The formal charges of $C$ and $O$ atoms in $CO_2$ $(\ddot{O}=C=\ddot{O})$ are,respectively

Let $\overrightarrow{a}=\hat{i}-2 \hat{j}+3 \hat{k}$,$\overrightarrow{b}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\overrightarrow{c}=\lambda \hat{i}+\hat{j}+(2 \lambda-1) \hat{k}$. If $\overrightarrow{c}$ is parallel to the plane containing $\overrightarrow{a}$ and $\overrightarrow{b}$,then $\lambda$ is equal to

The displacement equations of two waves are given as $y_1 = 10 \sin(3\pi t + \pi/3)$ and $y_2 = 5(\sin 3\pi t + \sqrt{3} \cos 3\pi t)$. What is the ratio of their amplitudes?

$A$ block placed on a rough inclined plane of inclination $\theta=30^{\circ}$ can just be pushed upwards by applying a force $F$ as shown. If the angle of inclination of the inclined plane is increased to $\theta=60^{\circ}$,the same block can just be prevented from sliding down by application of a force of the same magnitude $F$. The coefficient of friction between the block and the inclined plane is:

The area (in square units) of the circle which touches the lines $4x + 3y = 15$ and $4x + 3y = 5$ is

$A$ proton and an $\alpha$-particle are accelerated through a potential difference of $100 \ V$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is