If $\vec{a} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{b} = \lambda\hat{i} - 3\hat{j} + \hat{k}$ and the orthogonal projection of $\vec{b}$ on $\vec{a}$ is $\frac{4}{3}(\hat{i} - \hat{j} - \hat{k})$,then $\lambda$ is equal to:

The reaction $RCOCl + H_2 \xrightarrow{Pd/BaSO_4} RCHO + HCl$ is known as:

$A$ photon of energy $E$ ejects a photoelectron from a metal surface whose work function is $W_0$. If this electron enters into a uniform magnetic field of induction $B$ in a direction perpendicular to the field and describes a circular path of radius $r,$ then the radius $r$ is given by: (in the usual notation)

$A$ force applied by an engine on a train of mass $2.05 \times 10^6 \ kg$ changes its velocity from $5 \ m/s$ to $25 \ m/s$ in $5 \ minutes$. The power of the engine is (in $MW$)

In the given circuit, a charge of $+80\,\mu C$ is given to the upper plate of the $4\,\mu F$ capacitor. Then in the steady state, the charge on the upper plate of the $3\,\mu F$ capacitor is ..... $\mu C$.

If $\log _{0.3}(x - 1) < \log _{0.09}(x - 1),$ then $x$ lies in the interval