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A police car moving at 22 m/s, chases a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.

A rocket with an initial mass of $1000\text{kg}$ is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of $10\text{kg}$ per second. The burnt matter is ejected vertically downwards with a speed of $2000\text{m/s}$ relative to the rocket. If burning ceases after one minute, the maximum velocity of the rocket is

A ray of light incident on a ${60}^{\circ }$ angled prism of refractive index $\sqrt{2}$ suffers minimum deviation. Angle of incidence is

A plane flies 10 km east from city A to city B in 2 hrs and then 20 km south from city B to city C in 1 hr. For the total trip, what are the magnitude and direction of its average acceleration?

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is

Six point charges each having magnitude Q are placed at the vertices of regular hexagon of edge length a as shown in figure. Net electric field at the centre of hexagon will be



समान परिमाण Q के छः बिंदु आवेशों को चित्रानुसार a भुजा लम्बाई के सम षट्भुज के शीर्षों पर रखा गया है। षट्भुज के केन्द्र पर नेट विद्युत क्षेत्र होगा

Magnitude of the resultant of two vectors, $A$ and $B$ is given by square root of _____________.

Recently, the phenomenon of superconductivity has been observed at 95 K. This temperature is nearly equal to

If a particle is projected from origin and it follows the trajectory $y=x-\frac{1}{4}{x}^2$, then the time of flight is ($g$ = acceleration due to gravity)

A boat which has a speed of $5\text{km/h}$ in still water crosses a river of width $1\text{km}$ along the shortest possible path in $15\text{min}$. The velocity of the river water in $\text{km/h}$ is

Force constant of a weightless spring is $16\text{N/m}$. A body of mass $1.0\text{kg}$ suspended from it is pulled down through $5\text{cm}$ from its mean position and then released. The maximum kinetic energy of the body will be

Find the derivative of $f\left(x\right)=(x^3-2x{)}^2$

Find the force on charge q at point P.

identical condensers are joined in parallel and are charged to potential V . Now they are separated and joined in series. Then the total energy and potential difference of the combination will be

Two blocks of masses $4kg$ and $10kg$ are connected by a flexible inextensible string as shown in given figure. The pulley is assumed to be light and frictionless. The coefficient of friction between the $4kg$ block and the suface is $0.2$ (${\mu }_s={\mu }_k=0.2$). The angle of inclination of the plane is ${30}^{\circ }$. Assuming the sytem to be released from rest, the acceleration of $10kg$ block is $(g=10m{s}^{-2})$

The block is displaced towards right through a distance $x$ and released. Then, speed of the block as it passes through the mean position is

Find the tension (in $N$) in the string connecting the $2m$ mass. (Strings are massless and inextensible)

A block is placed on the top of a plane inclined at ${37}^{\circ }$ with horizontal. The length of the plane is 5m. The block slides down the plane and reaches the bottom. Find the speed of the block at the bottom if the coefficient of friction is 0.25.

What amount of work is done in increasing the length of a wire through unity?

Differentiate $y=\text{cosec}x\cot x$ w.r.t $x$

A small electric immersion heater is used to heat $100\text{g}$ of water. The power on the heater is labeled as $200\text{W}$. Calculate the time required to raise the temperature from $23{}^{\circ }\text{C}$ to $100{}^{\circ }\text{C}$.

$[$Specific heat capacity of water is $4200{\text{J/kg}}^{\circ }\text{C}]$

A bubble of 5.00 mol of helium is submerged at a certain depth in liquid water when the water (and thus the helium) undergoes a temperature increase $\Delta T$ of ${20.0}^{\circ }C$; at constant pressure. As a result, the bubble expands. The helium is monoatomic and ideal. How much work W is done by the helium as it expands against the pressure of the surrounding water during the temperature increase? Use the first law of thermodynamics.​

If $I_1$ is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass and $I_2$ is the moment of inertia of the ring (formed by bending the rod) about an axis perpendicular to the plane of ring and passing through its centre, then the ratio $\frac{I_1}{I_2}$ is

Statement1: In absence of air, projectile motion is always a 2D motion.

Statement2: In absence of any external force in 3D space, at any time during its flight Projectile's velocity has only two components.

