Which of the following has the longest $C-O$ bond length? (Free $C-O$ bond length in $CO$ is $1.128 \ \mathring{A}$)

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. If the total work done is $W$,then:

If $y=A \cos n x+B \sin n x$, then $y_2+n^2 y$ is equal to

When a wire of length $10 \ m$ is subjected to a force of $100 \ N$ along its length,the lateral strain produced is $0.01 \times 10^{-3} \ m$. The Poisson's ratio was found to be $0.4$. If the area of cross-section of the wire is $0.025 \ m^2$,its Young's modulus is

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$,moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$,is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$,length $l$ and a pressure difference of $p$ across its two ends,then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$,where $k$ is a dimensionless constant. The correct values of $a, b$ and $c$ are

${\left( -\frac{1}{2} + \frac{\sqrt{3}}{2}i \right)^{1000}} = .....$