NSEP 2018 25th Nov Question Paper

The SI unit of permeability of free space is

A uniform solid drum of radius R and mass M rolls without slipping down a plane inclined at an angle $$\theta$$. Its acceleration along the plane is

A particle moves according to the law $$x = at$$, $$y = at(1 - \alpha t)$$ where a and $$\beta$$ are positive constants and t is time. The time instant at which velocity makes an angle $$\frac{\pi}{4}$$ with acceleration is

The potential energy of a particle of mass m in a conservative force field can be expressed as
$$U = \alpha x - \beta y$$ where (x, y) denote the position coordinates of the body. The acceleration of the body is

A constant force F applied to the lower block of mass 15 kg makes it slide between the upper block of mass 5 kg and the table below, as shown. The coefficients of static and kinetic friction between the lower block and the table are 0.5 and 0.4 respectively and those between the two blocks are 0.3 and 0.1. The accelerations of the upper and the lower blocks are respectively

Two bodies of equal masses moving with equal speeds make a perfectly inelastic collision. If the speed after the collision is reduced to half, the angle between their velocities of approach is

A student performs an experiment with a simple pendulum and records the time for 20 oscillations. If he would have recorded time for 100 oscillations, the error in the measurement of time period would have reduced by a factor of

A satellite is launched from a point close to the surface of the earth (radius R) with a velocity $$v = \sqrt{1.5}\ v_0$$, where $$v_0$$ is the velocity in a circular orbit. If the initial velocity imparted to the satellite is horizontal, the maximum distance from the surface of the earth during its revolution is

The aperture diameter of a plano-convex lens is 6 cm and its thickness is 3 mm. If the speed of light through its material is $$v = 2\times 10^{8}$$ m/s, the focal length of the lens is

Under standard conditions of temperature and pressure a piece of ice melts completely on heating it. Obviously the increase in internal energy of the system (ice and water) is

Rocket fuel is capable of giving an exhaust velocity of $$v_{rel} = 2.4$$ km/s in the absence of any external forces. The fuel required per kg of the payload to provide a velocity of 12 km/s to the rocket is

A vertical spring of natural length $$l_0$$ and force constant K is stretched by l when a mass m is suspended from its lower end. By pulling the mass down a little the system is left off to oscillate. The time period of oscillation is

Let R be the radius of the earth. In general, the loss of gravitational potential energy of a body of mass m falling from a height h to the earth surface is

The velocity of a projectile at the highest point of its trajectory is $$\sqrt{0.4}$$ of its velocity at a point at half its maximum height. The angle of projection is

The combination of a steel wire (length 80 cm, area of cross section $$1\ \text{mm}^2$$) and an aluminium wire (length 60 cm, area of cross section $$3\ \text{mm}^2$$) joined end to end is stretched by a tension of 160 N. If the densities of steel and aluminium are 7.8 g/cc and 2.6 g/cc respectively then, the minimum frequency of a tuning fork which can produce standing waves in the composite wire, with the joint as a node, is

In a stationary wave

An empty earthen pitcher is kept under a water tap and starts filling with water as the tap is opened. The pitch of the sound produced

The molar specific heat of an ideal gas in a certain thermodynamic process is $$\frac{\alpha}{T}$$ where $$\alpha$$ is a constant. If the adiabatic exponent is $$\gamma = \frac{C_P}{C_V}$$, the work done in heating one mole of the gas from $$T_0$$ to $$nT_0$$ is

An aircraft flies at a speed v from city A to city B and back in time $$t_0$$. City B is to the east of city A at a distance d. The aircraft takes time $$t_1$$ for the round trip if wind blows with speed w along AB and time $$t_2$$ if the wind blows with the same speed perpendicular to AB. Then,

The Hubble telescope in orbit above the earth has a 2.4 m circular aperture. The telescope has equipment for detecting ultraviolet light. The minimum angular separation between two objects that the telescope can resolve in ultraviolet light of wavelength 95 nm is

A projectile is fired from ground with velocity u at an angle $$\theta$$ with the horizontal. It would be moving perpendicular to its initial direction of projection after a time t equal to

The critical angle for light passing from glass to air is minimum for the light of wavelength

A thin hollow equiconvex lens, silvered at the back, converges a beam of light parallel to the principal axis at a distance 0.2 m. When filled with water ($$\mu = \frac{4}{3}$$), the same beam will be converged at a distance of

An air bubble is situated at a distance 2.0 cm from the centre of a spherical glass paperweight of radius 5.0 cm and refractive index 1.5. The bubble is seen through the nearest surface. It appears at a distance v from the centre. Therefore, v is

A student while performing experiment with a sonometer with bridges separated by a distance of 80 cm, missed out some of the observations. However, he claimed that the three resonant frequencies for a given tuning fork were 84, 140 and 224 Hz. The speed of transverse waves on the wire is

Which of the following curves represents spectral distribution of energy of black body radiation?

A sphere and a cube having equal surface area are made of the same material. The two are heated to the same temperature and kept in identical surrounding. The ratio of their initial rates of cooling is

Consider the diffraction pattern due to a single slit. The first maximum for a certain monochromatic light coincides with the first minimum for red light of wavelength 660 nm. The wavelength of the monochromatic light is

A concave lens of focal length f produces an image $$\frac{1}{n}$$ times the size of the object. The distance of the object from the lens is

The Sun having radius R and surface temperature T emits radiation as a perfect emitter. The distance of the earth from the sun is r and the radius of the earth is $$R_e$$. The total radiant power incident on the earth is

A cylinder containing water (refractive index $$\frac{4}{3}$$) is covered by an equiconvex glass (refractive index $$\frac{3}{2}$$) lens of focal length 25 cm. At the mid-day when the sun is just overhead, the image of the sun will be seen at a distance of

A rectangular loop carrying a current is placed in a uniform magnetic field. The net force acting on the loop

The capacitor in the circuit shown below carries a charge of $$30\ \mu\text{C}$$ at a certain time instant. The rate at which energy is being dissipated in the $$3\ \text{k}\Omega$$ resistor at that instant is

A hollow conducting sphere of radius 15 cm has a uniform surface charge density $$+3.2\ \mu\text{C/m}^2$$. When a point charge q is placed at the centre of the sphere, the electric field at 25 cm from the centre just reverses its direction keeping the magnitude the same. Therefore, q is

An electron (e) and a proton (p) are situated on the straight line as shown below. The directions of the electric field at the points 1, 2 and 3 respectively, are shown as

In the circuit shown $$R_1 \neq R_2$$ the reading in the galvanometer is the same with switch S open or closed. Then,

A thin wire of length 1 m is placed perpendicular to the XY plane. It is moved with a velocity $$\overrightarrow{V} = 4i + j$$ $$m/s$$ in the region of magnetic induction $$\overrightarrow{B} = i + 4j$$ $$WB/m^2$$ The potential difference developed between the ends of the wire is

A steel cooking pan has copper coating at its bottom. The thickness of copper coating is half the thickness of steel bottom. The conductivity of copper is three times that of steel. If the temperature of blue flame is $$119^\circ\text{C}$$ and that of the interior of the cooking pan is $$91^\circ\text{C}$$, then the temperature at the interface between the steel bottom and the copper coating in the steady state is

The total capacitance between points A and B in the arrangement shown below is

A fiber sheet of thickness 1 mm and a mica sheet of thickness 2 mm are introduced between two metallic parallel plates to form a capacitor. Given that the dielectric strength of fiber is 6400 kV/m and the dielectric constants of fiber and mica are 2.5 and 8 respectively, the electric field inside the mica sheet just at the breakdown of fiber will be

The position vector of a point mass is expressed as $$\overrightarrow{r} = at{i} + bt^2 {j}$$. The trajectory of the particle is

In a series LCR circuit fed with an alternating emf $$E = E_0\sin\omega t$$,

A conducting wire is bent in the form of an n sided regular polygon enclosed by a circle of radius R. The magnetic field produced at its centre by a current i flowing through the wire is

The effective resistance between points A and B in the circuit arrangement shown below is

The magnetic dipole moment of an electron in the S state of hydrogen atom revolving in a circular orbit of radius 0.0527 nm with a speed $$2.2\times 10^{6}$$ m/s is

A steel cable hanging vertically can support a maximum load W. The cable is cut to exactly half of its original length, the maximum load that it can support now is

The strings AB and AC each of length 40 cm connect a ball of mass 200 g to a vertical shaft as shown. When the shaft rotates at a constant angular speed $$\omega$$, the ball travels in a horizontal circle with the strings inclined at $$\gamma = 30^\circ$$ to the shaft. If the tension in the string AC is 4 N, that in the string AB and the angular speed $$\omega$$ respectively, are

A tightly wound long solenoid carries a current 5 A. An electron shot perpendicular to the solenoid axis inside it revolves at a frequency $$10^{8}$$ rev/s. The number of turns per meter length of the solenoid is

The same alternating voltage $$v = V_0\sin(\omega t)$$ is applied in both the LCR circuits shown below. The current through the resistance R at resonance is

The switch S in the circuit shown is closed for a long time and then opened at time $$t = 0$$. The current in the $$100\ \text{k}\Omega$$ resistance at $$t = 3$$ s is

In the network shown below the voltage $$V_0$$ is nearly

The energy of the characteristic X-ray photon in a Coolidge tube comes from

The maximum wavelength that can ionize a hydrogen atom initially in the ground state is

The wavelength of the waves associated with a proton and a photon are the same. Therefore, the two have equal

Which of the following sources emits light having highest degree of coherence?

An alpha particle with kinetic energy K approaches a stationary nucleus having atomic number Z. The distance of closest approach is b. Therefore the distance of closest approach for a nucleus of atomic number 2Z is

In a photodiode the reverse current increases when exposed to light of wavelength 620 nm or less. The band gap of the semiconductor used is

An electron in hydrogen atom jumps from a level $$n = 4$$ to $$n = 1$$. The momentum of the recoiled atom is

For the Boolean equation $$Y = AB + A(B + C) + B(B + C) + \bar{B}C$$, which of the following statements is correct?

Refer to the common emitter amplifier circuit shown below, using a transistor with $$\beta = 80$$ and $$V_{BE} = 0.7$$ volt. The value of resistance $$R_B$$ is

A horizontal insulated cylinder of volume V is divided into four identical compartments by stationary semi-permeable thin partitions as shown. The four compartments from left are initially filled with 28 g helium, 160 g oxygen, 28 g nitrogen and 20 g hydrogen respectively. The left partition lets through hydrogen, nitrogen and helium while the right partition lets through hydrogen only. The middle partition lets through hydrogen and nitrogen both. The temperature T inside the entire cylinder is maintained constant. After the system is set in equilibrium,

After charging a capacitor C to a potential V, it is connected across an ideal inductor L. The capacitor starts discharging simple harmonically at time $$t = 0$$. The charge on the capacitor at a later time instant is q and the periodic time of simple harmonic oscillations is T. Therefore,

In the circuit arrangement shown two cells supply a current I to a load resistance $$R = 9\ \Omega$$. One cell has an emf $$E_1 = 9$$ V and internal resistance $$r_1 = 1\ \Omega$$ and the other cell has an emf $$E_2 = 6$$ V and internal resistance $$r_2 = 3\ \Omega$$. The currents are as shown. Then,

A transparent cylindrical rod of length $$l = 50$$ cm, radius $$R = 10$$ cm and refractive index $$\sqrt{3}$$ lies onto a horizontal plane surface. A ray of light moving perpendicular to its length is incident on the rod horizontally at a height h above the plane surface such that this ray emerges out of the rod at a height 10 cm above the plane surface. Therefore, h is

Two point charges $$+1\ \mu\text{C}$$ and $$-1\ \mu\text{C}$$ are placed at points $$(0, -0.1\ \text{m})$$ and $$(0, +0.1\ \text{m})$$ respectively in XY plane. Then, choose the correct statements from the following.

An inductance L, a resistance R and a battery B are connected in series with a switch S. The voltages across L and R are $$V_L$$ and $$V_R$$ respectively. Just after closing the switch S,

A string of length l, tied to the top of a pole, carries a ball at its other end as shown. On giving the ball a single hand blow perpendicular to the string, it acquires an initial velocity $$v_0$$ in the horizontal plane and moves in a spiral of decreasing radius by curling itself around the pole. Therefore,

A circular loop of conducting wire of radius 1 cm is cut at a point A on its circumference. It is then folded along a diameter through A such that the two semicircular loops lie in two mutually perpendicular planes. In this region a uniform magnetic field of magnitude 100 mT is directed perpendicular to the diameter through A and makes angles of $$30^\circ$$ and $$60^\circ$$ with the planes of the two semicircles. The magnetic field reduces at a uniform rate from 100 mT to zero in a time interval of 4.28 ms. Therefore,

A converging lens of focal length 40 cm is fixed at 40 cm in front of a screen. An object placed 120 cm from the fixed lens is required to be focused on the screen by introducing another identical lens in between. The second lens should be placed at a distance x from the object where x is

Mysteriously a charged particle moving with velocity $$\overrightarrow{v} = v_0 i$$ entered the tube of Thomson's apparatus where the parallel metallic plates of length 5 cm along X axis are separated by 2 cm. Under the influence of a magnetic field of magnitude $$ \overrightarrow{B} = 4.57\times 10^{-2}$$ T, the particle is found to deflect by an angle of $$5.7^\circ$$. When a potential of 2000 volt is applied between the two plates, the particle is found to move straight to the screen without any deflection. Then,