Sets, Relations & Functions · JEE Main previous year questions

2010 3 questions

1. Q92010 · 25 Apr 2010 · Shift 1

   Let $f:(-1,1)\to R$ be a differentiable function with $f(0)=-1$ and $f^{\prime }(0)=1$. Let $g(x)=[f(2f(x)+2){]}^2$. Then $g^{\prime }(0)=$

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

2. Q162010 · 25 Apr 2010 · Shift 1

   Let $p(x)$ be a function defined on $R$ such that $p^{\prime }(x)=p^{\prime }(1-x)$, for all $x\in [0,1],p(0)=1$ and $p(1)=41$. Then $\underset{0}{\overset{1}{\int }}p(x)dx$ equals :

   1. A.$21$
   2. B.$41$
   3. C.$42$
   4. D.$\sqrt{41}$
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   Answer: A

3. Q242010 · 25 Apr 2010 · Shift 1

   Consider the following relations $R=\{(x,y)\mid x,y\text{ are real numbers and }x=wy\text{ for some rational number }w\}$; $S=\left\{\left(\frac{m}{n},\frac{p}{q}\right)|m,n,p\text{ and }q\text{ are integers such that }n,q\ne 0\text{ and }qm=pn\right\}$. Then

   1. A.$R$ is an equivalence relation but $S$ is not an equivalence relation
   2. B.Neither $R$ nor $S$ is an equivalence relation
   3. C.$S$ is an equivalence relation but $R$ is not an equivalence relation
   4. D.$R$ and $S$ both are equivalence relations
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   Answer: C