a) Current is given as I = V/R from the Ohm’s law Therefore, I = 1A But, I = ne Avd vd = I/neA When the values for the above parameters are substituted, vd = 1/1.6 × 10-4 m/s The KE = (KE of one...

### In an experiment with a potentiometer, VB = 10V. R is adjusted to be 50 Ω. A student wanting to measure voltage E1 of a battery finds no null point possible. He then diminishes R to 10 Ω and is able to locate the null point on the last segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.

Equivalent resistance of the potentiometer = 50 Ohm + R’ Equivalent voltage across the potentiometer = 10 V Current through the main circuit I = 10/(50 Ohms +R’) Potential difference across wire of...

### A room has AC run for 5 hours a day at a voltage of 220V. The wiring of the room consists of Cu of 1 mm radius and a length of 10 m. Power consumption per day is 10 commercial units. What fraction of it goes in the joule heating in wires? What would happen if the wiring is made of aluminium of the same dimensions?

Power consumption in a day = 10 units Power consumption per hour = 2 units Power consumption = 2 units = 2 kW = 2000 J/s Power consumption in resistors, P = VI Which gives I = 9A We know that...

### Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively are connected in parallel with the positive end of the 10V battery connected to the negative pole of 2V battery. Find the effective voltage and effective resistance of the combination.

Kirchhoff’s law is applied at c, I1 = I + I2 Kirchhoff’s law is applied at efbae, 10 – IR – 10I2 = 0 10 = IR + 10I1 Kirchhoff’s law is applied at cbadc, -2-IR+5I2 = 0 2 = 5I2- RI I2 = I1 – I...

### Suppose there is a circuit consisting of only resistances and batteries and we have to double all voltages and all resistances. Show that currents are unaltered.

Reff is the equivalent internal resistance of the battery Veff is the equivalent voltage of the battery Using Ohm’s law, I = Veff/(Reff + R) When the resistance and effective voltage are increased...

### Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1 mm. Conductor B is a hollow tube of outer diameter 2 mm and inner diameter 1 mm. Find the ratio of resistance RA to RB.

Resistance of wire R = ρ l/A Where A is the cross-sectional area of the conductor L is the length of the conductor ρ is the specific resistance RA = ρl/π(10-3 × 0.5)2 RB = ρl/ π[10-3)2 × (0.5 ×...

### The circuit in the figure shows two cells connected in opposition to each other. Cell E1 is of emf 6V and internal resistance 2Ω; the cell E2 is of emf 4V and internal resistance 8 Ω. Find the potential difference between the points A and B.

Applying Ohm’s law, equivalent emf of the two cells = 6 – 4 = 2V Equivalent resistance = 2 + 8 = 10 Ω Electric current, I = 6-4/2+8 = 0.2A When the loop is considered in the anti-clockwise...

### Two cells of same emf E but internal resistance r1 and r2 are connected in series to an external resistor R. What should be the value of R so that the potential difference across the terminals of the first cell becomes zero.

Effective emf of two cells = E + E = 2E Effective resistance = R + r1 + r2 Electric current is given as I = 2E/R+r1+r2 Potential difference is given as V1 – E – Ir1 = 0 Which f=gives R = r1 –...

### Let there be n resistors R1……..Rn with Rmax = max(R1……Rn) and Rmin = min(R1…….Rn). Show that when they are connected in parallel, the resultant resistance Rp < Rmin and when they are connected in series, the resultant resistance Rs > Rmax. Interpret the result physically.

The current is represented as I = E/R+nR when the resistors are connected in series. Current is expressed as 10I = E/(R+R/n) when the resistors are connected in parallel....

### . A cell of emf E and internal resistance r is connected across an external resistance R. Plot a graph showing the variation of PD across R versus R.

The graphic depiction is as follows: The resistance r is connected across the external resistance R, and E is the cell's emf. V = ER/R+r is the connection between voltage and R....

### While doing an experiment with potentiometer it was found that the deflection is one-sided and i) the deflection decreased while moving from one end A of the wire to the end B; ii) the deflection increased, while the jockey was moved towards the end B. i) Which terminal +ve or –ve of the cell E, is connected at X in case

i) and how is E1 related to E?

ii) Which terminal of the cell E1 is connected at X in case ii)?

The positive terminal of cell E1 is linked to E, and E is connected to X. Furthermore, E1 > E ii) cell E1's negative terminal is linked to X.

### Power P is to be delivered to a device via transmission cables having resistance Rc. If V is the voltage across R and I the current through it, find the power wasted and how can it be reduced.

P = i2Rc is the power utilised by transmission lines. The resistance of connecting wires is denoted by Rc. P = VI is the formula for calculating power. Power...

### Power P is to be delivered to a device via transmission cables having resistance Rc. If V is the voltage across R and I the current through it, find the power wasted and how can it be reduced.

Power consumed by the transmission lines is given as P = i2Rc. Where Rc is the resistance of connecting cables. Power is given as P = VI. The transmission of power takes places either during low...

### Why are alloys used for making standard resistance coils?

Alloys are used in the making of the standard resistance coils because they have less temperature coefficient of resistance and the temperature sensitivity is also less.

### For wiring in the home, one uses Cu wires or Al wires. What considerations are involved in this?

The main considerations in the selection of the wires is the conductivity of the metal, cost of metal, and their availability.

### What are the advantages of the null-point method in a Wheatstone bridge? What additional measurements would be required to calculate R unknown by any other?

The advantage of a null-point in the Wheatstone bridge is that the resistance of the galvanometer is not affected by the balance point. The R unknown is calculated by using Kirchhoff’s rule.

### The relaxation time τ is nearly independent of applied E field whereas it changes significantly with temperature T. First fact is responsible for Ohm’s law whereas the second fact leads to a variation of ρ with temperature. Elaborate why?

Relaxation time is the time interval between two successive collisions of the electrons.It is defined asτ = mean free path/rms velocity of electrons usually, the drift velocity of the electrons is...

### Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?

The momentum is not conserved when the charge crosses a junction in an electric circuit. This is because the drift velocity is proportional to the electric field.

### In a meter bridge, the point D is a neutral point.

a) the meter bridge can have no other neutral point for this set of resistances

b) when the jockey contacts a point on meter wire left of D, current flows to B from the wire

c) when the jockey contacts a point on a meter wire to the right of D, current flows from B to the wire through the galvanometer

d) when R is increased, the neutral point shifts to left

The correct answer is a) the meter bridge can have no other neutral point for this set of resistances c) when the jockey contacts a point on a meter wire to the right of D, current flows from B to...

### The measurement of an unknown resistance R is to be carried out using Wheatstone bridge. Two students perform an experiment in two ways. The first student take R2 = 10Ω and R1 = 5Ω. The other student takes R2 = 1000 Ω and R1 = 500 Ω. In the standard arm, both take R3 = 5 Ω. Both find R = R2/R1 R3 = 10 Ω within errors.

a) the errors of measurement of the two students are the same

b) errors of measurement do depend on the accuracy with which R2 and R1 can be measured

c) if the student uses large values of R2 and R1, the currents through the arms will be feeble. This will make determination of null point accurately more difficult

d) Wheatstone bridge is a very accurate instrument and has no errors of measurement

The correct answer is b) errors of measurement do depend on the accuracy with which R2 and R1 can be measured c) if the student uses large values of R2 and R1, the currents through the arms will be...

### Temperature dependence of resistivity ρ(T) of semiconductors, insulators, and metals is significantly based on the following factors:

a) number of charge carriers can change with temperature T

b) time interval between two successive collisions can depend on T

c) length of material can be a function of T

d) mass of carriers is a function of T

solution:The correct answer is a) number of charge carriers can change with temperature T b) time interval between two successive collisions can depend on T

### Consider a simple circuit in the figure.stands for a variable resistance R’.

R’ can vary from R0 to infinity. r is internal resistance of the battery,

a) potential drop across AB is nearly constant as R’ is varied

b) current through R’ is nearly a constant as R’ is varied

c) current I depends sensitively on R’

d) I ≥V/r+R always

solution: The correct answer is a) potential drop across AB is nearly constant as R’ is varied d) I ≥V/r+R always

### Kirchhoff’s junction rule is a reflection of

a) conservation of current density vector

b) conservation of charge

c) the fact that the momentum with which a charged particle approaches a junction is unchanged as the charged particle leaves the junction

d) the fact that there is no accumulation of charges at a junction

solution: The correct answer is b) conservation of charge d) the fact that there is no accumulation of charges at a junction

### Which of the following characteristics of electrons determines the current in a conductor?

v a) drift velocity alone

b) thermal velocity alone

c) both drift velocity and thermal velocity

d) neither drift nor thermal velocity

solution: The correct answer is a) drift velocity alone

### A metal rod of length 10 cm and a rectangular cross-section of 1 cm × 1/2 cm is connected to battery across opposite faces. The resistance will be

a) maximum when the battery is connected across 1 cm × 1/2 cm faces

b) maximum when the battery is connected across 10 cm × 1 cm faces

c) maximum when the battery is connected across 10 cm × 1/2 cm faces

d) same irrespective of the three faces

solution:The correct solution is a) maximum when the battery is connected across 1 cm × 1/2 cm faces

### Two cells of emf’s approximately 5V and 10V are to be accurately compared using a potentiometer of length 400 cm.

a) the battery that runs the potentiometer should have voltage of 8V

b) the battery of potentiometer can have a voltage of 15V and R adjusted so that the potential drop across the wire slightly exceeds 10V

c) the first portion of 50 cm of wire itself should have a potential drop of 10V

d) potentiometer is usually used for comparing resistances and not voltages

Solution: The correct solution is b) the potentiometer's battery can be set to 15V and R adjusted so that the potential drop across the wire is a little higher than 10V.

