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A wire has a resistance of $6\Omega$ . It is cut into two parts and both half value are connected in parallel the new resistance is

A sphere of brass released in a long liquid column attains a terminal speed ${\upsilon }_0$ . If the terminal speed attained by the sphere of marble of the same radius and released in the same liquid is $n{\upsilon }_0$, then the value of n will be. [ Given: The specific gravities of brass, marble and the liquid are 8.5,2.5 and 0.8 respectively.]

Find the direction of deflection of the electron.

Uniform magnetic filed B = 10 T is acting in a region of length L = 2m as shown. A square loop of side $\frac{L}{2}$ enters in it with constant acceleration $a=1m/s^2$. Resistance per unit length of the square frame is $\frac{1\Omega }{m}$. At, t = 1s

A uniform rod of mass m is bent into the form of a semicircle of radius R. The moment of inertia of the rod about an axis passing through A and perpendicular to the plane of the paper is

The current flowing in the given circuit is $0.2A$. The potential difference between the points $A$ and $B$ will be

Six identical conducting rods are joined as shown in the figure. Points A and D are maintained at temperatures ${200}^{o}C$ and $20{}^{o}C$ respectively. The temperature of junction B will be

In the electric field of a point charge q, a certain point charge is carried from point A to B, C, D and E as shown in figure. The work done is

An insect is travelling in between the two inclined mirrors as shown in the figure. The number of images formed of the insect by the mirrors are

A mass $m$ moving horizontally (along the x-axis) with velocity $v$ collides and sticks to a mass $3\text{m}$ moving vertically upward (along the y-axis) with velocity $2\text{v}$. The final velocity of the combination is

In List - I condition on initial velocity $\overrightarrow{u}$, force $\overrightarrow{F}$ and acceleration $\overrightarrow{a}$ of a particle is given.
Resultant motion is described in List-II.
Match List-I with List-II
$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(I)}& \overrightarrow{u}\times \overrightarrow{F}=0\text{and}& \text{(P)}& \text{Path will be}\\ & \overrightarrow{F}=\text{constant}& & \text{circular path}\\ \text{(II)}& \overrightarrow{u}.\overrightarrow{F}=0\text{and}& \text{(Q)}& \text{Speed will increase}\\ & \overrightarrow{F}=\text{constant}& & \\ \text{(III)}& \overrightarrow{v}.\overrightarrow{F}=0\text{all the time}& \text{(R)}& \text{Path will be}\\ & \text{and}|\overrightarrow{F}|=\text{constant}& & \text{straight line}\\ & \text{and the particle}& & \\ & \text{always remains in}& & \\ & \text{one plane}\left(\overrightarrow{v}\text{is instantaneous velocity}\right)& & \\ \text{(IV)}& \overrightarrow{u}=2\hat{i}-3\hat{j}\text{and}& \text{(S)}& \text{Path will be}\\ & \text{acceleration at all time}& & \text{parabolic}\\ & \overrightarrow{a}=6\hat{i}-9\hat{j}& & \end{array}$

Six moles of an ideal gas undergoes a thermodynamic cycle as shown in figure. If the temperatures are $T_A=600\text{K},T_B=800\text{K},T_C=2200\text{K}$ and $T_D=1200\text{K}$, the work done per cycle is approximately:
(Take universal gas constant, $R=\frac{25}{3}\text{J/mole. K}$)

A cubical block rests on a plane of $\mu =\sqrt{3}$. The angle through which the plane should be inclined to the horizontal so that the block just slides down will be

The area enclosed by a $PV$ graph for one thermodynamic cycle of a heat engine is $610\text{J}$. The total thermal energy absorbed by the gas in one cycle is $1300\text{J}$. Determine the efficiency of the cycle.

An elevator and its load have a total mass of $800\text{kg}$. If the elevator, originally moving downward at $10\text{m/s}$, is brought to rest with constant deceleration in a distance of $25\text{m}$, the tension in the supporting cable will be ($g=10{\text{m/s}}^2$)

A stretched string of $1\text{m}$ length fixed at both ends, having a mass of $5\times {10}^{-4}\text{kg}$ is under a tension of $20\text{N}$. It is plucked at a point situated at $25\text{cm}$ from one end. The stretched string would vibrate with a frequency of

A boy standing on a long railroad car throws a ball straight upwards. The car is moving on the horizontal road with an acceleration of $1m/s^2$ and the projection speed in the vertical direction is $9.8m/s$. How far behind the boy will the ball fall on the car?

Which of the given compound has highest dipole moment?

Himanshu tries to calculate the force exerted by 2 spherical objects of radius 1m each, having charges 3C and 5C and travelling at 4m/s with respect to each other. At an instant when the separation between them is 10 m, Himanshu theoretically calculates the force exerted by the one on another. He only applies Coulomb's law and let us assume that he manages to apply it correctly but gets his answer wrong. Possible explanations could be?

