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When $100 \, V$ $DC$ is applied across a solenoid,a current of $1 \, A$ flows in it. When $100 \, V$ $AC$ is applied across the same coil,the current drops to $0.5 \, A$. If the frequency of the $AC$ source is $50 \, Hz$,the impedance and inductance of the solenoid are:

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is: (Assume $\ln 12 = 2.6$)

The Test-tube Baby Programme employs which one of the following techniques?

Let $f$ be a differentiable function such that $f(1)=2$ and $f^{\prime}(x)=f(x)$,for all $x \in \mathbb{R}$. If $h(x)=f(f(x))$,then $h^{\prime}(1)$ is equal to

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