A truck travelled the first one-third of the distance $d$ at a speed of $10{\text{kmh}}^{-1}$, the second one-third of the distance at a speed of $12{\text{kmh}}^{-1}$ and the last one-third of the distance at a speed of $20{\text{kmh}}^{-1}$. The average speed of the truck is approximately equal to (in ${\text{kmh}}^{-1}$)

One end of a uniform rod of mass M and cross-sectional area A is suspended from a rigid support and an equal mass M is suspended from the other end. The stress at the mid-point of the rod will be

A block of steel of size 5 cm $\times$ 5 cm $\times$ 5 cm is weighed in water. If the relative density of steel is 7, its apparent weight is

Hydrogen atom does not emit X-rays because

A composite rod is made of copper $\alpha =1.8\times {10}^{-5}{K}^{-1}$ and steel $1.2\times {10}^{-5}{K}^{-1}$ as shown in figure, is heated up, then it

Two transverse waves passing through a region are represented by $y_1=\left(2\text{cm}\right)\sin \left[\right(2\pi {\text{cm}}^{-1})x-(100\pi {\text{s}}^{-1}\left)t\right]$ and $y_2=\left(3\text{cm}\right)\sin \left[\right(\pi {\text{cm}}^{-1})x-(200\pi {\text{s}}^{-1}\left)t\right]$.

Find the net displacement of the particle at $x=4.5\text{cm}$ and time $t=5\text{ms}$.

[Assume, $\uparrow$ for positive $y-$ direction and $\downarrow$ for negative $y-$ direction]

A single conservative force $F\left(x\right)$ acts on $1\text{kg}$ particle that moves along $x$ axis. The potential energy $U\left(x\right)$ is given by $U\left(x\right)=10+(x-1{)}^2$. At $x=2\text{m}$, The particle has kinetic energy of $20\text{J}$. The maximum kinetic energy of the particle is

When a sound wave of wavelength $\lambda$ is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of wave is:

A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop. If a steady current I is established in the wire, as shown in Fig., the loop

The resistivity vs. Temperature variation of a certain material is shown below. At $2^{\circ }C$, this material will act as?

A wave is represented by the equation

y = (0.001 mm) sin[(50 $s^{-1}$)t + (2.0 $m^{-1}$)x].

A trolley of mass m is connected to two identical springs, each of force constant k, as shown in figure. The trolley is displaced from its equilibrium position by a distance x and released. The trolley executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)

Work done by a system under isothermal change from a volume $V_{1}to{V}_2$ for a gas which obeys Vander Waal's equation $(V-\beta n)(P+\frac{a{n}^2}{V})=nRT$

A block of mass m is placed on a surface with a vertical cross-section given by $y=\frac{x^3}{6}$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is

A block slides along a track from one level to another level, by moving through an intermediate valley. Find the maximum value of $h$ (height) that the block can reach, if the initial speed of the block is $v_0$. (Assume track is frictionless)

Three partricles $A,B$ and $C$ of different masses $1\text{kg},2\text{kg}$ and $3\text{kg}$ are moving with different velocities $v_A=\hat{i}+2\hat{j},v_B=2\hat{i}+4\hat{j}$ and $v_C=3\hat{j}$. At time $t$, particles $A,B$ & $C$ are at points $(2,3),(3,2)$ & $(1,4)$ respectively. The total angular momentum of the system of $3$ particles about the origin [in ${\text{kg m}}^2\text{/s}$] is

For the given situation, which of the following options correctly represents the equation for SHM?

A particle is projected from the bottom of an inclined plane of angle ${30}^{\circ }$ with a velocity of $20\text{m/s}$ at an angle of ${45}^{\circ }$ with the horizontal. Find the horizontal distance travelled by the particle before it hits the plane.

A force $F=\frac{-k}{x^2}(x\ne 0,(k\left)\text{is a positive constant}\right),$ acts on a particle in $x$ direction. The work done by this force in displacing the particle from $x=+a$ to $x=+2a$ is

The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

From a uniform circular disc of radius $20\text{cm}$, two small circular discs of radius $10\text{cm}$ are removed in such a way that both have common tangent as shown in the figure given below. The distance of centre of mass of the remaining part from the centre of original disc is:

A body of mass $m$ moves with speed $2v$ and a body of mass $2m$ moves with speed $v$ on a smooth horizontal surface, both along positive $x$ axis. After some time, they collide and stick together. What is the speed of the system after they stick together?

Three blocks $A$, $B$ and $C$ weighing $1kg,8kg$ and $27kg$ respectively are connected as shown in the figure, with an inextensible string and are moving on a smooth surface. If tension $T_3$ is equal to $36N$, then tension $T_2$ is

An express train is moving with a velocity $v_1$. Its driver finds another train is moving on the same track in the same direction with velocity $v_2$ $(v_2<v_1)$. To escape collision, driver applies a retardation a on the train. The minimum time to escape the collision is