Total energy per unit length of a line charge in space, from perpendicular distance ${\epsilon }_0$ to $2{\epsilon }_0$, from line charge, is given by ($\lambda$ denotes charge per unit length)

A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potential $\frac{3V_0}{2},\frac{5V_0}{4},\frac{3V_0}{4}$ and $\frac{V_0}{4}$ have radius $R_1$ , $R_2, R_3$ and $R_4$ respectively. Then

Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

Directions: Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.

Every rash driver becomes a ____ killer.

Three charges are placed at the three vertices of an equilateral triangle of side $a$ as shown in the figure. The force experienced by the charge placed at the vertex $A$ in a direction normal to $BC$ is

Two sentences are given below and you are required to find the correct sentence which combines both the sentences.

Which is the correct combination of the given two sentences?

He is too tired. He could not stand.

In the following sentence, a blank space with four options is given. Select whichever preposition or determiner you consider the most appropriate for the blank space.

These are the good rules to live _____.

Four point charges $q_A=2 \mu C, q_B=-5 \mu C, q_C=2 \mu C, q_D=-5 \mu C$ are located at the corners of a square $ABCD$ of side $10 \mathrm{cm}.$ The force acting on a charge of $1 \mu \mathrm{C}$ placed at centre of the square is

Eleven equal point charges, all of them having a charge $+Q,$ are placed at all the hour positions of a circular clock of radius $r$ except at the $10 \mathrm{h}$ position. What is the electric field strength at the centre of the clock?

Shown in the figure is a shell made of a conductor. It has inner radius $a$ and outer radius $b$, and carries charge $Q$ . At its centre a dipole $\overrightarrow{\mathit{p}}$ is placed as shown then: