JEE Main & Advanced Sample Paper JEE Main Sample Paper-43

  • question_answer
    Let \[f:\,R\to R\] be defined by \[f(x)=2x+\sin \,x\]for \[x\,\in R\]. Then, \[f\] is

    A)  one-one and onto                      

    B)  one-one but not onto

    C)  onto but not one-one                   

    D)  neither one-one nor onto

    Correct Answer: A

    Solution :

      We have, \[\tan \theta =\frac{r}{h/2}\] \[\theta ={{45}^{o}},\] for all \[r=\frac{h}{2}\] \[\theta ={{45}^{o}}\]         \[n'=\frac{v}{v-{{v}_{s}}}\times n\] is strictly increasing. \[\Rightarrow \]            \[\frac{n'}{n}=\frac{v}{v-{{v}_{s}}}\] is one-one

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