The numbers \(2.745\) and \(2.735\) on rounding off to \(3\) significant figures will give respectively,
1. | \(2.75\) and \(2.74\) | 2. | \(2.74\) and \(2.73\) |
3. | \(2.75\) and \(2.73\) | 4. | \(2.74\) and \(2.74\) |
In a two-dimensional motion, instantaneous speed is a positive constant. Then which of the following is necessarily true?
1. | the average velocity is not zero at any time. |
2. | average acceleration must always vanish. |
3. | displacements in equal time intervals are equal. |
4. | equal path lengths are traversed in equal intervals. |
The horizontal range of a projectile fired at an angle of \(15^\circ\) is \(50\) m. If it is fired with the same speed at an angle of \(45^\circ\), its range will be:
1. \(60\) m
2. \(71\) m
3. \(100\) m
4. \(141\) m
If \(|\vec{A}|=2\) and \(|\vec{B}|=4\), then match the relations in column-I with the angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\) in column-II.
Column-I | Column-II | ||
(a) | \(\vec{A}.\vec{B}=0\) | (i) | \(\theta=0^{\circ}\) |
(b) | \(\vec{A}.\vec{B}=8\) | (ii) | \(\theta=90^{\circ}\) |
(c) | \(\vec{A}.\vec{B}=4\) | (iii) | \(\theta=180^{\circ}\) |
(d) | \(\vec{A}.\vec{B}=-8\) | (iv) | \(\theta=60^{\circ}\) |
Choose the correct answer from the options given below:
1. | (a)–(iii), (b)-(ii), (c)-(i), (d)-(iv) |
2. | (a)–(ii), (b)-(i), (c)-(iv), (d)-(iii) |
3. | (a)–(ii), (b)-(iv), (c)-(iii), (d)-(i) |
4. | (a)–(iii), (b)-(i), (c)-(ii), (d)-(iv) |
A body of mass \(10\) kg is acted upon by two perpendicular forces, \(6\) N and \(8\) N. The resultant acceleration of the body is:
(a) | \(1~\text{ms}^{-2}\) at an angle of \(tan^{-1}\Big(\frac43\Big)\) w.r.t. \(6\) N force |
(b) | \(0.2~\text{ms}^{-2}\) at an angle of \(tan^{-1}\Big(\frac34\Big)\) w.r.t. \(8\) N force |
(c) | \(1~\text{ms}^{-2}\) at an angle of \(tan^{-1}\Big(\frac34\Big)\) w.r.t. \(8\) N force |
(d) | \(0.2~\text{ms}^{-2}\) at an angle of \(tan^{-1}\Big(\frac34\Big)\) w.r.t. \(6\) N force |
Choose the correct option:
1. | (a), (c) |
2. | (b), (c) |
3. | (c), (d) |
4. | (a), (b), (c) |
A body with a mass of \(5\) kg is acted upon by a force \(\vec{F}=\left ( -3\hat{i} +4\hat{j}\right )\) N. If its initial velocity at \(t=0\) is \(\vec{v}=\left ( 6\hat{i} -12\hat{j}\right )\) m/s, the time at which it will just have a velocity along the Y-axis is:
1. never
2. \(10\) s
3. \(2\) s
4. \(15\) s
During an inelastic collision between two bodies, which of the following quantities always remain conserved?
1. | total kinetic energy |
2. | total mechanical energy |
3. | total linear momentum |
4. | speed of each body |
A body is moving unidirectionally under the influence of a source of constant power supplying energy. Which of the diagrams shown in the figure correctly shown the displacement-time curve for its motion?
1. | 2. | ||
3. | 4. |
A body of mass \(0.5\) kg travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\mathrm{m^{-1/2}s^{-1}}\). The work done by the net force during its displacement from \(x=0\) m to \(x=2\) m is:
1. \(15\) J
2. \(50\) J
3. \(10\) J
4. \(100\) J
Which of the following points is the likely position of the center of mass of the system shown in the figure?
1. \(A\)
2. \(B\)
3. \(C\)
4. \(D\)
When a disc rotates with uniform angular velocity, which of the following is not true?
1. | the sense of rotation remains the same. |
2. | the orientation of the axis of rotation remains the same. |
3. | the speed of rotation is non-zero and remains the same. |
4. | the angular acceleration is non-zero and remains the same. |
A uniform cube of mass \(m\) and side \(a\) is placed on a frictionless horizontal surface. A vertical force \(F\) is applied to the edge as shown in the figure. Match the following (most appropriate choice).