### A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100Ω. He finds the null point at l1 = 2.9 cm . He is told to attempt to improve the accuracy. Which of the following is a useful way?

a) he should measure l1 more accurately

b) he should change S to 1000 Ω and repeat the experiment

c) he should change S to 3 Ω and repeat the experiment

d) he should give up hope of a more accurate measurement with a meter bridge

solution:The correct answer is c) he should change S to 3 Ω and repeat the experiment

### Two batteries of emf ε1 and ε2 and internal resistances r1 and r2 respectively are connected in parallel as shown in the figure.a) the equivalent emf εeq of the two cells is between ε1 and ε2 that is ε1 < εeq < ε2

b) the equivalent emf εeq is smaller than ε1

c) the εeq is given by εeq = ε1 + ε2 always

d) εeq is independent of internal resistances r1 and r2

solution: The correct answer is a) the equivalent emf εeq of the two cells is between ε1 and ε2 that is ε1 < εeq < ε2

### Consider a current-carrying wire in the shape of a circle. Note that as the current progresses along the wire, the direction of j changes in an exact manner, while the current I remain unaffected. The agent that is essentially responsible for is

a) source of emf

b) electric field produced by charges accumulated on the surface of wire

c) the charges just behind a given segment of wire which push them just the right way by repulsion

d) the charges ahead

solution: The correct answer is b) electric field produced by charges accumulated on the surface of wire

### A fix number of spherical drops of a liquid of radius ‘ ‘ coalesce to form a large drop of radius ‘ and volume ‘ . If ‘ is the surface tension then energy

A) is niether released nor absorbed

B) is released.

C) is released.

D) 3 VT is absorbed.

Correct option is B. $\begin{array}{l} \Delta \mathrm{U}=(\mathrm{T})(\Delta \mathrm{A}) \\ \mathrm{A}(\text { initial })=\left(4 \pi \mathrm{r}^{2}\right) \mathrm{n} \\ \mathrm{A}(\text { final...

### A note produces 4 beat/s with a tuning fork of frequency and 6 beat/s with a fork of frequency . The frequency of the note is

A)

B)

C)

D)

Correct option is A. It produces 4 beats/s with a fork of frequency $510 \mathrm{~Hz}$. Hence its frequency can be 514 or $506 \mathrm{~Hz}$. It also produces 6 beats/s with a fork of frequency $512...

### When a beam of unpolarised monochromatic light is incident on a plane glass plate at a polarising angle, then which one of the following statements is correct?

A) Reflected and refracted rays are completely polarised with their planes of polarisation perpendicular to each other.

B) Reflected light is partially polarised but refracted light is plane polarised.

C) Reflected and refracted rays are completely polarised with their planes of polarisation parallel to each other.

D) Reflected light is plane polarised light but transmitted light is partially polarised.

Correct option is D.

### Five capacitors each of capacitance ‘ are connected as shown in the figure. The ratio of equivalent capacitance between and and the equivalent capacitance between and is

A)$2: 3$ B)$1: 1$ C)$3: 1$ D)$5: 2$ Correct option is A. For the both cases the equivalent circuits are shown in figure. For (1) the equivalent capacitance between $\mathrm{P}$ and $\mathrm{R}$ is...

### What is the stopping potential, when a metal surface with work function is illuminated with light of energy ?

A)

B)

C)

D)

Correct option is D. $\begin{array}{l} e V s=E-W_{0} \\ \therefore V_{s}=\frac{E}{e}-\frac{W_{0}}{e}=\frac{3 e}{e}-\frac{1.2 e V}{e}=1.8 V \end{array}$

### A smooth sphere of mass ‘M’ moving with velocity ‘u’ directly collides elastically with another sphere of mass ‘ ‘ at rest. After collision, their final velocities are V’ and respectively. The value of is given by

A)

B)

C)

D)

Correct option is C. Using Newton's law of collision, $\begin{array}{l} \frac{\mathrm{V}-\mathrm{v}}{\mathrm{u}-0}=-\mathrm{e} \\ \frac{\mathrm{V}-\mathrm{v}}{\mathrm{u}-0}=-1 \quad \quad...

### A body performs S.H.M. due to force , with time period . If force is changed to , it executes S.H.M. with time period . Now both the forces act simultaneously in the same direction on the same body. New periodic time is

A)

B)

C)

D)

Correct option is A. $\ln \mathrm{SHM}, F=\frac{4 \pi^{2} m}{T^{2}} y$ or $T^{2} \propto \frac{1}{F}$ or $T \propto \frac{1}{\sqrt{F}}: \operatorname{So} 0.8 \propto \frac{1}{\sqrt{F_{1}}}$ and $0.6...

### An ideal gas occupies a volume ‘ ‘ at a pressure ‘ ‘ and absolute temperature . The mass of each molecule is ‘ ‘. If ‘ is the Boltzmann’s constant, then the density of gas is given by expression

A)

B)

C)

D)

Correct option is D. The ideal gas law is given by $\mathrm{PV}=\mathrm{nRT}$, where $\mathrm{n}$ is the number of moles of a gas. $\mathrm{n}=$ mass of the gas $/$ molecular weight of the gas....

### The depth of an ocean is . The compressibility of water is and density of water is . At the bottom of the ocean, the fractional compression of water will be

A)

B)

C)

D)

Correct option is C. compressibility is given as $\kappa=\frac{\frac{\Delta V}{V}}{\Delta P}$ $\Delta \mathrm{V}=\kappa \times \Delta \mathrm{P} \times \mathrm{V}$ Substituting values $\Delta...

### For an ideal gas, if the ratio of Molar specific heats , then the specific heat at constant pressure , specific heat at constant volume and corresponding molecule are respectively

A), monoatomic.

B), polyatomic.

C), non-rigid diatomic.

D) , rigid diatomic.

Correct option is D. Given, $\gamma=1.4=\frac{7}{5}$ We know, $C_p-C_v=R$ $\gamma=\frac{7}{5}=\frac{C_p}{C_v}$ $\therefore C_p=\frac{7}{5}C_v$ $\frac{7}{5}C_v-C_v=R$ $\frac{2}{5}C_v=R$...

### A uniform wire has length ‘ and weight ‘ . One end of the wire is attached rigidly to a point in the roof and weight ‘ is suspended from its lower end. If ‘ is the cross-sectional area of the wire then the stress in the wire at a height from its lower end is

A)

B)

C)

D)

Correct option is A. $\text { stress }=\frac{\text { Tension }}{\text { Area }}$ Tension at height $\frac{3 \mathrm{~L}}{4}$ from lower end $\text { is } \frac{3}{4} \mathrm{w}+\mathrm{w}_{1}$ So,...

### A small mass ‘ ‘ is suspended at the end of a wire having (negligible mass) length ‘L’ and cross-sectional area ‘ ‘. The frequency of oscillation for the S.H.M. along the vertical line is [ Young’s modulus of material of the wire ]

A)

B)

C)

D)

Correct option is B. Let $F$ be the force applied on the end of wire and $x$ be the extension in the length of wire, then longitudinal strain $=\mathrm{x} / \mathrm{L}$ Normal stress $=$ F/A Young's...

### Pascal’s law is not applied in

A) a hydraulic jack.

B) hydraulic breaks.

C) a hydraulic press.

D) an autuomiser.

Correct option is D.

### A body of mass ‘ is moving along a circle of radius ‘ ‘ with linear speed ‘v’. Now, to change the linear speed to and to move it along the circle of radius ‘ , required change in the centripetal force of the body is

A) decrease by

B) decrease by

C) increase by

D) increase by

Correct answer is A. $\begin{array}{l} F_{1}=\frac{m v^{2}}{r} \\ F_{2}=\frac{m}{4 r} \cdot \frac{v^{2}}{4}=\frac{1}{16} \frac{m v^{2}}{r}=\frac{F_{1}}{16} \\ \therefore...

### In communication with the help of antenna, the range covered (for the line of sight propagation) is initially ‘ ‘. If the height of antenna is doubled, the range covered would become

A)

B)

C)

D)

Correct option is A. Range of antenna $=d \sqrt{2 \mathrm{hr}}, \mathrm{h}=$ height of antenna, $\mathrm{R}=$ radius of earth if $\mathrm{h}$ is doubled i.e., $\mathrm{h}^{\prime}=2 \mathrm{~h}$,...

### The electric field intensity at a point near and outside the surface of a charged conductor of any shape is ‘. The electric field intensity due to uniformly charged infinite thin plane sheet is ‘ ‘. The relation between ‘ and ‘ ‘ is:

A)

B)

C)

D)

Correct option is C. Electric field outside the conductor $\mathrm{E}_{1}=\frac{\sigma}{\epsilon_{0}}$ Electric field due to uniformly charged infinitely thin plate $\mathrm{E}_{2}=\frac{\sigma}{2...

### The relation between force ‘ ‘ and density ‘ ‘ is . The dimensions of are

A)

B)

C)

D)

Correct option is A. $\text { The dimensions of } \mathrm{x} \text { are...

### In suspended type of moving coil galvanometer

A) coil is stationary.

B) magnet is stationary.

C) magnet and coil are stationary.

D) magnet and coil are moving.

Correct option is B.

### A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is then total kinetic energy of the disc is

A)3 J

B)4 J

C)5 J

D)6 J

Correct option is A. Total kinetic energy of the body $\mathrm{K} \cdot \mathrm{E}_{\text {total }}=\left(\frac{1}{2} \mathrm{mv}^{2}\right)_{\text {translational }}+$ $\left(\frac{1}{2}...

### The electron in the hydrogen atom is moving with a speed of in an orbit of radius . The magnetic moment of the revolving electron is

A)

B)

C)

D)

Correct option is D. $\text { Magnetic moment, } \mathrm{m}_{0}=\frac{\text { evr }}{2}$ $=\frac{1.6 \times 10^{-19} \times 2\times 10^{6} \times 0.5 \times 10^{-10}}{2}=8 \times 10^{-24}...

### A mass ‘ ‘ suspended from a spring stretches it by when on the surface of the earth . The mass is then taken on to a height of above earth’s surface and again suspended from the same spring. At this altitude the extension of the spring is (Radius of earth )

A)

B)

C)

D)

Correct option is A. $\begin{array}{l} g=\frac{G M}{r^{2}} \\ \therefore \frac{g^{\prime}}{g}=\frac{r^{2}}{r^{2}} \\ R=6400 \mathrm{~km}, r^{\prime}=6400+1600=8000 \mathrm{~km} \\...

### For a photocell, the work function is ‘ ‘ and the stopping potential is ‘ ‘. The wavelength of the incident radiation is

A)

B)

C)

D)

Correct option is A. $\begin{array}{l} h v=\phi+\frac{1}{2} m v_{\max }^{2} \text { or } \frac{h c}{\lambda}=\phi+e V_{s} \\ \therefore \lambda=\frac{h c}{\phi+e V_{s}} \end{array}$

### The period of oscillation of a mass M suspended from a spring of negligible mass is . If along with it another mass is also suspended, the period of oscillation will now be

A)

B)

C)

D)

Correct option is D$\sqrt{2} \mathrm{~T}$ $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{k}}}, \mathrm{T}^{\prime}=2 \pi \sqrt{\frac{2 \mathrm{M}}{\mathrm{k}}}=\sqrt{2} \mathrm{~T}$

### A Plano convex lens is made of glass of refractive index The of curvature of its convex surface is R. Its focal length:

A)

B)

C)

D)

Correct option is C) ${2} \mathrm{R}$ Given, Radius of curvature, $\mathrm{R}$. Refractive index $=1.5$ Focal length of lens, $f=\frac{\mathrm{R}}{(\mu-1)}=\frac{\mathrm{R}}{(1.5-1)}=2 \mathrm{R}$

### If and are the wavelengths of the first members of the Lyman and Paschen series respectively, then is:

A)

B)

C)

D)

Correct option is D) $7: 108$ For first line of Lyman series, $\begin{array}{l} \mathrm{m}_{1}=1 \text { and }_{\mathrm{n} 2}=3 \\ \therefore...

### A solenoid has core of a material with relative permeability 500 and its windings carry a current of . The number of turns of the solenoid is 500 per metre. The magnetization of the material is nearly.

A)

B)

C)

D)

Correct option is B) $2.5 \times 10^{5} \mathrm{Am}^{-1}$ Here, $\mathrm{n}=500$ turns $/ \mathrm{m}$ $\mathrm{I}=1 \mathrm{~A}, \mu_{\mathrm{r}}=500$ Magnetic intensity, $\mathrm{H}=\mathrm{nI}=500...

### Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by force due to the weight of the water. The surface tension of water is . The inner diameter of the capillary tube is nearly

A)

B)

C)

D)

Correct answer is B. Upwards force due to surface tension, $F_{u}=(2 \pi R) \times T$ where, $2 \pi R \rightarrow$ circumference of tube $F_{u}=(2 \pi R) \times T$ Because surface tension is force...

### When an alternating emf is applied across a capacitor , the graph of capacitive reactance with frequency ( ) of the source of alternating signal is

Correct answer is B.

### A proton moving in perpendicular magnetic field possess energy ‘ ‘. The magnetic field is increased four times. But the proton is constrained to move in the path of same radius. The kinetic energy will increase

A) 16 times.

B) 8 times.

C) 2 times.

D) 4 times.

Correct option is A. Radius, $\begin{aligned} R &=\frac{m v}{9 B}=\frac{\sqrt{m} \sqrt{m} v^{2}}{9 B} \\ &=\frac{\sqrt{m} \sqrt{E}}{9 B} \end{aligned}$ if $B \rightarrow 4 B$....

### The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is ‘I’. It is rotating with angular velocity Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss is kinetic energy is

A)

B)

C)

D)

Correct option is B $\frac{\mathrm{I} \omega^{2}}{4}$ Initial angular momentum, $\mathrm{L}_{1}=\mathrm{I} \omega$ $\mathrm{K}_{1}=\frac{1}{2} \mathrm{I} \omega^{2}$ When, second ring is put on it...

### A force acts on a particle in direction, where is in meters. Find the work done by this force during a displacement from to .

A)

B)

C)

D)

Correct option is D. Force $\mathrm{F}=10+0.5 \mathrm{x}$ Work done $\mathrm{W}=\int \mathrm{F} \mathrm{dx}$ $\begin{array}{l} \mathrm{W}=\int_{0}^{2}(10+0.5 \mathrm{x}) \mathrm{dx} \\...

### The effective length of a magnet is and its pole strength is . The magnetic moment, if it is bent in the form of a semicircle is

A)

B)

C)

D)

Correct option is C $0.16$ The effective length of magnet $=31.4 \mathrm{~cm}$ Pole strength $\mathrm{m}=0.8 \mathrm{Am}$ Length of semi-circle $=\pi \frac{\mathrm{D}}{2}=1$ where, $\mathrm{D}=$...

### A particle of mass is rotating in a plane in circular path of radius . Its angular momentum is . The centripetal force acting on the particle is.

A)

B)

C)

D)

Correct option is D) $\frac{\mathrm{L}^{2}}{\mathrm{mr}^{3}}$ Centripetal force, $F=\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{\mathrm{m}}{\mathrm{r}} \frac{\mathrm{L}^{2}}{\mathrm{~m}^{2}...

### The mutual inductance between two planar concentric rings of radii and with placed in air is given by

A)

B)

C)

D)

The correct option is $\mathbf{A}$$\frac{\mu_{0} \pi r_{2}^{2}}{2 r_{1}}$ Magnetic field due to the larger coil at its centre is $B=\frac{\mu_{0} I}{2 r_{1}}$ where $\mathrm{I}$ is the current in...

### A resistance wire connected in the left gap of a metre bridge balances a resistance in the right gap at a point which divides the bridge wire in the ratio . If the length of the resistance wire is , then the length of of the resistance wire is:

(1)

(2)

(3)

(4)

Correct option: (4) Explanation: Using the given ratio of wire, we have, $x \times 2 \lambda^{3}=10 \times 3 \lambda$ $x=15 \Omega$ $\therefore 15 \Omega \rightarrow 1.5 m$ $\therefore 1 \Omega...

### The increase in the width of the depletion region in a p-n junction diode is due to:

(1) both forward bias and reverse bias

(2) increase in forward current

(3) forward bias only

(4) reverse bias only

Correct option: (4) Explanation: The absence of electrons and holes in the depletion region causes the region's width to increase. This only happens in the case of reverse bias in a diode.

### In Young’s double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes :

(1) four times

(2) one-fourth

(3) double

(4) half

Correct option: (1) Explanation: In YDSE, the fringewidth is given by $\beta=\frac{\lambda D}{d} \quad \beta^{\prime}=\frac{\lambda 2 D}{d / 2}=4 \beta$

### A ray is incident at an angle of incidence i on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is , then the angle of incidence is nearly equal to:

(1)

(2)

(3)

(4)

Correct option: (1) Explanation: As we know, $1 \sin i=\mu . \sin A$ For small angle approximation $\sin \theta=\theta$ $i=\mu A$

### A capacitor is connected to a ac supply. The rms value of the current in the circuit is, nearly:

(1)

(2)

(3)

(4)

Correct option: (1) Explanation: As we know, $I_{r m s}=\frac{V_{r m s}}{Z}=\frac{200}{X_{C}}=200.2 \pi f . C$ Calculating the value by substituting the value, $=200 \times 2 \times 3.14 \times 50...

### The solids which have the negative temperature coefficient of resistance are :

(1) semiconductors only

(2) insulators and semiconductors

(3) metals

(4) insulators only

Correct option: (2) Insulators have a negative temperature coefficient because their resistance decreases as the temperature rises. As the temperature rises, the semiconductor material's resistivity...

### A charged particle having drift velocity of in an electric field of has a mobility in of :

(1)

(2)

(3)

(4)

Correct option: (4) As we know that, $v _{ d }=\mu E \Rightarrow \mu=\frac{ V _{ d }}{ E }$ Calculating, $=\frac{7.5 \times 10^{-4}}{3 \times 10^{-10}}$ $\mu=2.5 \times 10^{6}$ $(\mu=$ mobility...

### The capacitance of a parallel plate capacitor with air as medium is . With the introduction of a dielectric medium, the capacitance becomes . The permittivity of the medium is :

(1)

(2)

(3)

(4)

Correct option: (1) Explanation: Given: $C_{\text {air }}=6 \mu F , C_{\text {medium }}=30 \mu F$ As we know, $C_{\text {air }}=\frac{\varepsilon_{0} A}{d}, C_{\text {medium }}=\frac{\varepsilon_{0}...

### An iron rod of susceptibility 599 is subjected to a magnetising field of The permeability of the material of the rod is : )

(1)

(2)

(3)

(4)

Correct option (3) Explanation: Given: $x _{ m }=599, \mu_{0}=4 \pi \times 10^{-7}$ $H =1200 A / m , \mu=?$ As we know, $\mu=\mu_{0}\left(1+ x _{ m }\right)$ Now, $=4 \pi \times 10^{-7}(1+599)$ $=4...

### Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is :

(1) isochoric

(2) isobaric

(3) isothermal

(4) adiabatic

Correct option (4) When cock is removed, dQ = 0 for the thermally insulated system. Because dw = 0 in vacuum Walls that are thermally insulated du + dw = dQ So du also a zero.

### When a ray of light is incident normally on one refracting surface of an equilateral prism of refractive index 1.5, the emerging ray

A) just grazes the second refracting surface.

B) is deviated by .

C) is deviated by .

D) undergoes total internal reflection at second refracting surface.

Correct answer is D. Critical angle for the material of prism $C=\sin ^{-1}\left(\frac{1}{\mu}\right)$ $=\sin ^{-1}=42^{\circ}$ since angle of incidence at surface $A B\left(60^{\circ}\right)$ is...

### For the following combination of logic gates, when all the three inputs are first high and then low, the output ‘ ‘ will respectively be

A) 1,0

B) 0,0

C) 1,1

D) 0,1

Solution: Correct option is A. Here the gate $P$ is a logic symbol of AND gate and $Q$ is a NAND gate. So, the output of $P$ is $Y_{p}=A . B$ and the output of $Q$ is...

### In potentiometer experiment, the potential gradient can be increased by

A. increasing the cross-sectional area of the potentiometer wire.

B. using a wire of material of low specific resistance.

C. decreasing the cross-sectional area of the potentiometer wire.

D. decreasing the current through it.

Correct answer is C.

### When a resistance ‘ is connected across the terminal of a cell of e.m.f. ‘ ‘ the current is ‘ ‘. When the resistance is changed to ‘ the current is ‘ ‘. The internal resistance of the cell is

A.

B.

C.

D.

Correct answer is C. $\begin{array}{l} I_{1}=\frac{E}{r+R_{1}} \\ I_{2}=\frac{E}{r+R_{2}} \\ \frac{I_{1}}{I_{2}}=\frac{r+R_{2}}{r+R_{1}} \\ I_{1} r+I_{1} R_{1}=I_{2} r+I_{2} R_{2} \\...

### The dimensions of angular momentum are

A.

B.

C.

D.

Correct answer is A.

### Work done by the force on the body is the measure of the change in its

A. momentum.

B. mass.

C. potential energy.

D. kinetic energy.

Correct answer is D.

### A wire suspended vertically is stretched by , when mass of is attached to the lower end. Energy gained by the wire is (Take )

A.

B.

C.

D.

Correct answer is B

### Three vessels A, B, C of different shapes have same base area and are filled with water up to same height ‘ ‘. The respective forces exerted by water on the bases are ‘ and respective weights are . Then

A.

B.

C.

D.

Correct answer is B.

### In case of Light Emitting Diode (LED) light is emitted due to A. recombination of holes and electrons.

B. emission of holes and electrons.

C. diffusion of holes.

D. drifting of electrons

Correct answer is A.

### The sequence of harmonics of a pipe open at one end and closed at the other end is and . The resonating length of the air column in its fundamental mode will be (velocity of sound in air

A.

B.

C.

D.

Correct answer is C. $\begin{array}{l} 2 n=n_{2}-n_{1} \\ =350-250=100 \\ n=\frac{100}{2}=50 H z \\ n=\frac{v}{4 l_{0}}=\frac{340}{4 \times l_{0}} \\ \therefore l=\frac{340}{4 \times...

### The ratio of magnetization and magnetic intensity is called

A. permeability

B. magnetic induction

C. magnetic susceptibility

D. gyromagnetic ratio

Correct answer is C.

### The ratio of magnetic induction along the axis to magnetic induction along the equator of a bar magnet for a point at the same distance from the centre of magnet is

A.

B.

C.

D.

Correct answer is B. Magnetic induction at axial point $=\overrightarrow{\mathrm{B}}$ axial $=\frac{\mu \circ}{4 \pi} \frac{2 \overrightarrow{\mathrm{m}}}{\mathrm{r}^{3}}$ Magnetic induction at...

### A metal surface ejects electrons when irradiated by blue light, but not when irradiated by green light. The electrons will also be ejected by the surface, when irradiated by

A. red light

B. voilet light

C. orange light

D. yellow light

Correct answer is B.

### Two long, straight wires are set parallel to each other. Both the wires carry a current ‘I’ in opposite directions and separation between them is ‘ ‘. The magnetic induction at the midway between them is permeability of free space)

A. Zero

B.

C.

D.

Correct answer is A. $\begin{array}{l} \mathrm{x}=\frac{\mathrm{r}}{2} \\ \mathrm{~B}_{1}=-\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{x}} \\ \mathrm{B}_{2}=\frac{\mu_{0} \mathrm{i}}{2...

### The component of the vector along the direction of is

A.

B.

C.

D.

Correct answer is C.

### A charged capacitor has charge ‘ ‘ at potential ‘. The charge on capacitor is increased to ‘ ‘ so that its potential increases to , then the difference between final and initial energy stored in capacitor is

A.

B.

C.

D.

Correct answer is B.

### In the formula for high resolving power microscope, the numerical aperture of the object of the microscope is given as refractive index of oil and angle made by the object at the aperture = )

A.

B.

C.

D.

Correct answer is D.

### Bending of beam can be reduced by using

A. a material with large value of Young’s modulus.

B. small value of the depth of the bar

C. large value of the length of the beam.

D. small value of the breadth of the bar

Correct answer is A.

### ‘M’ weight is suspended from a weightless spring and it has period ‘ . If now ‘ weight is suspended from the same spring, the new period will be

A.

B.

C.

D.

Correct answer is B. $\begin{array}{l} \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}} \\ \mathrm{T}_{1}=\mathrm{T} \\ \mathrm{m}_{1}=1 \mathrm{~kg} \\ \mathrm{~m}_{2}=4 \mathrm{~kg} \\...

### A conical pendulum has bob of mass of and a length of . If the horizontal circle traced by the bob has a diameter of , then the tension in the string would be nearly

A.

B.

C.

D.

Correct answer is D.

### In Biprism experiment the distance between the two virtual images of the slits in the magnified and diminished position are and respectively. The distance between two coherent sources is

A.

B.

C.

D.

Correct answer is C. When, 1) magnified, distance between images, $\mathrm{d}_{1}=2.4$ 2) dimnished, distance between images, $\mathrm{d}_{2}=0.6$ $\therefore$ Distance between virtual sources...

### Half-lives of two radioactive elements A and B are 20 minute and 40 minute respectively. Initially the samples have equal nuclei. After 80 minute, the ratio of decayed number of A and B nuclei will be

A.

B.

C.

D.

Correct answer is B. $\begin{array}{l} \mathrm{n}=\mathrm{n}_{0} \mathrm{e}^{-\alpha t} \\ \alpha_{\mathrm{A}}=\ln 2 / 20 \\ \alpha_{\mathrm{B}}=\ln 2 / 40 \end{array}$ After 80 min, remaining...

### The S.I. unit of impulse is the same as that of

A. linear velocity.

B. angular velocity.

C. linear momentum.

D. angular momentum.

Correct answer is C.

### Dimensions of magnetic intensity are

A.

B.

C.

D.

Correct answer is A.

### Two vibrating tuning forks produce waves which are represented by and . The number of beats produced per minute by these two waves is

A. 60

B. 180

C. 360

D. 3

Correct answer is B. $\begin{array}{l} \mathrm{Y}_{1}=4 \sin (500 \pi \mathrm{t}) \\ \mathrm{Y}_{2}=2 \sin (506 \pi \mathrm{t}) \\ \mathrm{f}_{1}=\frac{\omega_{1}}{2 \pi}=\frac{500 \pi}{2 \pi}=250...

### The innermost orbit of the hydrogen atom has a diameter of , the diameter of the tenth orbit is

A.

B.

C.

D.

Correct answer is C. Radius of an atom is directly proportional to $n^{2}$ and radius of $n$th orbit which is equal to radius of first orbit multiplied by $n^{2}$ So that will give you. Diameter of...

### A sonometer wire of length ‘ ‘ is in unison with a tuning fork of frequency’n’. When the vibrating length of the wire is reduced to ‘ ‘, it produces ‘ ‘ beats per second with the fork. The frequency of the fork is

A.

B.

C.

D.

Correct answer is D. For the length $L_{1}, n_{1}=\frac{1}{2 L_{1}} \sqrt{\frac{T}{m}}=n \ldots(1)$ where $m=$ mass per unit length For the length $L_{2}, n_{2}=\frac{1}{2 L_{2}} \sqrt{\frac{T}{m}}...

### Which of the following statements is NOT true for a particle moving in circle with a constant angular speed?

A. The radial acceleration vector is tangent to the circle.

B. The linear velocity vector is tangent to the circle.

C. The radial acceleration vector points towards the centre of the circle.

D. The linear velocity and radial acceleration vectors at a point are perpendicular to each other.

Correct answer is A.

### A particle performs simple harmonic motion from mean position, with period . The distance travelled by it between 1 st and 2 nd second of its motion is (A = amplitude of S. H. M.)

A.

B.

C.

D.

Correct answer is C. In $2 \mathrm{~s}$ (which is equal to $\frac{T}{4}$ ), one amplitude will be convered. In $1 \mathrm{st}$ second $x=a \sin \left(\frac{\pi}{4}\right)=\frac{a}{\sqrt{2}}$...

### A capillary tube is dipped in water, the water rises in it to a height ‘h’. If ‘ ‘ is the radius of bore of tube then

A.

B.

C.

D.

Correct answer is B. We have, $\mathrm{h}=\frac{2 \sigma \cos \theta}{\mathrm{r} \rho \mathrm{g}}$ $\Rightarrow \mathrm{h} \cdot \mathrm{r}=$ constant

### When an npn transistor is used as an amplifier

A. electrons move from base to collector.

B. holes move from emitter to base.

C. electrons move from collector to base,

D. holes move from base to collector.

Correct answer is A.

### A charge ‘ ‘ is enclosed by a Gaussian spherical surface of radius ‘R’. If, now, radius of the spherical surface is doubled the outward electric flux will

A. doubled

B. remain same

C. increase four times

D. reduce to half

Correct answer is B. Method 1: Using Number of Field Lines - We know that, Electric flux is proportional to number of field lines. - Form figure, we see that the number of field lines crossing both...

### The rate of cooling of a body is when the body is at above the temperature of surroundings. When the body is at above the temperature of surroundings, its rate of cooling will be

A.

B.

C.

D.

Correct answer is C. Rate of cooling $\frac{\mathrm{dT}}{\mathrm{dt}}=-\frac{\mathrm{k}}{\mathrm{ms}}\left(\mathrm{T}-\mathrm{T}_{\mathrm{s}}\right)$ Or $2=\frac{-\mathrm{k}}{\mathrm{ms}}(50)$ Or...

### The mass and radius of earth is , and , respectively and that of moon is and respectively. The distance between the centre of earth and that of moon is ‘D’ . The minimum speed required for a body (mass ‘m’) to project from a point midway between their centres to escape to infinity is

A.

B.

C.

D.

Correct answer is C. From conservation of energy, since the velocity will be o at infinity, $\frac{1}{2} \mathrm{mv}^{2}-\frac{\mathrm{GmM}_{e}}{\mathrm{~d} / 2}-\frac{\mathrm{GmM}_{d}}{\mathrm{~d}...

### The magnitude of the induced e.m.f. produced in the coil when a magnet is inserted into it does ‘NOT’ depend upon the

A. speed of approach of the magnet.

B. magnetic moment of the magnet.

C. number of turns of the coil.

D. resistance of the coil.

Correct answer is D.

### From the position of smaller angular displacement , the bob of simple pendulum of length ‘L’ is released then its linear displacement at time ‘t’ is

A.

B.

C.

D.

Correct answer is B $\begin{array}{l} x=1 \cos w t \\ =1 \sqrt{\frac{g}{L}} t \cos \theta \end{array}$

### In a cyclotron the time required by positive ion to traverse semicircle does NOT depend upon

A. mass of the particle.

B. velocity of the particle.

C. strength of magnetic field.

D. charge of the particle.

Correct answer is C.

### A point source is placed in air. The spherical wavefront has radius ‘ ‘ after time ‘t’. If the same point source is placed in the medium of refractive index ‘ ‘, the radius of spherical wavefront in the medium in same time is

A.

B.

C.

D.

Correct answer is A. Here Velocity of wave front $=\frac{R_{9}}{t}$ $\begin{array}{l} u=-1 \\ \frac{e}{R a / t}=1 \\ e=R a / t \end{array}$ in the meduim $u$ $\text { velochy }=R \frac{a}{t}$ so,...

### If angular momentum of a rotating body about a fixed axis is increased by , its rotational kinetic energy will be increased by

A.

B.

C.

D.

Correct answer is B. Given, $\frac{\Delta \mathrm{L}}{\mathrm{L}}=10 \%$ The expression for the rotational kinetic energy in terms of angular momentum, $\mathrm{K}=\frac{\mathrm{L}^{2}}{2...

### When an a.c. source is connected across a pure inductor of self inductance (L) then e.m.f. induced in it

A. Leads the current by phase

B. Lags behind the current by phase

C. Lags behind the current by phase

D. Leads the current by phase

Correct answer is A.

### Acceleration due to gravity at height ‘h’ above the surface of the earth is Radius of the earth)

A.

B.

C.

D.

Correct option is C. let we consider, radius of earth $\mathrm{R}$ and mass is $\mathrm{M}$ and we know that acceleration due to gravity at surface G is universal gravitational constant. consider, a...

### The excess of pressure inside a soap bubble is twice the excess of pressure inside another soap bubble. The volume of first bubble is ‘n’ times the volume of second bubble. The value of ‘ ‘ must be

A.

B.

C.

D.

Correct answer is A. Given, $\frac{4 \mathrm{~T}}{\mathrm{r}_{1}}=2 \times \frac{4 \mathrm{~T}}{\mathrm{r}_{2}}$ or $\mathrm{r}_{2}=2 \mathrm{r}_{1}$ $\frac{4}{3} \pi \mathrm{r}_{1}^{3}=\mathrm{n}...

### If the telecast is to cover a range of , the height of tower should be (Radius of earth, )

A.

B.

C.

D.

Correct answer is C. Here, Range $=d=64 \mathrm{~km}$, height $=\mathrm{h}$ and radius of earth $=$ $r=6400 \mathrm{~km}$. $\begin{array}{l} \text { Now }, d=\sqrt{2 h R} \\ \Rightarrow...

### If two non-zero vectors and are perpendicular to each other then the magnitude of their vector product is ,

A.

B.

C.

D.

Correct answer is B. Vector product is calculated as, $\vec{P}\times\vec{Q}=PQsin90^{\circ}$ $\vec{P}\times\vec{Q}=PQ$

### A wall is hit elastically and normally by ‘ ‘ balls per second. If ‘ ‘ is the mass and ‘u’ is velocity for each molecule, the force exerted by the balls on the wall is

A.

B.

C.

D.

Correct answer is A. Since the ball rebounds with same speed but in opposite direction. So, change in linear momentum of one ball $\Delta...

### A solid sphere is rolling down a frictionless surface with translational velocity . It climbs the inclined plane from ‘A’ to ‘ and then moves away from ‘ on the smooth horizontal surface. The value of should be

A.

B.

C.

D.

Correct answer is B. Applying law of conservation of energy for rotating body, $\begin{array}{l} \frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2} \mathrm{I} \omega^{2}=\mathrm{mgh} \\ \frac{1}{2}...

### If the errors involved in the measurements of a side and mass of a cube are and respectively, what is the maximum permissible error in the density of the material ?

A.

B.

C.

D.

Correct answer is D. Density $\rho=\frac{M}{V}=\frac{M}{L^{3}}$ The percentage error in density is given by, $\begin{array}{l} \frac{\Delta \rho}{\rho} \times 100=\frac{\Delta M}{M} \times 100-3...

### Glass has refractive index and water has refractive index If the speed of light in glass is , then the speed of light in water will be

A.

B.

C.

D.

Correct answer is B. $\begin{array}{l} \quad \mathrm{v}_{\text {water }}=\frac{\mathrm{c}}{\mathrm{n}_{\text {water }}} \\ \therefore \quad \mathrm{v}_{\mathrm{water}}=\frac{3 \times 10^{8}}{(4 /...

### A transverse wave is travelling on a string with velocity ‘ The extension in the string is ‘ . If the string is extended by , then the speed of wave along the string will be nearly (Hooke’s law is obeyed)

A.

B.

C. D.

Correct option is A. $\begin{array}{l} v=\sqrt{\frac{T}{m}} \\ \therefore \frac{\mathrm{V}_{2}}{\mathrm{~V}_{1}}=\sqrt{\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}} \\ =\sqrt{1.5} \approx 1.22...

### A galvanometer of resistance is connected to a battery of with a resistance of in series. The deflection obtained is 30 divisions. To reduce this deflection by 10 divisions the additional resistance required to be connected in series is

A.

B.

C.

D.

Correct option is C. Total resistance in the circuit is $R=1900+100=2000 \Omega$ $\therefore$ Current $I_{1}=\frac{2}{2000}=10^{-3} A$ The deflection is decreased from 30 to 20 divisions $\therefore...

### Which one of the following is NOT correct?

A. A real, inverted and same size image can be obtained by using concave mirror

B. A real, inverted and same size image can be obtained by using convex mirror

C. the size of the image formed by convex mirror is always smaller than size of the object

D. A virtual, erect, magnified image can be obtained by using concave mirror.

The wrong option is (B).

### When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the photocurrent is When the surface is illuminated by monochromatic light of frequency , the stopping potential is . the threshold frequency for photoelectric emission is:

(A)

(B)

(C)

(D)

Correct option is (A) $\frac{3 \mathrm{v}}{2}$ $\begin{array}{l} \mathrm{hv}=\mathrm{W}+\frac{\mathrm{v}_{0}}{2} \mathrm{e} \\ \frac{\mathrm{h} v}{2}=\mathrm{W}+\mathrm{v}_{0} \mathrm{e}...

### The schematic symbol of light emitting diode is (LED)

Solution: The correct Answer is B.

### In balanced metre bridge, the resistance of bridge wire is . Unknown resistance ‘ ‘ is connected in left gap and in right gap, null point divides the wire in the ratio . Find the current drawn from the battery of having negligible resistance.

A)

B)

C)

D)

Answer is (A) $\frac{\ell_{1}}{\ell_{2}}=\frac{2}{3}=\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}$ Now $\quad \mathrm{v}_{1}+\mathrm{v}_{2}=\mathrm{v}=5 \mathrm{~V} \quad \mathrm{QV}=\mathrm{IR}$ For...

### The magnetic field (B) inside a long solenoid having ‘n’, turns per unit length and carrying current ‘I’ when iron core is kept in it is permeability of vacuum, magnetic susceptibility)

A)

B)

C)

D)

Answer is (D) $\mathrm{B}=\mu_{0} \mathrm{ni}(1+\chi)$

### When an electron in Hydrogen atom revolves in stationary orbit, it

A) does not radiate light though its velocity changes

B) does not radiate light and velocity remains unchanged

C) radiates light but its velocity is unchanged

D) radiates light with the change of energy

Answer is (A) For an electron revolving in stationary orbits it doesn't radiate light through is velocity change.

### Two particles and having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘ ‘ and ‘ ‘ respectively. The ratio of the mass of to that of is

A)

B)

C)

D)

Answer is (A) The force acting on the particle inside magnetic field is $F_{B}=q v B \sin \theta$ This provides the necessary centripetal force $F_{c}=\frac{m v^{2}}{r}$ $\begin{array}{l} \therefore...

### From Brewster’s law, except for polished metallic surfaces, the polarising angle

A) depends on wavelength and is different for different colours

B) independent of wavelength and is different for different colours

C) independent of wavelength and is same for different colours

D) depends on wavelength and is same for different colours

Answer is (A) According to Brewster's law, polarizing angle depends on wavelength and is different for different colors.

### When light of wavelength ‘ ‘ is incident on photosensitive surface, the stopping potential is ‘ ‘. When light of wavelength ‘ ‘ is incident on same surface, the stopping potential is . Threshold wavelength for the surface is

A)

B)

C)

D)

Answer is (D) Using $\frac{\mathrm{hc}}{\lambda}-\phi=\mathrm{eV}$ When, wavelength $\lambda$ is incident on metallic surface, the stopping potential required to stop most energetic electron is...

### Resolving power of telescope increases when

A) wavelength of light decreases

B) wavelength of light increases

C) focal length of eye-piece increases

D) focal length of eye-piece decreases

Answer is (A) Resolving power of telescope is given by $\mathrm{P}=\frac{\mathrm{d}}{1.22 \lambda}$ When $\lambda$ decreases, resolving power decreases and vice versa

### Magnetic flux passing through a coil is initially It reduces to of its Loriginal value in ‘t’ second. If the e.m.f. induced is then ‘t’ in second is

A)

B)

C)

D)

Answer is (C) $\begin{array}{l} \phi_{1}=4 \times 10^{-4} \mathrm{wb} \text { and } \phi_{2}=0.1 \times \phi_{1}=4 \times 10^{-5} \mathrm{wb} \\ \omega=0.72 \mathrm{~Hz} \\ \therefore \quad...

### The amount of work done in increasing the voltage across the plates of capacitor from to is ‘ ‘. The work done in increasing it from to will be

A)

B)

C)

D)

Answer is (D) The work done in increasing the potential is given by $\mathrm{W}=\mathrm{d} \mathrm{U} \propto\left(\mathrm{V}_{2}^{2}-\mathrm{V}_{1}^{2}\right)$ $\therefore...

### Two coherent sources ‘P’ and ‘Q’ produce interference at point ‘A’ on the screen where there is a dark band which is formed between bright band and bright band. Wavelength of light used is . The path difference between PA and QA is

A)

B)

C)

D)

Answer is (B) Here $\Delta \mathrm{x}=\frac{\lambda \delta}{2 \pi}$ For $n=4^{\text {th }}$ dark bone $\delta=(2 n+1) \pi \Rightarrow \delta=(8+1) \pi=9 \pi$ $\begin{array}{l} \Delta x=\frac{\lambda...

### A galvanometer of resistance is connected to a battery of emf with resistance in series. A full scale deflection of 20 divisions is obtained in the galvanometer. To reduce the deflection to 10 divisions, the resistance in series required is

A)

B)

C)

D)

Answer is (C) $\mathrm{i}=\frac{\mathrm{V}}{\mathrm{R}_{\mathrm{eff}}}=\frac{\mathrm{V}}{1790+30}=\frac{2}{2000}=1 \times 10^{-3} \mathrm{~A}=1 \mathrm{~mA}$ This current provides full scale...

### The LC parallel resonant circuit

A) has a very high impedance B) has a very high current

C) acts as resistance of very low value

D) has zero impedance

Answer is (A) LC parallel resonant circuit has very high impedance.

### Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. ‘V’. If one of the capacitor is completely filled with dielectric material of constant ‘ ‘, then potential difference of the other capacitor will become

A)

B)

C)

D)

Answer is (B) When capacitors are connected is series $C_{e q}=\frac{C_{1} C_{2}}{C_{1}+C_{2}}$ and the potential areas plates of capacitors is given by $\mathrm{V}=\frac{\mathrm{Q}}{\mathrm{C}}$ If...

### In Bohr’s theory of Hydrogen atom, the electron jumps from higher orbit ‘ ‘ to lower orbit, ‘p’. The wavelength will be minimum for the transition

A) to

B) to

C) to

D) to

Answer is (A) According to Bohr's theory the wavelength of radiation emitted is given by $\frac{1}{\lambda}=R\left(\frac{1}{\mathrm{ne}^{2}}-\frac{1}{\mathrm{ne}^{2}}\right)$ For $n_{i}=5$ and...

### The maximum frequency of transmitted radio waves above which the radio waves are no longer reflected back by ionosphere is – maximum electron density of ionosphere, acceleration due to gravity)

A)

B)

C)

D)

Answer is (C) For ionosphere, the maximum frequency of radio waves that can be reflected back is given by $g \sqrt{N}$. Where $N$ is maximum electron density of ionosphere and $g$ is acceleration...

### A ray of light travelling through rarer medium is incident at very small angle ‘i’ on a glass slab and after refraction its velocity is reduced by . The angle of deviation is

A)

B)

C)

D)

Answer is (B) As at interface, velocity of light reduces by $20 \%$ of $\mathrm{C}$ $\therefore \quad \delta=20 \% \mathrm{i}=\frac{20}{100} \times \mathrm{i}=\frac{\mathrm{i}}{5}$

### Light of wavelength ‘ ‘ which is less than threshold wavelength is incident on a photosensitive material. If incident wavelength is decreased so that emitted photoelectrons are moving with same velocity then stopping potential will

A) increase

B) decrease

C) be zero

D) become exactly half

Answer is (A) According to photoelectric equation, $\frac{\mathrm{hc}}{\lambda}-\phi=\mathrm{E} \quad$ where $\mathrm{E}=\frac{\mathrm{p}^{2}}{2 \mathrm{~m}}(\mathrm{~K} . \mathrm{E})$ If $E$ is...

### In an oscillator, for sustained oscillations, Barkhausen criterion is equal to voltage gain without feedback, feedback factor )

A) zero

B)

C) 1

D) 2

Answer is (A) For sustained oscillations according to Barkhausen criteria. $A \cdot \beta=1$

### Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area and the separation between the plates is ‘ ‘, ‘ ‘ and ‘ 3 d’ respectively. The equivalent capacity of combination is absolute permittivity of free space)

A)

B)

C)

D)

Answer is (B) $\mathrm{C}=\mathrm{QV} \quad$ and $\mathrm{C}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}$ As given $\mathrm{C}_{1}=\frac{\varepsilon_{0} \cdot \mathrm{A}}{3 \mathrm{~d}} ; \quad...

### Interference fringes are produced on a screen by using two light sources of intensities ‘I’ and ‘9I’. The phase difference between the beams is at point and at point on the screen. The difference between the resultant intensities at point and is

A)

B)

C)

D)

Answer is (C) At point $\mathrm{P}$, resultant intensity of interfering wave is $\left(\mathrm{I}_{\mathrm{p}}\right)_{\mathrm{res}}=\mathrm{I}_{1}+\mathrm{I}_{2}+2 \sqrt{\mathrm{I}_{1}...

### An electron of mass ‘ ‘ has de-Broglie wavelength ‘ ‘ when accelerated through potential difference ‘ When proton of mass ‘ ‘, is accelerated through potential difference ‘ ‘, the de-Broglie wavelength associated with it will be (Assume that wavelength is determined at low voltage)

A) B)

C)

D)

Answer is (C) When electron or any charged particle is accelerated through potential difference $v$, then kinetic energy gained is given by $E=e V$ $\begin{array}{l} E=\frac{1}{2} m...

### Alternating current of peak value ampere flows through the primary coil of the transformer. The coefficient of mutual inductance between primary and secondary coil is 1 henry. The peak e.m.f. induced in secondary coil is (Frequency of a.c. )

A)

B)

C)

D)

Answer is (B) Peak value of current $I_{0}=1_{\operatorname{nms}} \times\sqrt{2}=\left(\frac{2}{\pi}\right)$ Amp Co-efficient of mutual inductance is $M=1$ horn Induced emf in secondary is given by...

### An iron rod is placed parallel to magnetic field of intensity . The magnetic flux through the rod is and its cross-sectional area is . The magnetic permeability of the rod in is

A)

B)

C)

D)

Answer is (C) $\mu=\mathrm{B} \cdot \mathrm{H}=\frac{\phi}{\mathrm{A}} \times \mathrm{H}=\frac{6 \times 10^{-4}}{3 \times 10^{-4}} \times \frac{1}{2 \times 10^{3}}=10^{-3}$

### In potentiometer experiment, null point is obtained at a particular point for a cell on potentiometer wire long. If the length of the potentiometer wire is increased without changing the cell, the balancing length will (Driving source is not changed)

A) increase

B) decrease

C) not change

D) becomes zero

Answer is (A) For potentiometer, when null point is obtained for a particular cell (EV) at L $\mathrm{cm}$, (say). Whose length is $\mathrm{x} \mathrm{cm} \quad \therefore \mathrm{E}=\mathrm{L}...

### The value of gravitational acceleration ‘ ‘ at a height ‘h’ above the earth’s surface is then radius of earth)

A)

B)

C)

D)

Answer is (A) $g^{\prime}=g\left(\frac{R}{R+h}\right)^{2}$ When $g^{\prime}=\frac{g}{4}$ then. $\begin{array}{l} \frac{g}{4}=g \times\left(\frac{R}{R+h}\right)^{2} \Rightarrow...

