If $f: R \rightarrow R$ is defined by $f(x) = [x-3] + |x-4|$ for $x \in R$,then $\lim_{x \rightarrow 3^{-}} f(x)$ is equal to

An organ pipe $P_1$,closed at one end and containing a gas of density $\rho_1$ is vibrating in its first harmonic. Another organ pipe $P_2$,open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes,the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic).

$A$ current of $2\, A$ flows in a system of conductors as shown. The potential difference $(V_A - V_B)$ will be ................ $V$.

The incentre of the triangle with vertices $(1, \sqrt{3})$,$(0, 0)$ and $(2, 0)$ is

Do you expect the carbon hydrides of the type $(C_{n}H_{2n+2})$ to act as 'Lewis' acid or base? Justify your answer.

$\int_0^\pi \frac{x \tan x}{\sec x+\tan x} d x=$