$A $ gaseous hypothetical chemical equation $2A$ $ \rightleftharpoons  $ $4B + C$ is carried out in a closed vessel. The concentration of $ B$  is found to increase by $5 \times {10^{ - 3}}mol\,\,{l^{ - 1}}$ in $10 $ second. The rate of appearance of $B$  is

  • A

    $5 \times {10^{ - 4}}\,mol\,\,{l^{ - 1}}se{c^{ - 1}}$

  • B

    $5 \times {10^{ - 5}}\,mol\,\,{l^{ - 1}}se{c^{ - 1}}$

  • C

    $6 \times {10^{ - 5}}\,mol\,\,{l^{ - 1}}{\sec ^{ - 1}}$

  • D

    $4 \times {10^{ - 4}}\,mol\,{l^{ - 1}}{\sec ^{ - 1}}$

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  • [AIPMT 2011]

For the reaction, $2A + B\,\to $ products , when the concentrations of $A$ and $B$ both were doubled, the rate of the reaction increased from $0.3\,mol\,L^{-1}\,s^{-1}$ to $2.4 \,mol\,L^{-1}\,s^{-1}.$ When the concentration of $A$ alone is doubled, the rate increased from $0.3\,mol\,L^{-1}\,s^{-1}$ to $0.6\,mol\,L^{-1}\,s^{-1}.$ Which one of the following statements is correct?

  • [JEE MAIN 2019]