Haryana SET Physical Science Exam - English

An inverted cone is filled with water at a constant rate. The volume of water inside the cone as a function of time is represented by the curve :
​
 

A spacecraft flies at a constant height R above a planet of radius R. At the instant the spacecraft is over the north pole, the lowest latitude visible from the spacecraft is :

An experiment consists of tossing a coin 20 times. Such an experiment is performed 50 times. The number of heads and the number of tails in each experiment are noted. What is the correlation coefficient between the two ?

Which of these groups of numbers has the smallest mean ?
Group A : 1, 2, 3, 4, 5, 6, 7, 8, 9
Group B : 1, 2, 3, 4, 6, 6, 7, 8, 9
Group C : 1, 2, 2, 4, 5, 6, 7, 8, 9
​Group D : 1, 3, 3, 4, 5, 6, 7, 9, 9

Identical balls are tightly arranged in the shape of an equilateral triangle with each side containing n balls. How many balls are there in the arrangement ?

A shopkeeper has a faulty pan balance with a zero offset. When an object is placed in the left. plan it is balanced by a standard 100 g weight. When it is placed in the right pan it is bálanced by a standard 80 g weight. What is the actual weight of the object ?

A and B start from the same point in opposite directions along a circular track simultaneously. Speed of B is 2 / 3 rd that of A. How many times will A and B cross each other before meeting at the starting point ?

Consider a solid cube of side 5 units. After painting, it is cut into cubes of 1 unit. Find the probability that a randomly chosen unit cube has only one side painted .

How many integers in the set {1, 2, 3, .... 100} have exactly 3 divisors ?

The arithmetic and geometric means of two numbers are 65 and 25, respectively. What are these two numbers ?

Shyam spent half of his money and was left with as many as he had rupees before, but with half as many rupees as he had paise before. Which of the following is a possible amount of money he is left with ?

A cylindrical road roller having a diameter of 1.5 m moves at a speed of 3 km / h while levelling a road. How much length of the road will be levelled in 45 minutes ?

An intravenous fluid is given to a child of 7.5 kg, at the rate of 20 drop/minute. The prescribed dose of the fluid is 40 ml per kg of body weight. If the volume of a drop is 0.05 ml, how many hours are needed to complete the dose ?

A cousin is a non - sibling with a common ancestor. If there is exactly one pair of siblings in a group of 5 persons, then the maximum possible number of pairs of cousins in the group. is :

In a tournament with 8 teams, a win fetches 3 points and a draw, 1. After all teams have played three matches each, total number of points earned by all teams put together must lie between

An appropriate diagram to represent the relations between the categories KEYBOARD, HARDWARE, OPERATING SYSTEM and CPU is :

Trade figures and populations in appropriate units in a certain year are given for 7 countries .

If countries are ranked according to the difference in their per capita exports over import, then the best and worst ranking countries are respectively ​

At least two among three persons A, B and C are truthful. If A calls B a liar and if B calls C a liar, then which of the following is FALSE ?

The maximum area of a right - angled triangle inscribed in a circle of radius r is :

If we replace the mathematical operations in the expression (11 + 4 – 2) ÷ 2 × 6 as given in the table :
​
​then its new, value is :

A particle in one dimension executes oscillatory motion in a potential V (x) = A |x|, where A > 0 is a constant of appropriate dimension. If the time period T of its oscillation depends on the total energy E as Ea, then the value of a is :

The equation of motion of a one - dimensional forced harmonic oscillator in the presence of a dissipative force is described by
​
The general form of the particular soltion, in terms of constants A, B etc., is : ​

The vector potential for an almost point like magnetic dipole located at the origin is
​​where (r, θ, Ï•) denote the spherical polar coordinates and Ï•is the unit vector along Ï• f.​
A particle of mass m and charge q, moving in the equatorial plane of the dipole, starts at time = t = 0 with an initial speed v₀ and an impact parameter b. Its instantaneous speed at the point of closest approach is :

A particle, thrown with a speed v from the earth's surface, attains a maximum height h(measured from the surface of the earth). If v is half the escape velocity and Rdenotes the radius of earth, then h / R is :

