Class 12th

Ten charges are placed on the circumference of a circle of radius $10\mathrm{s}$ $$ with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q)$$ each, while $\mathrm{2,4},\mathrm{6,8},10$ $$ have charge $$ (-q)each. The potential v$$ and the electric field $$ E at the centre of the circle are respectively: (Take V = 0 $$ at infinity)

The correct match between the entries in column I and column II are:

An iron rod of volume ${10}^{-3}{\mathrm{m}}^3$ ${}^{}{}^{}$ and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of $0.5\mathrm{A}$ $$ is passed through the solenoid, then the magnetic moment of the rod will be:

In the circuit shown, charge on the $5\mu \mathrm{F}$ $$ capacitor is:

The rate of a certain biochemical reaction at physiological temperature (T) occurs ${10}^6$ ${}^{}$ times faster with enzyme than without. The change in the activation energy upon adding enzyme is :

The major product of the following reaction is :

Two coherent sources of sound, $S_1$ ${}_{}$ and $S_2$ ${}_{}$ produce source waves of the same wavelength, $\lambda =1\mathrm{m}$ $$ , in phase. $S_1$ ${}_{}$ and ${\mathrm{S}}_2$ ${}_{}$ are placed $1.5\mathrm{m}$ $$ apart (see fig). A listener located at $\mathrm{L}$ $$ , directly in front of $S_2$ ${}_{}$ finds that the intensity is at a minimum when he is $2\mathrm{m}$ $$ away from ${\mathrm{S}}_2$ ${}_{}$ . The listener moves away from $S_1$ ${}_{}$ , keeping his distance from $S_2$ ${}_{}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ $$ from ${}_{}$ $S_1$ . Then, $d$ $$ is:

The most suitable reagent for the given conversion is :

As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order :

Let $\vec{a},\vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$ . If $\lambda =\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a}$ and $\vec{d}=\vec{a}*\vec{b}+\vec{b}*\vec{c}+\vec{c}*\vec{a}$ , then the ordered pair, $(\lambda ,\vec{d})$ is equal to: