At a given temperature,the pressure of an ideal gas of density $\rho$ is proportional to

Monocyclic compounds $\text{P , Q , R}$ and $S$ are the major products formed in the reaction sequences given below.
image
The product having the highest number of unsaturated carbon atom$(s)$ is-

$A$ beam of light of wavelength $600\, nm$ from a distant source falls on a single slit $1\, mm$ wide and the resulting diffraction pattern is observed on a screen $2\, m$ away. The distance between the first dark fringes on either side of the central bright fringe is

The product of the perpendicular distances from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ to its asymptotes is

When a certain conductivity cell was filled with $0.1 \ M$ $KCl$,it had a resistance of $85 \ \Omega$ at $25 \ ^oC$. When the same cell was filled with an aqueous solution of $0.052 \ M$ unknown electrolyte,the resistance was $96 \ \Omega$. Calculate the molar conductivity of the unknown electrolyte at this concentration ............ $\Omega ^{-1} cm ^{2} mol ^{-1}$ (Given : Specific conductivity of $0.1 \ M$ $KCl = 1.29 \times 10^{-2} \ \Omega ^{-1} cm ^{-1}$)

The transformed equation of $3x^2 + 3y^2 + 2xy = 2$,when the coordinate axes are rotated through an angle of $45^{\circ}$,is