List- I | List- II | ||
(a) | \(mg/4<F<mg/2\) | (i) | cube will move up. |
(b) | \(F>mg/2\) | (ii) | cube will not exhibit motion. |
(c) | \(F>mg\) | (iii) | cube will begin to rotate and slip at A. |
(d) | \(F=mg/4\) | (iv) | normal reaction effectively at \(a/3\) from A, no motion. |
1. | a - (i), b - (iv), c - (ii), d - (iii) |
2. | a - (ii), b - (iii), c - (i), d - (iv) |
3. | a - (iii), b - (i), c - (ii), d - (iv) |
4. | a - (i), b - (ii), c - (iv), d - (iii) |
The figure below shows two identical particles 1 and 2, each of mass \(m,\) moving in opposite directions with the same speed \(v\) along parallel lines. At a particular instant, \(r_1\) and \(r_2\) are their respective position vectors drawn from point A, which is in the plane of the parallel lines.
Consider the following statements.
a. | angular momentum \(l_1\) of particle 1 about A is \(l_1=mv(d_1)\) ⊙ |
b. | angular momentum \(l_1\) of particle 2 about A is \(l_1=mv(r_2)\) ⊙ |
c. | total angular momentum of the system about A is \(l=mv(r_1+r_2)\) ⊙ |
d. | total angular momentum of the system about A is \(l=mv(d_2-d_1)\) ⊗ |
Choose the correct option:
1. | (a, c) |
2. | (a, d) |
3. | (b, d) |
4. | (b, c) |
Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the centre of mass causing translation and net torque at the centre of mass causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere):
1. | the torque is zero. |
2. | the torque causes the earth to spin. |
3. | the rigid body result is not applicable since the earth is not even approximately a rigid body. |
4. | the torque causes the earth to move around the sun. |
The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will:
1. | be doubled |
2. | be halved |
3. | be four times |
4. | remain the same |
Pressure is a scalar quantity because:
a. | it is the ratio of force to the area and both force and area are vectors. |
b. | it is the ratio of the magnitude of the force to the area. |
c. | it is the ratio of the component of the force normal to the area. |
d. | it does not depend on the size of the area chosen. |
Choose the correct alterative/s:
1. (b), (c)
2. (a), (d)
3. (b), (d)
4. (c), (d)
The angle of contact at the interface of the water glass is \(0^{\circ},\) ethyl-alcohol glass is \(0^{\circ},\) mercury-glass is \(140^{\circ}\) and methyl iodide-glass is \(30^{\circ}.\) A glass capillary is put in a trough containing one of these four liquids is observed that the meniscus is convex. The liquid in the trough is:
1. water
2. ethyl alcohol
3. mercury
4. methyl iodide
Consider a cycle followed by an engine (figure).
1 to 2 is isothermal,
2 to 3 is adiabatic,
3 to 1 is adiabatic.
Such a process does not exist, because:
a. | heat is completely converted to mechanical energy in such a process, which is not possible. |
b. | In this process, mechanical energy is completely converted to heat, which is not possible. |
c. | curves representing two adiabatic processes don’t intersect. |
d. | curves representing an adiabatic process and an isothermal process don't intersect. |
Choose the correct alternatives:
1. (a, b)
2. (a, c)
3. (b, c)
4. (c, d)
An ideal gas undergoes four different processes from the same initial state (figure). Four processes are adiabatic, isothermal, isobaric and isochoric. Out of \(1,\) \(2,\) \(3\) and \(4,\) which one is adiabatic?
1. | \(4\) | 2. | \(3\) |
3. | \(2\) | 4. | \(1\) |
Consider the \((P-V)\) diagram for an ideal gas shown in the figure.
Out of the following diagrams, which figure represents the \((T-P)\) diagram?
1. | 2. | ||
3. | 4. |
A cubic vessel (with faces horizontal + vertical) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of in the vertical direction. The pressure of the gas inside the vessel as observed by us on the ground:
1. | remains the same because \(500\) \(\mathrm{ms^{-1}}\) is very much smaller than \(v_{rms}\) of the gas. |
2. | remains the same because the motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls. |
3. | will increase by a factor equal to \(\Big(\frac{v_{rms}^2+(500)^2}{v_{rms}^2}\Big)\)where \(v_{rms}^2\) was the original mean square velocity of the gas. |
4. | will be different on the top wall and bottom wall of the vessel. |
The displacement of a particle is represented by the equation y = . The motion is
1. non-periodic
2. periodic but not simple harmonic
3. simple harmonic with period 2
4. simple harmonic with period
The relations between acceleration and displacement of four particles are given below. Which one of the particles is executing simple harmonic motion?
1. \(a_1 = +2x\)
2. \(a_1= +2x^2\)
3. \(a_1= -2x^2\)
4. \(a_1 = -2x\)
The following statements are given for a simple harmonic oscillator.
a. | Force acting is directly proportional to the displacement from the mean position and opposite to it. |
b. | Motion is periodic. |
c. | Acceleration of the oscillator is constant. |
d. | The velocity is periodic. |
Choose the correct alternatives:
1. (a, b, d)
2. (a, c)
3. (b, d)
4. (c, d)
Which of the following diagrams (figure) depicts ideal gas behaviour?
1. (a), (c)
2. (a), (d)
3. (c), (d)
4. (a), (b)
The electric field at a point is:
a. | always continuous |
b. | continuous if there is no charge at that point |
c. | discontinuous only if there is a negative charge at that point |
d. | discontinuous if there is a charge at that point |
1. (a, b)
2. (b, d)
3. (c, d)
4. (a, d)
If \(\int_S E.ds = 0\) over a surface, then:
a. | the electric field inside the surface and on it is zero. |
b. | the electric field inside the surface is necessarily uniform. |
c. | the number of flux lines entering the surface must be equal to the number of flux lines leaving it. |
d. | all charges must necessarily be outside the surface. |
1. (a, c)
2. (b, c)
3. (c, d)
4. (a, d)
Consider a uniform electric field in the \(\mathrm{z}\)-direction. The potential is a constant:
a. | in all space. |
b. | for any \(\mathrm{x}\) for a given \(\mathrm{z}.\) |
c. | for any \(\mathrm{y}\) for a given \(\mathrm{z}.\) |
d. | on the \(\mathrm{x-y}\) plane for a given \(\mathrm{z}.\) |
Choose the correct option:
1. | (c), (d) |
2. | (a), (c) |
3. | (b), (c), (d) |
4. | (a), (b) |
The electrostatic potential on the surface of a charged conducting sphere is \(100~\text{V}\). Two statements are made in this regard.
Statement I: | At any point inside the sphere, electric intensity is zero. |
Statement II: | At any point inside the sphere, the electrostatic potential is \(100~\text{V}\). |
Which of the following is a correct statement?
1. | Statement I is true but Statement II is false. |
2. | Both Statement I and Statement II are false. |
3. | Statement I is true, Statement II is also true and Statement I is the cause of Statement II. |
4. | Statement I is true, Statement II is also true but the statements are independent. |
Consider a current carrying wire (current I) in the shape of a circle. Note that as the current progresses along the wire, the direction of j (current density) changes in an exact manner, while the current I remains unaffected. The agent that is essentially responsible for it is:
1. | source of emf |
2. | the electric field produced by charges accumulated on the surface of the wire |
3. | the charges just behind a given segment of wire which push them just the right way by repulsion |
4. | the charges ahead |
Which of the following characteristics of electrons determines the current in a conductor?
1. Drift velocity alone
2. Thermal velocity alone
3. Both drift velocity and thermal velocity
4. Neither drift nor thermal velocity
Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field B = .
1. They have equal z-components of momenta.
2. They must have equal charges.
3. They necessarily represent a particle-antiparticle pair.
4. The charge to mass ratio satisfy:
Biot-Savart law indicates that the moving electrons (velocity v) produce a magnetic field B such that:
1. | B ⊥ v. |
2. | B || v. |
3. | it obeys inverse cube law. |
4. | it is along the line joining the electron and point of observation. |
1. | The electron will be accelerated along the axis. |
2. | The electron path will be circular about the axis. |
3. | The electron will experience a force at 45° to the axis and hence execute a helical path. |
4. | The electron will continue to move with uniform velocity along the axis of the solenoid. |
If the RMS current in a \(50~\text{Hz}\) AC circuit is \(5~\text{A}\), the value of the current \(\frac{1}{300}~\text{s}\) after its value becomes zero is:
1. \(5\sqrt2~A\)
2. \(5\sqrt{\frac32}~A\)
3. \(\sqrt{\frac56}~A\)
4. \(\frac{5}{\sqrt2}~A\)
When a voltage measuring device is connected to AC mains, the meter shows the steady input voltage of \(220~\text{V}\). This means:
1. | input voltage cannot be AC voltage, but a DC voltage |
2. | maximum input voltage is \(220~\text{V}\) |
3. | the meter reads not v but \(<v^2>\) and is calibrated to read \(\sqrt{<v^2>}\) |
4. | the pointer of the meter is stuck by some mechanical defect |
For light diverging from a point source:
(a) | the wavefront is spherical. |
(b) | the intensity decreases in proportion to the distance squared. |
(c) | the wavefront is parabolic. |
(d) | the intensity at the wavefront does not depend on the distance. |
1. | (a), (b) |
2. | (a), (c) |
3. | (b), (c) |
4. | (c), (d) |
Consider a light beam incident from air to a glass slab at Brewster's angle as shown in the figure. A polaroid is placed in the path of the emergent ray at point \(P\) and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid. Then:
1. | for a particular orientation, there shall be darkness as observed through the polaroid. |
2. | the intensity of light as seen through the polaroid shall be independent of the rotation. |
3. | the intensity of light as seen through the polaroid shall go through a minimum but not zero for two orientations of the polaroid. |
4. | the intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid. |
An electron (mass \(m\)) with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\mathrm{i}}\)
1. | \(\frac{\lambda_0}{\left(1+\frac{e E_0}{m} \frac{t}{\mathrm{v}_0}\right)}\) | 2. | \(\lambda_0\left(1+\frac{e E_0 t}{m \mathrm{v}_0}\right)\) |
3. | \(\lambda_0 \) | 4. | \(\lambda_0t\) |
Photons absorbed in matter are converted to heat. A source emitting n photon/sec of frequency is used to convert 1 kg of ice at to water at . Then, the time T taken for the conversion:
a. | decreases with increasing n, with ν fixed |
b. | decreases with n fixed, ν increasing |
c. | remains constant with n and ν changing such that n ν =constant |
d. | increases when the product n ν increases |
1. (b, d)
2. (a, c, d)
3. (a, d)
4. (a, b, c)
Taking the bohr radius as \(a_0=53\) pm, the radius of Li++ ion in its ground state on the basis of bohr's model will be about:
1. \(153\) pm
2. \(27\) pm
3. \(18\) pm
4. \(13\) pm
Fusion processes, like combining two deuterons to form a \(\mathrm{He}\)-nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact:
(a) | nuclear forces have short-range. |
(b) | nuclei are positively charged. |
(c) | the original nuclei must be completely ionized before fusion can take place. |
(d) | the original nuclei must first break up before combining with each other. |
1. (a), (c)
2. (a), (d)
3. (b), (d)
4. (a), (b)
The Balmer series for the H-atom can be observed:
a. | if we measure the frequencies of light emitted when an excited atom falls to the ground state |
b. | if we measure the frequencies of light emitted due to transitions between excited states and the first excited state |
c. | in any transition in a H-atom |
d. | as a sequence of frequencies with the higher frequencies getting closely packed |
1. (b, c)
2. (a, c)
3. (b, d)
4. (c, d)
Hole is:
1. | an anti-particle of electron. |
2. | a vacancy created when an electron leaves a covalent bond. |
3. | absence of free electrons. |
4. | an artificially created particle. |
In the figure given below, assuming the diodes to be ideal,
1. | D1 is forward biased and D2 is revers-biased and hence current flows from A to B. |
2. | D2 is forward biased and D1 is reverse-biased and hence no current flows from B to A and vice-versa. |
3. | D1 and D2 are both forward-biased and hence current flows from A to B. |
4. | D1 and D2 are both reverse-biased and hence no current flows from A to B and vice-versa. |
What happens during the regulation action of a Zener diode?
1. | the current and voltage across the Zener remain fixed. |
2. | the current through the series Resistance (Rs) changes. |
3. | the Zener resistance is constant. |
4. | the resistance offered by the Zener changes. |
Choose the correct option:
1. | (a, b) |
2. | (b, d) |
3. | (b, c) |
4. | (c, d) |