Recent questions tagged past papers

A block of mass m is placed on a surface with a vertical cross section given by $y = x^3 /6$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :

asked Dec 11, 2018 by pady_1

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The radiation corresponding to $3 \to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

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Hydrogen $(_1H^1 )$, Deuterium $(_1H^2 )$, singly ionised Helium $(_2He^4 )^+$ and doubly ionised lithium $(_3Li^6 )^{++}$ all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wave lengths of emitted radiation are $\lambda_1, \lambda_2, \lambda_3 \;and \;\lambda_4$ respectively then approximately which one of the following is correct?

asked Dec 11, 2018 by pady_1

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A green light is incident from the water to the air – water interface at the critical angle ($\theta$). Select the correct statement

asked Dec 11, 2018 by pady_1

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There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^{\circ}$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. ratio $d_1/d_2$ is

asked Dec 11, 2018 by pady_1

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A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

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Three rods of Copper, Brass and Steel are welded together to from a Y –shaped structure. Area of cross – section of each rod = $4\; cm^2$ . End of copper rod is maintained at $100^{\circ}C$ where as ends of brass and steel are kept at $0^{\circ}C$. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :

asked Dec 11, 2018 by pady_1

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A thin convex lens made from crown glass $( \mu = \frac{3}{2})$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is :

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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

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One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

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A mass â€˜mâ€™ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

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In the circuit shown here, the point â€˜Câ€™ is kept connected to point â€˜Aâ€™ till the current flowing through the circuit becomes constant. Afterward, suddenly, point â€˜Câ€™ is disconnected from point â€˜Aâ€™ and connected to point â€˜Bâ€™ at time $t = 0$. Ratio of the voltage across resistance and the inductor at $t = L/R$ will be equal to :

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During the propagation of electromagnetic waves in a medium:

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The forward biased diode connection is:

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The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 10^3 Am^{-1}$ . The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is:

asked Dec 11, 2018 by pady_1

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A particle moves with simple harmonic motion in a straight line. In first $\tau$ s, after starting from rest it travels a distance a, and in next $\tau$ s it travels 2a, in same direction, then :

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In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

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Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :

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A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

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A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3 \times 10^4 V/m$, the charge density of the positive plate will be close to :

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Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct option from the choices given below the lists:

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An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)

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The current voltage relation of diode is given by $I = (e^{1000V/T}– 1) \;mA$, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring $\pm 0.01 \;V$ while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

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A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :

asked Dec 11, 2018 by pady_1

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A conductor lies along the z-axis at $-1.5 \leq z < 1.5$ and carries a fixed current of 10.0 A in $-\hat{a}_{_z}$ direction (see figure). For a field $\overrightarrow{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_{_y} \;T$, find the power required to move the conductor at constant speed to $x = 2.0\; m, \;y = 0 \;m$ in $5 \times 10^{-3} s$. Assume parallel motion along the x-axis

asked Dec 11, 2018 by pady_1

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The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by $100^{\circ}C$ is : (For steel Young’s modulus is $2 \times 10^{11} N m^{–2}$ and coefficient of thermal expansion is $1.1 \times 10^{–5} K^{–1}$ )

asked Dec 11, 2018 by pady_1

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Two short bar magnets of length 1 cm each have magnetic moments $1.20\; Am^2$ and $1.00\; Am^2 $ respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centres is close to (Horizontal component of earth’s magnetic induction is $3.6 \times 10^{–5} Wb/m^2$)

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The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength is :

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Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is $2 \times 10^8$ m/s, the focal length of the lens is :

asked Dec 11, 2018 by pady_1

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The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals

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This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement – I : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f (\frac{1}{2} mv^2 )$ then $f = (\frac{m}{M+m})$. Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

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The I – V characteristic of an LED is

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If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$ the graph between the temperature T of the metal and time t will be closest to :

asked Dec 11, 2018 by pady_1

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A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is

asked Dec 11, 2018 by pady_1

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A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is:

asked Dec 11, 2018 by pady_1

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An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:

asked Dec 11, 2018 by pady_1

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A hoop of radius r and mass m rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

asked Dec 11, 2018 by pady_1

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Two capacitors $C_1$ and $C_2$ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then :

asked Dec 11, 2018 by pady_1

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A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j}) m/s$, where $\hat{i}$ is along the ground and ˆj is along the vertical. If $g = 10 m/s^2$, the equation of its trajectory is:

asked Dec 11, 2018 by pady_1

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What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

asked Dec 11, 2018 by pady_1

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This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement- I: Higher the range, greater is the resistance of ammeter. Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.

asked Dec 11, 2018 by pady_1

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A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 \;kg/m^3$ and $2.2 \times 10^{11}N/m^2$ respectively?

asked Dec 11, 2018 by pady_1

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The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

asked Dec 11, 2018 by pady_1

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Let $[\varepsilon_0]$ denote the dimensional formula of the permittivity of vaccum. If M = mass, L = length, T = time and A = electric current, then :

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The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by:

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Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is $\rho$ and $L$ is its latent heat of vaporization.

asked Dec 11, 2018 by pady_1

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In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n – 1). If n >> 1, the frequency of radiation emitted is proportional to

asked Dec 11, 2018 by pady_1

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A metallic rod of length $â€˜lâ€™$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field â€˜Bâ€™ in the region, the e.m.f. induced across the ends of the rod is:

asked Dec 11, 2018 by pady_1

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Two coherent point sources $S_1$ and $S_2$ are separated by a small distance â€˜dâ€™ as shown. The fringes obtained on the screen will be:

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The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows:

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A block of mass m is placed on a surface with a vertical cross section given by $y = x^3 /6$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :

A green light is incident from the water to the air – water interface at the critical angle ($\theta$). Select the correct statement

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^{\circ}$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. ratio $d_1/d_2$ is <br>

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

A thin convex lens made from crown glass $( \mu = \frac{3}{2})$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is :

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement: <br>

A mass â€˜mâ€™ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? <br>

During the propagation of electromagnetic waves in a medium:

The forward biased diode connection is:

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3 \times 10^3 Am^{-1}$ . The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is:

A particle moves with simple harmonic motion in a straight line. In first $\tau$ s, after starting from rest it travels a distance a, and in next $\tau$ s it travels 2a, in same direction, then :

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is :

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3 \times 10^4 V/m$, the charge density of the positive plate will be close to :

Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct option from the choices given below the lists: <br>

A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :

The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength is :

Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is $2 \times 10^8$ m/s, the focal length of the lens is :

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals

The I – V characteristic of an LED is

If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$ the graph between the temperature T of the metal and time t will be closest to :

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is: <br>

A hoop of radius r and mass m rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Two capacitors $C_1$ and $C_2$ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then :

A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j}) m/s$, where $\hat{i}$ is along the ground and ˆj is along the vertical. If $g = 10 m/s^2$, the equation of its trajectory is:

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 \;kg/m^3$ and $2.2 \times 10^{11}N/m^2$ respectively?

<br> The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

Let $[\varepsilon_0]$ denote the dimensional formula of the permittivity of vaccum. If M = mass, L = length, T = time and A = electric current, then :

The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by:

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is $\rho$ and $L$ is its latent heat of vaporization.

In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n – 1). If n >> 1, the frequency of radiation emitted is proportional to

Two coherent point sources $S_1$ and $S_2$ are separated by a small distance â€˜dâ€™ as shown. The fringes obtained on the screen will be: <br>

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows: