If $f(t) = \int_{-t}^t \frac{e^{-|x|}}{2} dx$,then $\lim_{t \rightarrow \infty} f(t)$ is equal to:

The circuit shown in the following figure contains two diodes $D_1$ and $D_2$, each with a forward resistance of $50 \, \Omega$ and infinite backward resistance. If the battery voltage is $6 \, V$, find the current through the $100 \, \Omega$ resistor (in amperes).

The second and third rows of transition elements resemble each other much more than they resemble the first row. Explain why?

$A$ thin hollow sphere of mass $m$ is completely filled with a liquid of mass $m$. When the sphere rolls with a velocity $v$,the kinetic energy of the system is (neglect friction).

The logical statement $(\sim(\sim p \vee q) \vee(p \wedge r)) \wedge(\sim q \wedge r)$ is equivalent to

If $y=A \cos n x+B \sin n x$, then $y_2+n^2 y$ is equal to