### Angular speed of hour hand of a clock in degree per second is

A)

B)

C)

D)

Answer is (C) $\omega=\frac{\theta}{t}=\frac{2 \pi^{c}}{12 \times 3600}=\frac{360^{\circ}}{12 \times 3600}=\frac{1}{12 \times 10}=\frac{1}{120} \mathrm{deg} / \mathrm{sec}$

### A simple pendulum of length ‘ ‘ has maximum angular displacement ‘ ‘. The maximum kinetic energy of the bob of mass ‘ ‘ is (g = acceleration due to gravity)

A)

B)

C)

D)

Answer is (C) When bob is at rest, the pendulum has only potential energy which is given as $\mathrm{P.E}=\mathrm{mg} \ell$. When bob displaces by small angler displacement $\theta$, the pendulum...

### Let ‘ ‘ be the mass and ‘ ‘ be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is

A) 1

B)

C)

D)

Answer is (B) M.I of rod whose axis of rotation is passing through center and perpendicular to the plane of rod is $\mathrm{I}=\frac{\mathrm{ML}^{2}}{12} \quad$ and $\quad...

### A liquid drop having surface energy ‘ ‘ is spread into 512 droplets of same size. The final surface energy of the droplets is

A)

B)

C)

D)

Answer is (C) The surface area of the liquid drop is $A=4 \pi R^{2}$ Its surface energy is $\mathrm{E}$ When the drop splits in 512 droplets, the surface area of each droplets is $A_{2}=512 \times...

### A black rectangular surface of area ‘A’ emits energy ‘E’ per second at . If length and breadth are reduced to rd of initial value and temperature is raised to then energy emitted per second becomes

A)

B)

C)

D)

Answer is (D) $\mathrm{E}=\mathrm{e} \sigma \cdot \mathrm{A}\left(\mathrm{T}^{4}-\mathrm{T}_{0}^{4}\right) \text { and } \mathrm{A}=\ell \mathrm{b}$ When $\ell$ and $b$ changes to $\frac{\ell}{3}$...

### Two particles of masses ‘ ‘ and ‘ ‘ are separated by a distance ‘ ‘. At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is (G = Universal constant of gravitation)

A)

B)

C)

D)

Answer is (C) For the system described above $\mathrm{U}=\mathrm{m} \cdot \mathrm{V} \quad \therefore \mathrm{V}=\frac{\mathrm{U}}{\mathrm{m}}=\frac{-\mathrm{GM}}{\mathrm{X}}$ Here $M=16...

### A progressive wave is represented by . On this wave, how far away are the two points having phase difference of ?

A)

B)

C)

D)

Answer is (C) $y=12 m(5 t-4 y)$ Comparing in $y=A \sin (w t-k x)$ We have $A=12, w=5$ and $k=4$ $(w t-k x)=$ phase difference $=\frac{\pi}{2}$ $\therefore \quad 5 t-4 x=\frac{\pi}{2}$ When $t=0,4...

### If the end correction of an open pipe is then the inner radius of that pipe will be

A)

B)

C)

D)

Answer is (B) For open organ pipe $\begin{array}{l} \Delta \mathrm{L}=1.2 \times \mathrm{r} \\ \therefore \mathrm{r}=\Delta \mathrm{L} \times \frac{1}{1.2}=\frac{0.8}{1.2}=\frac{2}{3} \mathrm{~cm} ....

### Which of the following quantity does NOT change due to damping of oscillations?

A) Angular frequency

B) Time period

C) Initial phase

D) Amplitude

Answer is (C) $\delta$ is the initial phase. When oscillations of pendulum are damped, $\delta$ doesn't change

### Let a steel bar of length ‘ ‘, breadth ‘b’ and depth ‘d’ be loaded at the centre by a load ‘ ‘. Then the sag of bending of beam is ( Young’s modulus of material of steel)

A)

B)

C)

D)

Answer is (B) The sag of bending of beam is given by. $\delta=\frac{W L^{3}}{48 \mathrm{YI}} \quad$ Where $W$ is load, $L$ is length, $Y$ is young's modules and $I$ is $\frac{b d^{3}}{12}$ (area...

### A disc of radius ‘ ‘ and thickness has moment of inertia ‘I’ about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is

A)

B)

C)

D)

Answer is (A) Volume of disc is $\mathrm{A} \cdot \mathrm{d}=\pi \cdot \mathrm{R}^{2} \times \frac{\mathrm{R}}{6}=\frac{\mathrm{R}^{3} \times \pi}{6}$ Moment of inertia of disc is...

### When open pipe is closed from one end then third overtone of closed pipe is higher in frequency by than second overtone of open pipe. The fundamental frequency of open end pipe will be A) B) C) D)

Answer is (D) Let $f_{0}=\frac{v_{0}}{2 L}$ be the fundamental frequency of the open pipe $\therefore$ is second overtone is $\frac{3}{2} f_{0}=\frac{3 v_{0}}{2 L}$ Let...

### In a capillary tube of radius ‘ ‘, a straight thin metal wire of radius ‘ ‘ is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is surface tension of water, density of water, gravitational acceleration

A)

B)

C)

D)

Answer is (C) $\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\rho g(\mathrm{R}-\mathrm{r})}$ For $\cos \theta=0, \mathrm{~h}=\frac{2 \mathrm{~T}}{\rho g(\mathrm{R}-\mathrm{r})}$

### The bob of a simple pendulum performs S.H.M. with period ‘ ‘ in air and with period ‘ , in water. Relation between ‘ ‘ and ‘ ‘ is (neglect friction due to water, density of the material of the bob is , density of water )

A)

B)

C)

D)

Answer is (A) $\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}_{\mathrm{eff}}}}$ In air $\mathrm{g}_{\text {eff }}=\mathrm{g}$ where as in water $\begin{array}{l} g_{\text {eff...

### Two strings and of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed ‘ ‘ and on string with speed ‘ ‘. The ratio is

A)

B)

C) 2

D) 4

Answer is (C) The velocity of wave travelling on string is $\begin{array}{l} v=n \lambda=\frac{\lambda}{2 L} \sqrt{\frac{T}{\mu}}=\sqrt{\frac{T}{\mu}} \\ \because \quad n=\frac{1}{2 L}...

### A particle moves along a circle of radius ‘r’ with constant tangential acceleration. If the velocity of the particle is ‘ ‘ at the end of second revolution, after the revolution has started then the tangential acceleration is

A)

B)

C)

D)

Answer is (A) Using $v^{2}-u^{2}=2 a s$ and $u=u_{1}$ and $s=4 \pi r$ $\therefore \quad 2 \mathrm{as}=\mathrm{v}^{2} \Rightarrow \frac{\mathrm{v}^{2}}{2...

### A mass ‘ ‘ connected to a horizontal spring performs S.H.M. with amplitude ‘‘. While mass ‘ ‘ is passing through mean position another mass ‘ ‘ is placed on it so that both the masses move together with amplitude , The ratio of is

A)

B)

C)

D)

Answer is (A) P.E of the oscillating mass is given by $E=\frac{1}{2} m \omega x^{2}=\frac{1}{2} k x^{2} \quad \text { Where } k=m \omega^{2}$ When only black is oscillating, at $x=A$ $E=E_{\max...

### Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that pressure is

A) kinetic energy per unit volume of a gas

B) kinetic energy per unit volume of a gas

C) kinetic energy per unit volume of a gas

D) kinetic energy per unit volume of a gas

Answeris (B) The pressure exerted by the gas on the walls of container is $\mathrm{P}=\mathrm{P}_{0}+\mathrm{P}_{1}+\mathrm{P}_{2}$ i.e. $\quad \mathrm{P}=\mathrm{P}_{0}+\frac{1}{3} 8...

### Wire having tension 225 N produces six beats per second when it is tuned with a fork. When tension changes to 256 N, it is tuned with the same fork, the number of beats remain unchanged. The frequency of the fork will be

A) 186 Hz

B) 225 Hz

C) 256 Hz

D) 280 Hz

Answer is (A) For wire vibrating under tension, the fundamental frequency is given by $\mathrm{f}_{1}=\frac{1}{2} \sqrt{\frac{\mathrm{T}}{\mu}}$, Where $\mathrm{T}$ is tension \& $\mathrm{r}$...

### When the observer moves towards the stationary source with velocity, ‘’, the apparent frequency of emitted note is ‘’. When the observer moves away from the source with velocity ‘’, the apparent frequency is ‘’. If ‘’ is the velocity of sound in air and then

A) 2

B) 3

C) 4

D) 5

Answer is (B) $\frac{\mathrm{f}_{1}}{\mathrm{f}_{2}}=2, \quad$ Speed of approach $=$ Speed of leaving The apparent frequency of sound level by observer when it is approaching source is given by...

### A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is

A) 3 J

B) 4 J

C) 5 J

D) 6 J

Answer is (A) Total K.E of the rolling disc or ring is given by. $\mathrm{K} . \mathrm{E}=\frac{1}{2} \mathrm{mv}^{2}+\frac{1}{2} \mathrm{I} \omega^{2}$ For ring and disk, translational kinetic...

### Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1 : 3. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is

A) 3 : 1

B) 9 : 1

C) 27 : 1

D) 81 : 1

Answer is (B) Strain energy per unit volume $\mathrm{u}=\frac{\mathrm{U}}{\mathrm{v}}=\frac{1}{2} \times$ Stress $\times$ Strain $\begin{array}{l} \frac{U}{V}=\frac{1}{2} \times...

