For an infinitely long wire with uniform line-charge density, λ, along the z-axis, the electric field at a point (a,b,0) away from the origin is are unit vectors in Cartesian − coordinate system. )
A 1 W point source at origin emits light uniformly in all the directions. If the units for both the axes are measured in centimetre, then the Poynting vector at the point (1,1,0) in W/cm2 is are unit vectors in Cartesian − coordinate system. )
A charged particle in a uniform magnetic field starts moving from the origin with velocity The trajectory of the particle and the time t at which it reaches 2 meters above the xy- plane are
are unit vectors in Cartesian − coordinate system. )
Consider a particle of mass m following a trajectory given by x = x0 cos ω1t and y = y0 sin ω2t,
where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle is
Which one of the following points represent the complex number
The eigenvalues of the matrix representing the following pair of linear equations
ix+y = 0
The solution of the Boolean equation
A spherical closed container with smooth inner wall contains a monoatomic ideal gas. If the collisions between the wall and the atoms are elastic, then the Maxwell speed-distribution function for the atoms is best represented by:
Two sinusoidal signals of frequencies ωx and ωy having same amplitude are applied to x- and ychannels of a cathode ray oscilloscope (CRO), respectively. The following stationary figure will be observed when
The phase difference (δ) between input and output voltage for the following circuits (i) and (ii)
For the given set of equations:
x +y = 1
y + z = 1
x + z = 1,
which one of the following statements is correct?
The tangent line to the curve x2 + cy+ 5 = 0 at (1, 1) is represented by
In the following RC circuit, the capacitor was charged in two different ways.
(i) The capacitor was first charged to 5V by moving the toggle switch to position P and then it
was charged to 10V by moving the toggle switch to position Q.
(ii) The capacitor was directly charged to 10V, by keeping the toggle switch at position Q.
Assuming the capacitor to be ideal, which one of the following statements is correct?
If a constant voltage +V is applied to the input of the following OPAMP circuit for a time t, then the output voltage Vo will approach
Light travelling between two points takes a path for which
In the following RC network, for an input signal frequency and the phase angle ψ between v0 and v1 respectively are
Consider a free electron (e) and a photon (ph) both having 10 eV of energy. If λ and P represent wavelength and momentum respectively, then
(mass of electron = 9.1 x 10-31 kg; speed of light = 3 x 108 m/s)
For an ideal gas, which one of the following T-S diagrams is valid?
If U. F, H and G represent internal energy, Helmholtz free energy, enthalpy, and Gibbs free energy respectively, then which one of the following is a correct thermodynamic relation?
A train passes through a station with a constant speed. A stationary observer at the station platformmeasures the tone of the train whistle as 484 Hz when it approaches the station and 442 Hz when itleaves the station. If the sound velocity in air is 330 m/s, then the tone of the whistle and the speedof the train are
The minimum length of a plane mirror to see the entire full-length image of an object is half of the object’s height. Suppose δ is the distance between eye and top of the head of a person of height h. The person will be able to see his entire full-length image with a mirror of height h/2 fixed on the wall
A particle is moving in a plane with a constant radial velocity of 12 m/s and constant angular velocity of 2 rad/s. When the particle is at a distance r = 8 m from the origin, the magnitude of the instantaneous velocity of the particle in m/s is
A cylindrical rod of length L has a mass density distribution given by where x is measured from one end of the rod and ρ0 is a constant of appropriate dimensions. The center of mass of the rod is
A particle travels in a medium along a horizontal linear path. The initial velocity of the particle is v0 and the viscous force acting on it is proportional to its instantaneous velocity. In the absence of any other forces, which one of the following figures correctly represents the velocity of the particle as a function of time?
A lightly damped harmonic oscillator with natural frequency ω0 is driven by a periodic force of frequency ω. The amplitude of oscillation is maximum when
A block of mass 0.38 kg is kept at rest on a frictionless surface and attached to a wall with a spring of negligible mass. A bullet weighing 0.02 kg moving with a speed of 200 m/s hits the block at time t = 0 and gets stuck to it. The displacement of the block (in metre) with respect to the equilibrium position is given by
(Spring constant = 640 N/m.)
One mole of an ideal gas with average molecular speed v0 is kept in a container of fixed volume. Ifthe temperature of the gas is increased such that the average speed gets doubled, then
An arbitrarily shaped conductor encloses a charge q and is surrounded by a conducting hollow sphere as shown in the figure. Four different regions of space, 1, 2, 3, and 4, are indicated in the figure. Which one of the following statements is correct?
Consider a small bar magnet undergoing simple harmonic motion (SHM) along the x-axis. A coilwhose plane is perpendicular to the x-axis is placed such that the magnet passes in and out of itduring its motion. Which one of the following statements is correct? Neglect damping effects.
An incompressible, non-viscous fluid is injected into a conical pipe at its orifice as schematically shown in the figure. The pressure at the orifice of area A0 is P0. Neglecting the effect of gravity and assuming streamline flow, which one of the following plots correctly predicts the pressure along axis of the cone?
Consider a spherical dielectric material of radius ‘a’, centered at origin. If the polarization vector where P0 is a constant of appropriate dimensions, then
are unit vectors in Cartesian − coordinate system. )
For an electric dipole with moment placed at the origin, (p0 is a constant of appropriate dimensions and are unit vectors in Cartesiancoordinate system.)
