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Two forces P and Q, of magnitude $2F\text{and}3F$ respectively are at an angle $\theta$ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then the angle $\theta$ is

A two lane urban road with one way traffic has a maximum capacity of $2400veh/hr$. Under the jam condition, the average length occupied by the vehicle is $5m$. Speed versus density relationship is linear. If traffic volume is $1000veh/hr$ then the density of the traffic (in $veh/km/2$ lane) is

If vectors P, Q and R have magnitude 5, 12 and 13 units and $\overrightarrow{P}+\overrightarrow{Q}=\overrightarrow{R}$, the angle between Q and R is

A projectile is thrown so as to have a maximum possible horizontal range of $400\text{m}$. Taking the point of projection as the origin, the co-ordinates of the point where the velocity of the projectile is minimum is

A projectile fired with initial velocity u at some angle $\theta$ has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be

A potentiometer wire has a length of $10\text{m}$ and resistance $4\Omega {\text{m}}^{-1}$. An accumulator of emf $2\text{V}$ and a resistance box are connected in series with it. Calculate the resistance to be introduced in the box to get a potential gradient of $0.1\text{V/m}$.

A sinusoidal wave travelling in the positive direction on a stretched string has an amplitude $20\text{cm}$, wavelength $1.0\text{m}$ and wave velocity $5\text{m/s}$. At $x=0$ and $t=0$ , it is given that $y=0$ and $\frac{\partial y}{\partial t}<0$. Find the wave function $y(x,t)$

1. 49.5

At NTP water boils at ${100}^{o}C$. Deep down the mine, water will boil at a temperature

Two particles are executing SHM, one with angular frequency $\omega$ and the other with ${}^{\prime }2{\omega }^{\prime }$, which of the following $v-x$ graph correctly represent simple hormonic motions of two particles of same amplitude.

If $E=6\text{V}$, $r=2R$ then maximum power dissipated through $R$ is

The area under acceleration -time graph represents the _________

A. Initial velocity

B. Final velocity

C. Change in velocity

D. Distance travelled

In Young's double slit experiment using yellow and blue lights of wavelengths $560\text{nm}$ and $420\text{nm}$ respectively, the value of $n$ for which $n^{th}$ order of yellow bright fringe coincides with $(n+1{)}^{th}$ order of blue bright fringe is

The greatest possible acceleration or deceleration that a train may have is $a$ , and its maximum speed is $v$ and total distance is $s$. What is the minimum time in which the train can get from one station to another?

Three thin uniform rods each of mass $m$and length $l$ are placed along the three axes of a Cartesian co-ordinate system with their one end at the origin. The moment of inertia of the system about $z-axis$ is

A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta .$ Its time period of vibration will be

A rocket of mass $20\text{kg}$ has $180\text{kg}$ fuel. The exhaust velocity of the fuel is $1.6\text{km/s}$. Calculate the minimum rate of ejection of fuel so that the rocket may rise from the ground. (Take $g=9.8{\text{m/s}}^2$)

If velocity of a particle is $v\left(t\right)=t^2-5t\text{m/s}$, the average speed and magnitude of average velocity of the particle in $10\text{sec}$ respectively are

A conducting circular loop of face area $2.5\times {10}^{-3}{\text{m}}^2$ is arranged with its plane perpendicular to a magnetic field which varies as $B=0.5\sin \left(100\pi t\right)$. Find the net charge flowing through the loop during the interval $t=0$ to $t=20\text{ms}$.



[Take resistance of the conducting wire as $10\Omega$]

Two particles $A$ and $B$ are moving in same direction on a circular path. Initially particle $A$ and $B$ are diametrically opposite to each other. Particle $A$ moves with angular velocity $\pi rad/s$ and angular acceleration $\frac{\pi }{2}rad/s^2$ and particle $B$ moves with constant angular velocity $2\pi rad/s$. Find the time after which both particles $A$ and $B$ collides.

The relation between time and distance is $t=\alpha x^2+\beta x$ where $\alpha$ and $\beta$ are constants. The retardation is

A parallel plate capacitor has the space between its plates filled by two slabs of thickness $d/2$ each with dielectric constants $k_1$ and $k_2$. Given that $d$ is the plate separation of the capacitor, the effective capacitance is

If a car at rest accelerates uniformly to a speed of $144\text{km/h}$ in $20\text{s}$, it covers a distance of

A ball is thrown vertically downward with a velocity $u$ from the top of a tower. It strikes the ground with a velocity $3u$. The time taken by the ball to reach the ground is given by

Potential difference between centre and surface of the non conducting sphere of radius $R$ and uniform volume charge density $\rho$ within it will be

Match the column $\text{I}$ and column $\text{II}$ correctly.

A 10
kW drilling machine is used to drill a bore in a small aluminium
block of mass 8.0 kg. How much is the rise in temperature of the
block in 2.5 minutes, assuming 50% of power is used up in heating the
machine itself or lost to the surroundings. Specific heat of
aluminium = 0.91 J g^–1
K^–1.

The magnetic field inside a toroidal solenoid of radius R is B. If the current through it is doubled and its radius is also doubled keeping the number of turns per unit length the same; magnetic field produced by it will be:

The three rods shown in the figure have identical dimensions. Heat flows from the hot end at a rate of $40\text{W}$ in the arrangement (a). Find the rate of heat flow when the rods are joined as in the arrangement shown in (b).

[Assume $K_{Al}=200{\text{W/m}}^{\circ }\text{C}$ and $K_{cu}=400{\text{W/m}}^{\circ }\text{C}$]

An infinite conducting sheet has surface charge density $\sigma$. The distance between two equipotential surfaces is $r$. The potential difference between these two surfaces is