### In vertical circular motion, the ratio of kinetic energy of a particle at highest point to that at lowest point is

A) 5

B) 2

C) 0.5

D) 0.2

Answer is (D) $\mathrm{K} . \mathrm{E}=\frac{1}{2} \mathrm{mv}^{2}$ At lowest point in vertical circular motion. $V_{L}=\sqrt{5 r g}$ and at highest point $V_{h}=\sqrt{r g}$ $\therefore \quad...

### For a gas where ‘R’ is the universal gas constant and ‘’ is molar specific heat at constant volume. The gas is made up of molecules which are

A) rigid diatomic

B) monoatomic

C) non-rigid diatomic

D) polyatomic

1:Answer is (A) $\begin{array}{l} \frac{R}{C_{v}}=0.4 \Rightarrow \quad \frac{C_{p}-C_{v}}{C_{v}}=0.4 \\ \frac{C_{p}}{C_{v}}-1=0.4 \end{array}$ $\therefore \quad \frac{C_{p}}{C_{v}}=1.4 \Rightarrow...

### The quantities of heat required to raise the temperature of two søidacboper spheres of radii and through are in the ratio :

(1)

(2)

(3)

(4)

Correct option (3) As we know that, $Q = ms \Delta T s$ is same as the material is same $$ \begin{aligned} &\frac{Q_{1}}{Q_{2}}=\frac{m_{1}}{m_{2}}=\frac{\rho \frac{4}{3} \pi r_{1}^{3}}{\rho...

### A series LCR circuit is connected to an AC voltage source. When is removed from the circuit, the phase difference between current and voltage is . If instead is removed from the circuit, the phase difference is again between current and voltage. The power factor of the circuit is : (1) (2) (3) zero (4)

Correct option (1) Accoridng to question when inductor alone is removed, $\Delta \phi=\frac{\pi}{3}$ As we know that, $\tan \Delta \phi=\frac{X_{C}}{R}$ Thus, $\tan...

### In a quitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency . When tension in is slightly decreased, the beat frequency increases to . If the frequency of is , the original frequency of B will be :

(1)

(2) 537 Hz

(3)

(4)

Correct option (4) Given, Frequency of $A=f_{a}=530 H z, f_{B}=?$ $\left|f_{A}-f_{B}\right|=6$, $\Rightarrow f_{B}<_{524}^{536}$ When Tension $\mathrm{B}$ decreases then $\mathrm{f}_{\mathrm{B}}$...

### Taking into account of the significant figures, what is the value of ? (1) (2) (3) (4)

Correct option: 4) 9.99m−0.0099m=9.9801m However, the least accurate number should have the same number of significant figures as our answer.

### The energy equivalent of of a substance is :

(1)

(2)

(3) J

(4)

Correct option (4) According to Einstien's energy-mass equation, $E=\Delta m c^{2}=0.5 \times 10^{-3} \times\left(3 \times 10^{8}\right)^{2}$ $=0.5 \times 10^{-3} \times 9 \times 10^{16}$ $E=4.5...

### For which one of the following, Bhor model is not valid? (1) Deuteron atom (2) Singly ionised neon atom (Ne ) (3) Hydrogen atom (4) Singly ionised helium atom (

Correct option (2) The Bohr Model is only valid for atoms with one electron in orbit.

### A long solenoid of length having 100 turns carries a current of . The magnetic field at the centre of the solenoid is: )

(1)

(2)

(3)

(4)

Correct option is 3) Magnetic field for solenoid is given by formula $\mathrm{B}=\mu_{0} \mathrm{nI}$ $\mathrm{n}=\frac{\mathrm{N}}{\ell}$ Evaluating, $=4 \pi \times 10^{-7} \times 200 \times 2.5$...

### The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is : speed of electromagnetic waves)

(1)

(2)

(3) c: 1

(4)

Correct option: 4) Because the energy distribution is the same, The electric-to-magnetic-field ratio will be $1:1$.

### Which of the following graph represents the variation of resistivity ( ) with temperature (T) For copper?

The correct option is 1) As we know that the Relation between resistivity and temperature is given by $\rho=\rho_{0} e^{-\alpha T}$

### A capillary tube of radius is immersed in water and water rises in it to a height . The mass of the water in the capillary is . Another capillary tube of radius is immersed in water. The mass of water that will rise in this tube is :

(1)

(2)

(3)

(4)

Correct option: 1) As we know that, $h=\frac{2 T \cos \theta}{ rg }$ Given, $m =\rho \times$ volume $=\rho \times h \times \pi r ^{2}=5 gm$ According to information in the question, $r ^{\prime}=2...

### A short electric dipole has a dipole moment of . The electric potential due to the dipole at a point at a distance of from the centre of the dipole, situated on a line making an angle of with the dipole axis is :

(1)

(2) Zero

(3)

(4)

Correct option 4) Using the formula and evaluating, $\quad \mathrm{V}=\frac{\mathrm{kP} \cos \theta}{\mathrm{r}^{2}}=\frac{9 \times 10^{9} \times 16 \times 10^{-9} \times 1}{(0.6)^{2} \times...

### For the logic circuit shown, the truth table is :

Correct option is 3) According to de-Morgan rule, $\overline{\bar{A}+\bar{B}}=\overline{\bar{A}} \cdot \overline{\bar{B}}=A \cdot B$

### A ball is thrown vertically downward with a velocity of from the top of a tower. It hits the ground after some time with a velocity of . The height of the tower is : (1) (2) (3) (4)

Correct option: 2) Using the equation of motion, $v^{2}-u^{2}=2 a s$ Substituting and calculating the value, $(80)^{2}-(-20)^{2}=2(-10) \times s$ $6400-400=2 \times(-10) \times s$...

### The mean free path for a gas, with molecular diameter and number density can be expressed as : (1) (2) (3) (4)

Correct option: 4) In physics, the mean free path is the average distance over which a moving particle's direction or energy changes significantly, usually as a result of one or more successive...

### A cylinder contains hydrogen gas at pressure of and temperature . Its density is :

(1) (2) (3) (4)

Correct option: 4) Using the ideal gas equation, we evaluate the value of density by making modification, $$ \begin{aligned} &\therefore PV = nRT \\ &\Rightarrow PV =\frac{ m }{ M } RT \quad...

### In a certain region of space with volume 0.2 cubic meters, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is : (1) 1 N/C (2) 5 N/C (3) Zero (4) 0.5 N/C

Correct option: 3) Given $v=$ const. (5 volt) $As E =-\frac{ dv }{ dr }$ So differentiation of a constant is zero, thus, $E =0$

### Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is : (1) g/5 (2) g/10 (3) g (4) g/2

Correct option: 1) According to the figure, the force equation on both the blocks are, 6g – T = 6a T – 4g = 4a Solving both we get the value of a = g/5 $m/s^2$

### A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is : (1) 0.5 mm (2) 1.0 mm (3) 0.01 mm (4) 0.25 mm

Correct option: 1) As we know that, Least Count $=\frac{\text { Pitch }}{\text { no. of division on circular scale }}$ Thus evaluating according to given information, $=0.01=\frac{\text { pitch...

### Dimensions of stress are : (1) (2) (3) [ MLT-2] (4)

Correct option 2) Solving using the dimension formula according to the formula of stress: Stress $=\frac{F}{A}=\frac{M^{1} L^{1} T^{-2}}{L^{2}}=M L^{-1} T^{-2}$

### Assume that light of wavelength is coming from a star. The limit of resolution of telescope whose objective has a diameter of is:

(1) rad

(2)

(3)

4)

Correct option: 3) As we know that the formula of limit of resolution of telescope, $\Delta \theta_{\min }=\frac{1.22 \lambda}{ d }=\frac{1.22 \times 600 \times 10^{-9}}{2}$ $\Delta \theta_{\min...

### A spherical conductor of radius has a charge of distributed uniformly. what is the magnitude of electric field at a point from the centre of the sphere?

Answer: option 4 As we know the formula for electric field, so evaluating according to given info, $E=\frac{k Q}{r^{2}}=\frac{9 \times 10^{9} \times 3.2 \times 10^{-7}}{15 \times 15 \times 10^{-4}}$...

### For transistor action, which of the following statements is correct ? (1) Both emitter junction as well as the collector junction are forward biased. (2) The base region must be very thin and lightly doped. (3) Base, emitter and collector regions should have same doping concentrations. (4) Base, emitter and collector regions should have same size.

Correct option: 2) The base junction must be lightly doped for transistor action, resulting in a very thin base region.

### Match the corresponding entries of column 1 with column 2. [Where is the magnification produced by the mirror]

A and and and and

B and and and b; and

C and and and and

D and and and and

Correct Option A Answer: The term "positive magnification" refers to an image that is upright in relation to the object. Negative magnification refers to an image that is inverted in relation to the...

### A car is negotiating a curved road of radius . The road is banked at an angle . The coefficient of friction between the tyres of the car and the road is s. The maximum safe velocity on this road is:

A

B

C

D

Correct Option B Solution: For vertical equilibrium on the curved road we have, $N \cos \theta=m g+f_{1} \operatorname{Sin} \theta----(1)$ Forhorizontal equilibrium on the curved road we have,...

### A small signal voltage is applied across an ideal capacitor C:

A Current I , lags voltage by

B Over a full cycle the capacitor does not consume any energy from the voltage source.

C Current I (t) is in phase with voltage V (t).

D Current I leads voltage by .

Correct Option B Solution: In AC circit the power is given by formula, $P=V I \operatorname{Cos} \phi$ Because the phase difference in a purely capacitive circuit is 90 degrees, no power is...