Propanal on treatment with dilute sodium hydroxide forms

If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

An electron revolves in a circle of radius $0.4 \text{ \AA}$ with a speed of $10^6 \text{ m/s}$ in a hydrogen atom. The magnetic field produced at the centre of the orbit due to the motion of the electron (in Tesla) is: $\left[\mu_0 = 4\pi \times 10^{-7} \text{ H/m}, e = 1.6 \times 10^{-19} \text{ C}\right]$

If the radius of a nucleus with mass number $125$ is $1.5 \text{ fermi}$,then the radius of a nucleus with mass number $64$ is: (in $text{ fermi}$)

One mole of an ideal gas having initial volume $V$,pressure $2P$ and temperature $T$ undergoes a cyclic process $ABCDA$ as shown in the figure. The net work done in the complete cycle is:

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is