A logic circuit provides the output $$Y$$ as per the following truth table :
The expression of the output Y is :
The terminal voltage of the battery, whose emf is $$10 \mathrm{~V}$$ and internal resistance $$1 \Omega$$, when connected through an external resistance of $$4 \Omega$$ as shown in the figure is:
In a uniform magnetic field of $$0.049 \mathrm{~T}$$, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $$9.8 \times 10^{-6} \mathrm{~kg} \mathrm{~m}^2$$. If the magnitude of magnetic moment of the needle is $$x \times 10^{-5} \mathrm{~Am}^2$$, then the value of '$$x$$' is :
A wire of length '$$l$$' and resistance $$100 \Omega$$ is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is: