Recent questions tagged past papers

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree ($=0.5^{\circ}$), then the least count of the instrument is

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Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by $\Delta$ x on applying force F, how much force is needed to stretch wire 2 by the same amount ?

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The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where g = the acceleration due to gravity on the surace of the earth) in terms of R, the radius of the earth is

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Three sound waves of equal amplitudes has frequencies $(v-1), v, (v+1)$. They superpose to give beats. The number of beats produced per second will be

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A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is

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A long metallic bar is carrying heat from one of its end to the other end under steady-state. The variation of temperature $\theta$ along the length x of the bar from its hot end is best described by which of the following figure :

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A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, tthen the Q/q equals

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Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be

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A motor cycle starts from rest and acceleration along a straight path at $2\; m/s^2$. At the starting point of the motor cycle there is a stationary electric sire. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest ? (speed of sound = 330 $ms^{-1}$ )$

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A particle has an initial velocity $3 \hat{i} + 4 \hat{j}$ and an acceleration of $0.4 \hat{i} + 0.3 \hat{j}$. Its speed after 10 s is

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The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV nm)

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Two points P and Q are maintained at the potentials of 10V and -4V respectively. The work done in moving 100 electrons from P to Q is

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A mixture of light, consisting of wavelength 590 nm and an unknown wavelength , illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the $4^{th}$ bright fringe of the unknown light. From this data, the wavelength of the unknown light is

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Due to the presence of the current I, at the origin

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The magnitude of the magnetic field (B) due to loop ABCD at the origin (O) is

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This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : The temperature dependence of resistance is usually given as $R = R_o(1+ \alpha \Delta t)$. The resistance of a wire changes from $100 \Omega$ to $150 \Omega$ when its temperature is increased from $27^{\circ}C$ to $227^{\circ}C$. This implies that $\alpha = 2.5 \times 10^{-3} /^{\circ} C$. Statement 2 : $R = R_i (1 + \alpha \Delta T)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R= (R-R_o) < < R_o$.

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One kg of a diatomic gas is at a pressure of $8 \times 10^4\;N/m^2$. The density of the gas is $4\; kg/m^{3}$. What is the energy of the gas due to its thermal motion ?

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The transition from the state $n=4$ to $n=3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

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Let $P(r) = \frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius R and total charge Q for a point 'p' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

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A thin uniform rod of length $\ell$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of

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In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v$, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45^{\circ}$ with the $x$-axis meets the experimental curve at $P$. The coordinates of $P$ will be

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If $x, v$ and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time ?

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The logic circuit below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform.

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A p-n junction (D) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit.

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The above is a plot of binding energy per nucleon $E_b$, against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions : (i) $ A + B \to C + \varepsilon \; \; \; \;$ (ii) $ C \to A + B + \varepsilon \; \; \; \;$ (iii) $D+ E \to F + \varepsilon \; and \; \; \; \; $ (iv) $ F \to D + E + \varepsilon$ where $\varepsilon$ is the energy released ? In which reactions is $\varepsilon$ positive ?

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This question contains Statement - 1 and Statement - 2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - 1 : For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q. Statement -2 : The net work done by a conservative force on an object moving along a closed loop is zero.

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In the following sequence of reactions, the alkene affords the compound ‘B’ $CH_3CH = CHCH_3 \xrightarrow{O_3} A \xrightarrow[\text{Zn}]{\text{$H_2O$}} B$ The compound is :

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An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure $P_1$ and temperature $T_1$. The other chamber has volume $V_2$ and contains ideal gas at pressure $P_2$ and temperature $T_2$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

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Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of - 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

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Relative permittivity and permeability of a material are $\varepsilon_r$ and $\mu_r$, respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

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A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is $(\mu_0 = 4\pi\times 10^{-7} T m A^{-1})$

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A 5V battery with internal resistance $2\Omega$ and a 2V battery with internal resistance $1\Omega$ are connected to a $10\Omega$ resistor as shown in the figure. The current in the $10\Omega$ resistor is <img src""/>

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A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range $0\leq r\infty$, where r is the distance from the centre of the shell?

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An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

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A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x- direction with a constant speed. The position of the first body is given by $x_1$(t) after time ‘t’ and that of the second body by $x_2$(t) after the same time interval. Which of the following graphs correctly describes $(x_1 – x_2)$ as a function of time ‘t’?

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In the circuit below, A and B represent two inputs and C represents the output <img src""/> The circuit represents

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Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area $A = 10 cm^2$ and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is ($\mu_0= 4\pi \times 10^{-7} Tm A^{-1}$)

asked Nov 29, 2018 by pady_1

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A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos ($\alpha x-\beta t$). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\alpha$ and $\beta$ in appropriate units are

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Suppose an electron is attracted towards the origin by a force k/r where ‘k’ is a constant and ‘r’ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be $‘r_n’$ and the kinetic energy of the electron to be $T_n$. Then which of the following is true?

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A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

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A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

asked Nov 29, 2018 by pady_1

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91. A student measures the focal length of convex lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like

asked Nov 29, 2018 by pady_1

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Consider a block of conducting material of resistivity â€˜pâ€™ shown in the figure. Current â€˜Iâ€™ enters at â€˜Aâ€™ and leaves from â€˜Dâ€™. We apply superposition principle to find voltage â€˜$\triangle$Vâ€™ developed between â€˜Bâ€™ and â€˜Câ€™. The calculation is done in the following steps: (i) Take current â€˜Iâ€™ entering from â€˜Aâ€™ and assume it to spread over a hemispherical surface in the block (ii) Calculate field E(r) at distance â€˜râ€™ from A by using Ohmâ€™s law E = pj, where j is the current per unit area at â€˜r (iii) From the â€˜râ€™ dependence of E(r), obtain the potential V(r) at r. (iv) Repeat (i), (ii) and (iii) for current â€˜Iâ€™ leaving â€˜Dâ€™ and superpose results for â€˜Aâ€™ and â€˜Dâ€™. QUESTION : For current entering at A, the electric field at a distance â€˜râ€™ from A is

asked Nov 29, 2018 by pady_1

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Consider a block of conducting material of resistivity â€˜pâ€™ shown in the figure. Current â€˜Iâ€™ enters at â€˜Aâ€™ and leaves from â€˜Dâ€™. We apply superposition principle to find voltage â€˜$\triangle$Vâ€™ developed between â€˜Bâ€™ and â€˜Câ€™. The calculation is done in the following steps: (i) Take current â€˜Iâ€™ entering from â€˜Aâ€™ and assume it to spread over a hemispherical surface in the block (ii) Calculate field E(r) at distance â€˜râ€™ from A by using Ohmâ€™s law E = pj, where j is the current per unit area at â€˜r (iii) From the â€˜râ€™ dependence of E(r), obtain the potential V(r) at r. (iv) Repeat (i), (ii) and (iii) for current â€˜Iâ€™ leaving â€˜Dâ€™ and superpose results for â€˜Aâ€™ and â€˜Dâ€™. QUESTION : $\triangle$V measured between B and C is

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78. A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor?

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A jar filled with two non mixing liquids 1 and 2 having densities $p_1 and P_2$ respectively. A solid ball, made of a material of density $p_3$, is dropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following is true for $P_1, p_2\; and\; p_3$?,

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This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement – I: For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is $4\pi GM.$. and Statement – II If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as $\frac{1}{r^2}$,its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

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This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement – I: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. and Statement – II For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decrease with increasing Z.

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The speed of sound in oxygen $(O_2)$ at a certain temperature is $460 ms^{-1}$. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

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78. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1=3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now

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Ask Questions, Get Answers

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree ($=0.5^{\circ}$), then the least count of the instrument is

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by $\Delta$ x on applying force F, how much force is needed to stretch wire 2 by the same amount ?

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where g = the acceleration due to gravity on the surace of the earth) in terms of R, the radius of the earth is

Three sound waves of equal amplitudes has frequencies $(v-1), v, (v+1)$. They superpose to give beats. The number of beats produced per second will be

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is <br>

A long metallic bar is carrying heat from one of its end to the other end under steady-state. The variation of temperature $\theta$ along the length x of the bar from its hot end is best described by which of the following figure :

A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, tthen the Q/q equals

Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be

A particle has an initial velocity $3 \hat{i} + 4 \hat{j}$ and an acceleration of $0.4 \hat{i} + 0.3 \hat{j}$. Its speed after 10 s is

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV nm)

Two points P and Q are maintained at the potentials of 10V and -4V respectively. The work done in moving 100 electrons from P to Q is

Due to the presence of the current I, at the origin

The magnitude of the magnetic field (B) due to loop ABCD at the origin (O) is

One kg of a diatomic gas is at a pressure of $8 \times 10^4\;N/m^2$. The density of the gas is $4\; kg/m^{3}$. What is the energy of the gas due to its thermal motion ?

The transition from the state $n=4$ to $n=3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from <br>

Let $P(r) = \frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius R and total charge Q for a point 'p' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

A thin uniform rod of length $\ell$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of

If $x, v$ and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time ?

The logic circuit below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform. <br>

A p-n junction (D) shown in the figure can act as a rectifier. An alternating current source (V) is connected in the circuit. <br>

In the following sequence of reactions, the alkene affords the compound ‘B’ $CH_3CH = CHCH_3 \xrightarrow{O_3} A \xrightarrow[\text{Zn}]{\text{$H_2O$}} B$ <br> The compound is :

Relative permittivity and permeability of a material are $\varepsilon_r$ and $\mu_r$, respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is $(\mu_0 = 4\pi\times 10^{-7} T m A^{-1})$

A 5V battery with internal resistance $2\Omega$ and a 2V battery with internal resistance $1\Omega$ are connected to a $10\Omega$ resistor as shown in the figure. The current in the $10\Omega$ resistor is<br> <img src""/>

A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range $0\leq r\infty$, where r is the distance from the centre of the shell?

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

In the circuit below, A and B represent two inputs and C represents the output <br> <img src""/><br> The circuit represents

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area $A = 10 cm^2$ and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is ($\mu_0= 4\pi \times 10^{-7} Tm A^{-1}$)

A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos ($\alpha x-\beta t$). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\alpha$ and $\beta$ in appropriate units are

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

91. A student measures the focal length of convex lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like

A jar filled with two non mixing liquids 1 and 2 having densities $p_1 and P_2$ respectively. A solid ball, made of a material of density $p_3$, is dropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following is true for $P_1, p_2\; and\; p_3$?,<br>

The speed of sound in oxygen $(O_2)$ at a certain temperature is $460 ms^{-1}$. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)