Sets, Relations & Functions · JEE Main previous year questions

2009 3 questions

1. Q102009 · 27 Apr 2009 · Shift 1

   Let $y$ be an implicit function of $x$ defined by $x^{2x}-2x^x\cot y-1=0$. Then $y^{\prime }(1)$ equals

   1. A.1
   2. B.$\log 2$
   3. C.$-\log 2$
   4. D.$-1$
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   Answer: D

2. Q152009 · 27 Apr 2009 · Shift 1

   $\underset{0}{\overset{\pi }{\int }}[\cot x]dx$, where $[.]$ denotes the greatest integer function, is equal to:

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

3. Q222009 · 27 Apr 2009 · Shift 1

   If $A,B$ and $C$ are three sets such that $A\cap B=A\cap C$ and $A\cup B=A\cup C$, then :

   1. A.$A=C$
   2. B.$B=C$
   3. C.$A\cap B=\varphi$
   4. D.$A=B$
   Show answer

   Answer: B