$x=-2$
   3. C.$x=0$
   4. D.$x=1$
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   Answer: A

4. Q322006 · 29 Apr 2006 · Shift 1

   Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R=\{(x,y)\in W\times W\mid \text{the words }x\text{ and }y\text{ have at least one letter in common}\}$. Then, $R$ is

   1. A.reflexive, symmetric and not transitive
   2. B.reflexive, symmetric and transitive
   3. C.reflexive, not symmetric and transitive
   4. D.not reflexive, symmetric and transitive
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   Answer: A

5. Q332006 · 29 Apr 2006 · Shift 1

   ABC is a triangle, right angled at A. The resultant of the forces acting along $\overrightarrow{AB},\overrightarrow{AC}$ with magnitudes $\frac{1}{AB}$ and $\frac{1}{AC}$ respectively is the force along $\overrightarrow{AD}$, where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

   1. A.$\frac{A{B}^2+A{C}^2}{(AB{)}^2(AC{)}^2}$
   2. B.$\frac{(AB)(AC)}{AB+AC}$
   3. C.$\frac{1}{AB}+\frac{1}{AC}$
   4. D.$\frac{1}{AD}$
   Show answer

   Answer: D