Assume that an electric field $$\overrightarrow{E}=30x^2\hat{i}$$ exists in space. Then the potential difference $$V_A-V_O,$$ where $$V_O$$ is the potential at the origin and $$V_A$$ the potential at $$x=2$$ $$m$$ is :

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

The coercivity of a small magnet where the ferromagnet gets demagnetized is $$3\times 10^{3}A{m}^{-1}.$$ The current required to be passed in a solenoid of length $$10$$ $$cm$$ and number of turns $$100,$$ so that the magnet gets demagnetized when inside the solenoid, is :

Four particles, each of mass $$M$$ and equidistant from each other, move along a circle of radius $$R$$ under the action of their mutual gravitational attraction. The speed of each particle is :

Two beams, $$A$$ and $$B$$, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $$A$$ has maximum intensity (and beam $$B$$ has zero intensity), a rotation of polaroid through $$30^{\circ }$$ makes the two beams appear equally bright. If the initial intensities of the two beams are $${\mathrm{I}}_A$$ and $${\mathrm{I}}_B$$ respectively, then {{{{\rm I}_A}} \over {{{\rm I}_B}}} equals:

A parallel plate capacitor is made of two circular plates separated by a distance $$5$$ $$mm$$ and with a dielectric of dielectric constant $$2.2$$ between them. When the electric field in the dielectric is $$3\times 10^{4}V/m$$ the charge density of the positive plate will be close to:

A pipe of length $$85$$ $$cm$$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $$1250$$ $$Hz$$. The velocity of sound in air is $$340$$ $$m/s$$.

A conductor lies along the $$z$$-axis at $$-1.5\le z<1.5m$$ and carries a fixed current of $$10.0$$ $$A$$ in $$-{\hat{a}}_z$$ direction (see figure). For a field $$\overrightarrow{B}=3.0\times 10^{-4}{e}^{-0.2x}{\hat{a}}_{y}T,$$ find the power required to move the conductor at constant speed to $$x=2.0$$ $$m$$, $$y=0$$ $$m$$ in $$5\times 10^{-3}s.$$ Assume parallel motion along the $$x$$-axis.

A block of mass $$m$$ is placed on a surface with a vertical cross section given by y = {{{x^3}} \over 6}. If the coefficient of friction is $$0.5,$$ the maximum height above the ground at which the block can be placed without slipping is:

A mass $${}^{\prime }{m}^{\prime }$$ is supported by a massless string wound around a uniform hollow cylinder of mass $$m$$ and radius $$R.$$ If the string does not slip on the cylinder, with what acceleration will the mass fall or release?

A bob of mass $$m$$ attached to an inextensible string of length $$l$$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $$\omega rad/s$$ about the vertical. About the point of suspension:

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

The octahedral complex of a metal ion M3+ with four monodentate ligands L1, L2, L3 and L4 absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is :

The equation which is balanced and represents the correct product(s) is :

The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:

CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following expressions is correct?

The major organic compound formed by the reaction of 1, 1, 1– trichloroethane with silver powder is:

In SN2 reactions, the correct order of reactivity for the following compounds: CH3Cl, CH3CH 2Cl, (CH3)2CHCl and (CH3)3CCl is:

For the non – stoichiometre reaction 2A + B $$\to$$ C + D, the following kinetic data were obtained in three separate experiments, all at 298 K. .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg .tg-s6z2{text-align:center} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-hgcj{font-weight:bold;text-align:center} Initial Concentration (A) Initial Concentration (B) Initial rate of formation of C (mol L-1 s-1) 0.1 M 0.1 M 1.2 x 10-3 0.1 M 0.2 M 1.2 x 10-3 0.2 M 0.1 M 2.4 x 10-3 The rate law for the formation of C is:

The most suitable reagent for the conversion of R - CH2 - OH $$\to$$ R - CHO is: