A thin equiconvex lens of radius of curvature R made up of glass \( (\mu_g = 1.5) \) is dipped in water \( (\mu_w = 1.3) \). Its focal length in water is:

The mass of the chlorine \( {}_{17}^{35}\text{Cl} \) nucleus is 34.98 amu, which has protons of mass 17.133025 amu and neutrons of mass 18.155970 amu.
The binding energy of the nucleus is nearly:

Identify the correct statements among the following.
(A) The wavefront for a point source of light is in a spherical shape, rays are all radial from the point source,
(B) All the points on a cylindrical wavefront vibrate in the same phase,
(C) A set of straight lines perpendicular to a wavefront are called rays of light. Light energy does not flow along these lines.
(D) Every point of a given wavefront acts as a fresh source of a secondary wavelet
Choose the correct answer from the options given below:

A printed page is kept pressed by a glass cube-shaped paper-weight of edge 3.0 cm. The refractive index of the glass is \( \mu = 1.5 \).
By what amount will the printed letters appear to be shifted when viewed from the top?

The distance between an object and its virtual image of magnification \( \frac{1}{2} \) as produced by a lens is 20 cm.
The focal length of the lens is

A charge q is enclosed by a spherical Gaussian surface of radius R. If the radius of the sphere is doubled, how will the outward electric flux change?

At a place, the horizontal component of earth's magnetic field is \( 4 \times 10^{-4} \text{ T} \) and angle of dip is \( 60^\circ \). The value of horizontal component of earth's magnetic field at the equator is :

Let the degree and order of the differential equation \(2 x^3 \frac{d y}{d x}-5\left(\frac{d^2 y}{d x^2}\right)^2=6\left(\frac{d y}{d x}\right)^3\) be \(m\) and \(n\) respectively. Then
(A) \(m=2\)
(B) \(n=3\)
(C) \(m=3\)
(D) \(m n=4\)

In a nuclear fission reaction given below, the three neutrons are released. The value of x and y are\( {}_{0}^{1}n + {}_{92}^{235}U \rightarrow {}_{56}^{x}Ba + {}_{y}^{89}Kr + 3{}_{0}^{1}n \)

The typical test cross is performed between -

Consider the following L.L.P.
Minimize \(z=30 x-30 y+1800\);
subject to \(x+y \leq 30, x \leq 15, y \leq 20, x+y \geq 15\) and \(x, y \geq 0\).
Then it attains its optimal value at the point

The following are the natural methods of contraception except :

The properties which depend on the number of solute particles irrespective of their nature relative to the total number of particles in the solution are called colligative properties. These are relative lowering of vapour pressure of the solvent, depression of freesing point of the solvent, elevation of boiling point of the solvent and osmotic pressure of the solution. All of these properties help in calculating the observed molar mass of the solute.
Determination of osmotic pressure is considered best for the determination of molecular mass of the solute.
Based on solute-solvent interactions, arrange the following in order of increasing solubility in n-octane.
(A) Cycloheptane
(B) NaCl
(C) \(CH _3 OH\)
(D) \(CH _3 CN\)
Choose the correct answer from the options given below :