The flux linked with a coil at any instant $t$ is given by $\phi = 10t^2 - 50t + 250$. The induced emf at $t = 3 \ s$ is ....... $V$.

If $\overrightarrow{a}=-\hat{i}+\hat{j}+2 \hat{k}$,$\overrightarrow{b}=2 \hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{c}=-2 \hat{i}+\hat{j}+3 \hat{k}$,then the angle between $2 \overrightarrow{a}-\overrightarrow{c}$ and $\overrightarrow{a}+\overrightarrow{b}$ is

Find the value$(s)$ of $k$ such that the distance between the two parallel lines represented by $(x-2y)^2 + k(x-2y) = 0$ is $3$ units.

If $y=a e^x+b e^{-x}+c$,where $a, b, c$ are parameters,then $y^{\prime \prime \prime}$ is equal to

The vapour pressure in $mm$ of $Hg$,of an aqueous solution obtained by adding $18 \ g$ of glucose $(C_6H_{12}O_6)$ to $180 \ g$ of water at $100^{\circ} C$ is

Which layer of the uterus undergoes cyclical changes during the menstrual cycle?