Which of the following graphs correctly represents uniform angular retardation of a body?

A constant force $\overrightarrow{F}=(\hat{i}-2\hat{j}+\hat{k})\text{N}$ is acting on a body to displace it from $(0,1,1)\text{m}$ to $(0,-2,3)\text{m}$, the amount of work done by force is

Sun rays are reflected from a horizontal mirror and falls on a vertical screen .a vertical object of height h is placed on the mirror .length of the shadow on the screen is?

Classify the below given measures as scalars and vectors:

(i) 10 kg

(ii) 2 m north-west

(iii) ${40}^{\circ }$

(iv) 40 W

(v) ${10}^{-19}C$

(vi) $20m/s^2$

A wire of 5ohm is bent to form a square.What is the equivalent resistance in ohm across the diagonally opposite vertice of the square?

A projectile of mass $0.5kg$ is thrown with a velocity of $30m/s$ at an angle of ${60}^{\circ }$ with the horizontal. Find the net force acting on the body.

In the shown figure the tension in the horizontal cord is 30N. Find the weight of the body B.

A solid copper cube of edge $10\text{cm}$ is subjected to a hydraulic pressure of $7\times {10}^6\text{Pa}$. If compressibility of copper is $\frac{1}{140}{\text{GPa}}^{-1}$, then contraction in its volume will be

A thin brass sheet at ${10}^{\circ }C$ and a thin steel sheet at ${20}^{\circ }C$ have same surface area. The common temperature at which both would have the same area is :

Coefficient of areal expension for brass and steel are ${10\times {10}^{-6}}^{\circ }{C}^{-1}$ and ${20\times {10}^{-6}}^{\circ }{C}^{-1}$ respectively.

Where was the first telescope made and who made it?

A man running on a horizontal road at $8{\text{ms}}^{-1}$ finds rain falling vertically. If he increases his speed to $12{\text{ms}}^{-1}$, he finds that drops make ${30}^{\circ }$ angle with the vertical. Find the velocity of rain with respect to the road.

What is meant by the statement "variation of heat capacity of solids as a function of temperature"?

Hint: This was a phenomenon which the classical phisics wave nature of light could not explain.

A man of mass $m$ is standing on weighing machine in an elevator accelerating upwards with an acceleration $a$. What will be the reading of weighing machine?

Two particles $A$ and $B$ are projected simultaneously from the towers of same height as shown in the figure with velocities $V_A=20\text{m/s}$ and $V_B=10\text{m/s}$ respectively. They collide in air after 0.5 seconds. Find '$x$'.

A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is 50 m where 'm' is the mass of the one shell. If the muzzle velocity of the shell is 200 m/s, the recoil speed of car after second shot is

The electrostatic force $F_e$ that an object of charge $Q$ exerts on another object of charge $q$ is given by Coulomb's law:
$F_e=\frac{1}{4\pi {ϵ}_0}\frac{Qq}{r^2}$
Where the charges of the two objects are $Q$ and $q$, are measured in units of coulombs $\left(C\right)$ and $r$ is the distance separating the two objects.
What are the units of the constant ${ϵ}_0$ ?

A brass rod and a lead rod each $80\text{cm}$ long at $0{}^{\circ }\text{C}$ are clamped together at one end with their free ends coinciding. The separation the of free ends of the rods, if the system is placed in a steam bath is
$[{\alpha }_{\text{brass}}=18\times {10}^{-6}/{}^{\circ }\text{C}$ and ${\alpha }_{\text{lead}}=28\times {10}^{-6}/{}^{\circ }\text{C}\text{and temperature of steam}={100}^{\circ }\text{C}]$

A square wire frame of side 'L' is dipped in a liquid. On taking it out a membrane is formed. If the surface tension of liquid is T, the force acting on the liquid surface will be?

A solid sphere of radius $4\text{cm}$ and a hollow sphere of same material and having outer radius $4\text{cm}$ and inner radius $2\text{cm}$ are heated to the same temperature and allowed to cool in the same room. The ratio of the rate of fall of temperatures is

A resonant ac circuit contains a capacitor of capacitance ${10}^{-6}F$ and an inductor of ${10}^{-4}H$. The frequency of electrical oscillations will be

The normal reaction between the blocks $N_1,N_2$ are

If The base and altitude of a triangle are doubled, whats happens to The area?

The surface energy of a drop of water of radius $r$ is proportional to:

If the maximum acceleration that is tolerable for passengers in a subway train is 1.34 m/$s^2$ and subway stations are located 880 m apart. What is the maximum speed, a subway train can attain between stations?

Calculate the time required to heat 20 kg of water from ${10}^{\circ }C$ to ${35}^{\circ }C$ using an immersion heater rated 1000 W. Assume that 80% of the power input is used to heat the water. Specific heat capacity of water $=4200Jk{g}^{-1}{K}^{-1}$.