List of practice Questions

Seeta and Geeta start moving towards each other from two places 200 m apart. After walking 40 m, Geeta turns left and goes 15m, then she turns right and goes 25 m. She then turns right again and comes back to the road on which she had started walking. If Seeta and Geeta walk with the same speed, what is the distance between them now?

Suppose that there is a dispersive medium whose refractive index depends on the wavelength as given by \(n(λ) = n_0 +\frac{ a}{λ^2}-\frac{b}{λ^4}\) . The value of 𝜆 at which the group and phase velocities would be the same, is:

If two traveling waves, given by
𝑦₁=𝐴₀ sin(α𝑘𝑥 -𝜔𝑡) and 𝑦₂=𝐴₀ sin(α𝑘𝑥 − β𝜔𝑡) 
are superposed, which of the following statements is correct?

A gas consists of particles, each having three translational and three rotational degrees of freedom. The ratio of specific heats, Cp/Cv, is: (C_p and C_v are the specific heats at constant pressure and constant volume, respectively).

A cylinder-piston system contains N atoms of an ideal gas. If 𝑡_𝑎𝑣𝑔 is the average time between successive collisions of a given atom with other atoms. If the temperature T of the gas is increased isobarically, then 𝑡_𝑎𝑣𝑔 is proportional to :

An incompressible fluid is flowing through a vertical pipe (height h and crosssectional area 𝐴_𝑜). A thin mesh, having n circular holes of area 𝐴_ℎ is fixed at the bottom end of the pipe. The speed of the fluid entering the top-end of the pipe is 𝑣_𝑜. The volume flow rate from an individual hole of the mesh is given by:
(g is the acceleration due to gravity)

A tank, placed on the ground, is filled with water up to a height ℎ. A small hole is made at a height ℎ1 such that ℎ1 < ℎ. The water jet emerging from the hole strikes

the ground at a horizontal distance D, as shown schematically in the figure. Which of the following statements is correct? (g is the acceleration due to gravity)

A 15.7mW laser beam has a diameter of 4mm. If the amplitude of the associated magnetic field is expressed as \(\frac{𝐴}{\sqrt{ε_0𝑐^3}}\) , the value of A is: (𝜀₀ is the free space permittivity and 𝑐 is the speed of light)

Linearly polarized light (free space wavelength 𝜆₀= 600nm) is incident normally on a retarding plate (𝑛_𝑒-𝑛_𝑜 = 0.05 at 𝜆₀= 600nm). The emergent light is observed to be linearly polarized, irrespective of the angle between the direction of polarization and the optic axis of the plate. The minimum thickness (in µm) of the plate is:

In a Newton’s rings experiment (using light of free space wavelength 580nm), there is an air gap of height d between the glass plate and a plano-convex lens (see figure). The central fringe is observed to be bright.

The least possible value of d (in nm) is:

Given that the rest mass of electron is 0.511MeV/c ² , the speed (in units of c) of an electron with kinetic energy 5.11MeV is closest to:

The ultraviolet catastrophe in the classical (Rayleigh-Jeans) theory of cavity radiation is attributed to the assumption that

The roots of the polynomial, 𝑓(𝑧)=𝑧 ⁴-8𝑧 ³+27𝑧 ²-38𝑧+26, are 𝑧₁, 𝑧₂, 𝑧₃,& 𝑧₄, where 𝑧 is a complex variable. Which of the following statements is correct?

Consider the following logic circuit.

The output Y is LOW when:

The number of atoms in the basis of a primitive cell of hexagonal closed packed structure is:

A crystal plane of a lattice intercepts the principal axes \(\overrightarrow𝑎_1, \overrightarrow𝑎_2,\) and  \(\overrightarrow{a_3}\) at 3𝑎₁, 4𝑎₂, and 2𝑎₃, respectively. The Miller indices of the plane are:

Which of the following types of motion may be represented by the trajectory,
𝑦(𝑥)=𝑎𝑥 ²+𝑏𝑥+𝑐 ? 
(Here a, b, and c are constants; x, y are the position coordinates)

A particle moving along the x-axis approaches 𝑥=0 from 𝑥 =−∞ with a total energy E. It is subjected to a potential 𝑉(𝑥). For time 𝑡→∞, the probability density P(x) of the particle is schematically shown in the figure.

The correct option for the potential 𝑉(𝑥) is:

The magnitudes of spin magnetic moments of electron, proton and neutron are μ_e, μ_p and μ_n, respectively. Then

The sum of three binary numbers, 10110.10, 11010.01, and 10101.11, in decimal system is:

The total number of Na and Cl ions per unit cell of the NaCl crystal is:

The mRNA of a hypothetical plant gene HSDU is 800-nucleotide long and encodes a protein of 160 amino acid residues. The calculated length of HSDU CDS would be____ nucleotides (in integer).

The transfer function of a process is \( G(s) = \frac{K_p}{T_p s + 1} \), where \( K_p \) is the gain and \( T_p \) is the time constant. This is a _____ process.

If ‘→' denotes increasing order of intensity, then the meaning of the words [sick → infirm ← moribund] is analogous to [silly→ ___ ← daft]. Which one of the given options is appropriate to fill the blank?.

The X-ray diffraction pattern of a monatomic cubic crystal with rigid spherical atoms of radius 1.56 Å shows several Bragg reflections of which the reflection appearing at the lowest 2𝜃 value is from (111) plane. If the wavelength of X-ray used is 0.78 Å, the Bragg angle (in 2𝜃, rounded off to one decimal place) corresponding to this reflection and the crystal structure, respectively, are