An aluminium (resistivity $\rho = 2.2 \times 10^{-8} \Omega \cdot m$) wire of a diameter $1.4 \text{ mm}$ is used to make a $4 \Omega$ resistor. The length of the wire is: (in $\text{ m}$)

$\frac{\sin 5 \theta}{\sin \theta}$ is equal to

Three processes form a thermodynamic cycle as shown on the $P-V$ diagram for an ideal gas. Process $1 \to 2$ takes place at a constant temperature $(300\,K)$. Process $2 \to 3$ takes place at a constant volume. During this process,$40\,J$ of heat leaves the system. Process $3 \to 1$ is adiabatic and the temperature $T_3$ is $275\,K$. The work done by the gas during the process $3 \to 1$ is...... $J$.

The two curves $x=y^2$ and $xy=a^3$ cut orthogonally at a point, then $a^2$ is equal to

Among the following statements,the incorrect one is:

Select the incorrect statement.