10-question readiness test

Given below are two statements

Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source.

Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light

In the light of above statements, choose the most appropriate answer from the options given below.

If the sum of all the solutions of \(tan^{-1}\bigg(\frac{2x}{1-x^{2}}\bigg)+cot^{-1}\bigg(\frac{1-x^{2}}{2x}\bigg)=\frac{\pi}{3},\)  -1

An object of mass ‘m’ initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle  \(\theta\)  (as shown in figure) between the direction of force and horizontal varies as  \(\theta=kx\)  where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be   \(E=\frac{n}{k}\)   \(sin\theta\)  , the value of n is ______.

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity \(\omega\) . The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu. \)  The beaker will revolve with the disc if :

(Numerical Answer Type)

When 200 mL of 0.2 M acetic acid is shaken with 0.6 g of wood charcoal, the final concentration of acetic acid after adsorption is 0.1 M. The mass of acetic acid adsorbed per gram of carbon is ____________.g.

The number of paramagnetic species from the following is _______.

\([Ni(CN) _4]^{2-} ,[Ni(CO) _4], [NiCl _4] ^{2-},\)

\([Fe(CN) _6]^{4-} , [Cu(NH _3) _4]^{2+}\)

\([Fe(CN) _6]^{3-} and [Fe(H_2O)_6 ] ^{2+}\)

 Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be

(Numerical Value Type Questions)

 A point charge   \(q_{1} = q_{0}\) is placed at origin. Another point charge   \(q_{2} = -q_{0}\)   is placed at x=12 cm. Charge of proton is   \(q_{0}\) The proton is placed on x axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from origin is____________ cm

Out of the following, which type of interaction for the stabilisation of   helix structure
of protons ?

A man is walking on a straight line. The arithmetic mean of the reciprocals of the
intercepts of this line on the coordinate axes is \(\frac{1}{4}\) . Three stones A, B and C are placed at
the points (1, 1), (2, 2) and (4, 4) respectively. Then which of these stones is/are on the
path of the man?