A particle of mass 1GeV/c² and its antiparticle, both moving with the same speed v, produce a new particle X of mass 10 GeV/c² in a headon collision. The minimum value of v required for this process is closest to :

The volume of the region common to the interiors of two infinitely long cylinders defined by x² + y² = 25 and x² + 4 z² = 25 is best approximated by :

The volume integral  is over a region V bounded by a surface (an infinitesimal area element being , where is the outward unit normal). If it changes to  when the vector A is changed to A + A, then ​I can be expressed as

A generic 3 x 3 real matrix.A has eigenvalues 0, 1 and 6, and I is the 3 x 3 identity matrix. The quantity/quantities that cannot be determined from this information is/are the :

A discrete random variable X takes a value from the set { –1, 0, 1, 2} with the corresponding probabilities p (X) = 3 / 10,2 / 10,2 / 10 and 3 / 10, respectively. The probability distribution q(Y) = (q(0), q(1), q(4)) of the random variable Y = X² is :

The components of the electric field, in a region of space devoid of a y charge or current sources, are given to be ​where a_i and b_ij are constants independent of the coordinates. The number of independent components of the matrix b_ij is :

A conducting wire in the shape of a circle lies on the (x, y) - plane, with its centre at the origin. A bar magnet moves with a constant velocity towards the wire along the z - axis (as shown in the figure below) .
​
We take t = 0 to be the instant at which the midpoint of the magnet is at the centre of the wire loop and the induced current to be positive when it is counter - clockwise as viewed by the observer facing the loop and the incoming magnet. In these conventions, the besi schematic representation of the induced curren I (t) as a function of t, is :

In an experiment to measure the charge to mass ratio e / m of the electron by Thomson's method, the values of the deflecting electric field and the accelerating potential are 6 x10⁶ N / C (newton per coulomb) and 150 V, respectively. The magnitude of the magnetic field that leads to zero deflection of the electron beam is closest to :

A monochromatic source emitting radiation with a certain frequency moves with a velocity v away from a stationary observer. A. It is moving towards another observer B (also at rest) along a line joining the two. The frequencies of the radiation recorded by A and B are v_A and v_B, respectively. If the ratio
​then the value of v / c is:

The Hamiltonian of a particle of mass m in one - dimension is â€‹ where > 0 is. a constant. If E₁ and E₂, respectively. denote the ground stàte energies of the particle for = 1 and = 2 (in appropriate units) the ratio E₂ / E₁ is best approximated by :

A particle of mass m is in a one dimensional infinite potential well of length L, extending from x = 0.to x = L. When it is in the energy eigenstate labelled by n, (n = 1,2,3, ...) the probability of finding it in the interval ​is 1 / 8. The minimum value of n for which this is possible is :

A two - state system evolves under the action of the  are its two orthonormal states. These states transform to one another under parity, i.e.,  If at time t = 0 the system is in a state of definite parity P = 1,the earliest time t at which the probability of finding the system in a state of parity P = -1 is one, is :

The figures below depict three different wavefunctions of a particle confined to a onedimensional box 

​​The wavefunctions that correspond to the maximum expectation values â€‹(absolute value of the mean position) and ​ respectively, are :

Which of the following two physical quantities cannot be measured simultaneously with arbitrary accuracy for the motion of a quantum particle in three dimensions ?

The ratio C_p / C_V of the specific heats at constant pressure and volume of a monoatomic ideal gas in two dimensions is :

The volume and temperature of a spherical cavity filled with black body radiation are V and 300 K, respectively. If it expands adiabatically to a volume 2 V, its temperature will be closest to :

The total number of phonon modes in a solid of volume where N is the number of primitive cells, w_D is the Debye frequency and density of photon modes is g(w) = AVw² (with A > 0 a constant). If the density of the solid doubles in a phase transition, the Debye temperature Q_D will :

The position of a particle in one dimension changes in discrete steps. With each step it moves to the right, however, the length of the step is drawn from a uniform distribution from the interval where  and w are positive constants. If X denotes the distance from the starting point after N steps, the standard deviation â€‹ for large values of N is :​

In the LCR circuit shown below, the resistance R = 0.05  the inductance L = 1 H and the capacitance C = 0.04 F.
​
​If the input vin is a square wave of angular frequency 1 rad / s, the output v_out is best approximated by a :