Three infinitely-long conductors carrying currents l1, l2, and l3 lie perpendicular to the plane of the paper as shown below.
If the value of the integral or the loops C1, C2, and C3 are 2μ0, 4μ0, and μ0 in the units of N/A, respectively, then
In the optical arrangement as shown below, the axes of two polarizing sheets P and Q are oriented such that no light is detected. Now when a third polarizing sheet (R) is placed in between P and Q, then light is detected. Which of the following statement(s) is(are) true?
The P-V diagram below shows three possible paths for an ideal gas to reach the final state f from an initial state i. Which among the following statement(s) is(are) correct?
Potential energy U as a function of r is shown below. If a particle of mass m1 and energy E
, starting from r ≫ a, moves towards the origin, then
A particle moves in a circular path in the xy -plane centered at the origin. If the speed of the particleis constant, then its angular momentum
A pn junction was formed with a heavily doped (1018cm-3) p-region and lightly doped (1014 cm-3) n-region. Which of the following statement(s) is(are) correct?
A slit has width ‘d’ along the x-direction. If a beam of electrons, accelerated in y-direction to aparticular velocity by applying a potential difference of 100 ± 0.1 kV passes through the slit, then,which of the following statement(s) is(are) correct?
A free particle of energy E collides with a one-dimensional square potential barrier of height V andwidth W. Which one of the following statement(s) is(are) correct?
Fourier series of a given function f(x) in the interval 0 to L is
If f(x)= x in the region (0, π), b2 = _________.
Consider a function f(x,y) = x3 + y3, where y represents a parabolic curve x2 + 1. The total derivative of f with respect to x, at x =1 is _______.
A rectangular area (A1) is formed by two vectors as shown in figure (i). A new set of vectors, representing the area (A2) as shown in figure (ii), are given as:
where k is a dimensionless constant.
The Jacobian of the frame is _______.
A particular radioisotope has a half-life of 5 days. In 15 days the probability of decay in percentage will be ______.
In a photoelectric experiment both sodium (work function = 2.3 eV) and tungsten (work function = 4.5 eV) metals were illuminated by an ultraviolet light of same wavelength. If the stopping potential for tungsten is measured to be 1.8 V, the value of the stopping potential for sodium will be
The addition of two binary numbers 1000.01 and 0001.11 in binary representation is _________.
The number of second-nearest neighbor ions to a Na+ ion in NaCl crystal is________.
The output voltage VO of the OPAMP circuit given below is ________V.
A cylinder contains 16 g of O2. The work done when the gas is compressed to 75% of the original volume at constant temperature of 27°C is _________ J.
[Universal gas constant R = 8.31 J/(mole K)]
When sunlight is focused on a paper using a bi-convex lens, it starts to burn in the shortest time if the lens is kept 0.5 m above it. If the radius of curvature of the lens is 0.75 m then, the refractive index of the material is ______.
Consider a closed triangular contour traversed in counter-clockwise direction, as shown in the figure below.
The value of the integral evaluated along this contour, for a vector field, is ___________.
are unit vectors in Cartesian − coordinate system. )
A hemispherical shell is placed on the xy– plane centered at the origin. For a vector field the value of the integral over the hemispherical surface is _________ π.
( is the elemental surface area. are unit vectors in Cartesian −
coordinate system. )
The shape of a dielectric lamina is defined by the two curves y = 0 and y = 1 − x2. If the charge density of the lamina σ = 15y C/m2, then the total charge on the lamina is _______C.
In the circuit given below, the collector to emitter voltage VCE is ________V.
(Neglect VBE, take β = 100)
The de Broglie wavelength of a relativistic electron having 1 MeV of energy is ________× 10-12 m. (Take the rest mass energy of the electron to be 0.5 MeV. Planck constant = 6.63×10-34 Js, Speed of light= 3×108 m/s, Electronic charge = 1.6×10-19C)
X-ray diffraction of a cubic crystal gives an intensity maximum for Bragg angle of 20°
corresponding to the (110) plane. The lattice parameter of the crystal is __________nm.
(Consider wavelength of X-ray = 0.15 nm)
X-rays of 20 keV energy is scattered inelastically from a carbon target. The kinetic energy transferred to the recoiling electron by photons scattered at 90° with respect to the incident beam is
(Planck constant = 6.6×10-34 Js, Speed of light = 3×108 m/s, electron mass = 9.1×10-31 kg, Electronic charge = 1.6×10-19C)
An aluminum plate of mass 0.1 kg at 95oC is immersed in 0.5 litre of water at 20oC kept inside an insulating container and is then removed. If the temperature of the water is found to be 23oC, then the temperature of the aluminum plate is ___________ oC.
(The specific heat of water and aluminum are 4200 J/kg-K and 900 J/kg-K respectively, the density of water is 1000 kg/m3)
The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively. The ratio of the aphelion distance of the comet to the radius of the Earth’s orbit is ______.
(Assume that Earth moves in a circular orbit of radius 1.5 × 108 km with a speed of 30 km/s.)
If there is a 10% decrease in the atmospheric pressure at a hill compared to the pressure at sea level, then the change in the boiling point of water is_____ oC.
(Take latent heat of vaporisation of water as 2270 kJ/kg and the change in the specific volume at the boiling point to be 1.2 m3/kg.)