Which of the following is responsible for the formation of peat?

An archaeologist analyses the wood in a prehistoric structure and finds that the ratio of ${C^{14}}$ (half-life $= 5700 \, years$) to ${C^{12}}$ is only one-fourth of that found in the cells of living plants. The age of the wood is about ........ $years$.

The periodic time of a particle doing simple harmonic motion is $4 \ s$. The time taken by it to go from its mean position to half the maximum displacement (amplitude) is

Observe the statements given below :
Assertion $(A)$ : $f(x)=x e^{-x}$ has the maximum at $x=1$
Reason $(R)$ : $f^{\prime}(1)=0$ and $f^{\prime \prime}(1) < 0$
Which of the following is correct?

$A$ common emitter transistor amplifier has a current gain of $50$. If the load resistance is $4 \ k\Omega$ and input resistance is $500 \ \Omega$,the voltage gain of the amplifier is