In an experiment, the velocity of a nonrelativistic neutron is determined by measuring the time(~50 ns) it takes to travel from the source to the detector kept at a distance L. Assume that the error in the measurement of L is negligibly small. If we want to estimate the kinetic energy T of the neutron to within 5 % accuracy, i.e.,​ 0.05, the maximum permissible error $|delta t|$ in measuring the time of flight is nearest to :

The door of an X- ray machine room is fitted with a sensor D (0 is open and 1 is closed). It is also equipped with three fire sensors F_1, F₂ and F₃ (each is 0 when disabled and 1 when enabled). The X - ray machine can operate only if the door is closed and at least 2 fire sensors are enabled. The logic circuit to ensure that the machine can be operated is :

If we use the Fourier transform (x, y) = to solve the partial differential equation  in the half - plane the Fourier modes (y) depend on y as y^B and y^B. The values of a and b are : 

The Newton - Raphson method is to be used to determine the reciprocal of the number x = 4. If we start with the initial guess 0.20, then after the first iteration the reciprocal is :

The Legendre polynomials P_n(x), n = 0, 1, 2, ..., satisfying the orthogonality condition .
​ on the interval [-1,+1] may be defined by the Rodrigues formula
​ The value of the definite interval
​

A particle of mass m moves in a potential that is in the coordinates of a non - inertial frame F. The frame F is rotating with respect to an inertial frame with an angular velocity , where â€‹ is the unit vector along their common z - axis. The motion of the particle is unstable for all angular frequencies satisfying :

Which instrument is used to measure altitude in aircraft's ?

A perfectly conducting fluid, of permittivity e and permeability m, flows with a uniform velocity v in the presence of time dependent electric and magnetic fields E and B, respectively. If there is a finite current density in the fluid, then :

A laser beam propagates from fiber 1 to fiber 2 in a cavity : made up of two optical fibers (as shown in the figure). The loss factor of fiber 2 is 10 dB / km .
​
​If E₂ (d) denotes the magnitude of the electric field in fiber 2 at a distance d from the interface, the ratio E₂(0) / E₂(d) for d = 10 km, is :

A particle in two dimensions is found to trace an orbit â€‹ If it is moving under the influence of a central potential V(r) = c₁ r^-a + c₂ r^-b, where r₀, c₁ and c₂ are constants of appropriate dimensions, the values of a and b, respectively, are :​

A satellite of mass m orbits around earth in an elliptic trajectory of semi - major axis a. At a radial distance r = r₀, measured from the centre of the earth, the kinetic energy is equal to half the magnitude of the total energy. If M denotes the mass of the earth and the total energy is 
​the value of r₀ / a is nearest to :

A particle of mass $m$ in one dimension is in the ground state of a simple harmonic oscillator
described by a Hamiltonian ​in the standard notation. An impulsive force at time t = 0 suddenly imparts a momentum​ â€‹to it. The probability that the particle remains in the original ground state is :​

The energies of a two - state quantum system are E₀ and E₀ + ah, (where a > 0 is a constant) and the corresponding normalized state vectors are |0 > and |1 >, respectively. At time t = 0, when the system is in the state |0 >, the potential is altered by a​​ time independent term V such that  he transition probability to the state​ â€‹

In an elastic scattering process at an energy E, the phase shifts satisfy  , while the other phase shifts are zero. The polar angle at which the differential cross section peaks is closest to :

The unnormalized wavefunction of a particle in one dimension in an infinite square well - with walls at x = 0 and x = a, is y (x) = x (a - x). If Ψ(x)Ψis expanded as a linear combination of the energy eigenfunctions,  is proportional to the infinite series​
(You may use ​​

The pressure of a gas in a vessel needs be maintained between 1.5 barr to 2.5 bar in an experiment. The vessel is fitted with a pressure transducer that generates 4 mA to 20 mA current for pressure in the range 1 bar to 5 bar. The current output of the transducer has a linear dependence on the pressure .
​
​The reference voltages V₁ and V₂ in the comparators in the circuit (shown in figure above) suitable for the desired operating conditions, are, respectively :

The nuclei of ¹³⁷Cs decay by the emission of $beta$ - particles with a half life of 30.08 years. The activity (in units of disintegrations per second or Bq) of a 1 mg source of ¹³⁷Cs, prepared on January 1, 1980, as measured on January 1, 2021 is closest to :

In the following circuit the input voltage V_in is such that |V_in| < |V_sat |, where V_sat is the saturation voltage of the op - amp. (Assume that the diode is an ideal one and R_LC is much larger than the duration of the measurement.)

