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

  • question_answer
    Let M be a \[3\times 3\] non-singular matrix with\[|M|\,=\alpha \]. If \[{{M}^{-1}}\]\[adj\,\,(adj\,M)=kl,\] then the value of k is

    A)  1                                

    B)  \[\alpha \]

    C)  \[{{\alpha }^{2}}\]             

    D)  \[{{\alpha }^{3}}\]

    Correct Answer: D

    Solution :

     Given,                         \[\frac{\Delta n}{n}=\frac{{{v}_{s}}}{v-{{v}_{s}}}\] and      \[\frac{2.5}{100}=\frac{{{v}_{s}}}{320-{{v}_{s}}}=\frac{1}{40}\] \[40{{v}_{s}}=320-{{v}_{s}}\]       \[{{v}_{s}}=\frac{320}{41}\simeq 8\,m/s\] \[V=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{Q}{R} \right]+\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{q}{r} \right]\] \[=\frac{1}{{{\varepsilon }_{0}}}\left[ \frac{Q}{4\pi {{R}^{2}}}\times R+\frac{q}{4\pi {{r}^{2}}}\times r \right]\]          \[\frac{Q}{4\pi {{R}^{2}}}=\frac{q}{4\pi {{r}^{2}}}=\sigma \] \[\therefore \]    \[V=\frac{1}{{{\varepsilon }_{0}}}\,[\sigma R+\sigma r]=\frac{\sigma }{{{\varepsilon }_{0}}}[R+r]\]

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