​For the input voltage as shown in the figure above, the output voltage Vout is best represented by :

To measure the height h of a column of liquid helium in a container, a constant current I is sent through an NbTi wire of length l, as shown in the figure. The normal state resistance of the NbTi wire is R .
​
​If the superconducting transition temperature of NbTi is ≈ 10 K, then the measured voltage V(h) is best described by the expression:

The energy levels of a non-degenerate quantum system are ​= nE₀, where E₀ is a constant and n = 1, 2, 3, .... At a temperature T, the free energy F can be expressed in terms of the average energy E by :

A polymer, made up of N monomers, is in thermal equilibrium at temperature T. Each monomer could be of length a or 2 a. The first contributes zero energy, while the second one contributes ϵ. The average length (in units of Na) of the polymer at temperature T = ϵ / k_B is :

Balls of ten different colours labelled by a = 1, 2, ..., 10 are to be distributed among different coloured boxes. A ball can only go in a box of the same colour, and each box can contain at most one ball. Let n_a and N_a denote, respectively, the numbers of balls and boxes of colour a. Assuming that N_a >> n_a >>1, the total entropy (in units of the Boltzmann constant) can be best approximated by :

The dispersion relation of a gas of noninteracting bosons in d dimensions is E (k) = ak^s, where a and s are positive constants. Bose - Einstein condensation will occur for all values of :

Lead is superconducting below 7 K and has a critical magnetic field 800 x 10^-4 tesla close to 0 K. At K the critical current that flows through a long lead wire of radius 5 mm is closest to :

Potassium chloride forms an FCC lattice, in which K and Cl occupy alternating sites. The density of KCl is 1.98 g / cm³ and the atomic weights of K and Cl are 39.1 and 35.5, respectively. The angles of incidence (in degrees) for which Bragg peaks will appear when X - ray of wavelength 0.4 nm is shone on a KCl crystal are :

In the reaction p + n p + K + + X, mediated by strong interaction, the baryon number B, strangeness S and the third component of isospin I₃ of the particle X are, respectively :

A ⁶⁰ Co nucleus b - decays from its ground state with Ip = 5⁺ to a state of ⁶⁰ Ni with Ip = 4 ⁺. From the angular momentum selection rules, the allowed values of the orbital angular momentum L and the total spin S of the electron - antineutrino pair are :

The Q - value of the a - decay of ²³² Th to the ground state of ²²⁸ Ra is 4082 keV. The maximum possible kinetic energy of the a - particle is closest to :

The |3, 0, 0 > state (in the standard notation |n, l, m >> of the H-atom in the non - relativistic theory decays to the state |1, 0, 0 > via two dipole transitions. The transition route and the corresponding probability are :

A linear diatomic molecule consists of two identical small electric dipoles with an equilibrium separation R, which is assumed to be a constant. Each dipole has charges ±q of mass m separated by r when the molecule is at equilibrium. Each dipole can execute simple harmonic motion of angular frequency ω .


​
Recall that the interaction potential between tw o dipoles of m om ents p₁ and p₂ separated by 
​
​The angular frequencies of small oscillations of the diatomic molecule are :

Diffuse hydrogen gas within a galaxy may be assumed to follow a Maxwell distribution at temperature 10⁶ K, while the temperature appropriate for the H gas in the inter - galactic space, following the same distribution, may be taken to be 10⁴ K. The ratio of thermal broadening ∆∨_G / ∆∨_G of the Lyman - a line from the H-atoms within the galaxy to that from the inter - galactic space is closest to :

A couple lives in a house with their sons and daughters and no one else. The couple has four sons and each of the sons has exactly two sisters. How many persons live in that house ?