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If two points $P=(0,–1)$ and $Q=(4,1)$ are on a straight line, find equation of the Straight line.

Two particles of mass 'm' each are attached to a light rod of length 'd', one at its centre and the other at a free end. The rod is fixed at the other end and is rotated in a plane at an angular speed $\omega$. Calculate the angular momentum of the particle at the end with respect to the particle at the centre.

Figure shows an overhead view of a corridor with a plane mirror M mounted at one end. A burglar B sneaks along the corridor directly toward the center of the mirror. If d = 3.0 m, how far from the mirror will she be when the security guard S first sees her in the mirror?

The angle turned by a body undergoing circular motion depends on time as $\theta =(2t^2-{\theta }_0{t}^3)\text{rad}$, where ${\theta }_0$ is constant. Then the angular acceleration of the body at $t=2\text{s}$ is

Two waves represented by equation,

$y_1=2\sin (\pi t-0.1x)$ and $y_2=2\sin (\pi t-0.1x+\varphi )$ are superimposed. If the resultant wave has a maximum amplitude equal to $4\text{cm}$, the value of $\varphi$ is :

The equivalent resistance of a voltmeter with coil resistance $R_c=1k\Omega$ and series resistance of 100 k$\Omega$ is .

In the equation representing wave function,

$y=A\sin (kx-\omega t+{\varphi }_0)$

The term phase is defined as:

Two wires A and B of same length and of the same material have the respective radii $r_1$ and $r_2$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

In a Bohr atom the electron is replaced by a particle of mass 150 times the mass of the electron and the same charge. If $a_0$ is the radius of the Bohr orbit, then that of the new atom will be

Two balls having masses $m_1=5\text{kg}$ and $m_2=10\text{kg}$ moving with velocities $u_1=10\text{m/s}$ and $u_2=5\text{m/s}$ collide elastically. Find the change in momentum of the ball having mass $m_1$ due to collision

A diatomic gas $(\gamma =1.4)$ of mass $m$ at a pressure of $2$ atmospheres is compressed adiabatically so that its temperature rises from ${27}^{\circ }\text{C}$ to ${927}^{\circ }\text{C}.$ The pressure of the gas in final state is

A cylinder of radius R made of a material of thermal conductivity k, is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity $k_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

A rod CD of thermal resistance 5.0 K/W is joined at the middle of an identical rod AB as shown in figure The ends A, B and D are maintained at 100${}^{\circ }$C, 0 ${}^{\circ }$ C and 25 ${}^{\circ }$ C respectively. Find the heat current in CD.

For a given density of planet the orbital period of a satellite near the surface of planet of radius R is proportional to

A iron rod of length 50 cm is joined at an end to an aluminum rod of length 100 cm. All measurements refer to ${20}^{\circ }C$. The coefficients of linear expansion of iron and aluminum are $12\times {10}^{-6}{/}^{\circ }C$ and $24\times {10}^{-6}{/}^{\circ }C$ respectively. The average coefficient of composite system is

An L-shaped glass tube is kept inside a bus that is moving with constant acceleration. During the motion, level of the liquid in the left arm is at $12\text{cm}$ whereas in the right arm, it is at $8\text{cm}$ when the orientation of the tube is as shown. Assuming that the diameter of the tube is much smaller than the levels of the liquid and neglecting effects of surface tension, the acceleration of the bus will be $\left({\text{g=10 m/s}}^2\right)$

A six-foot-tall person is $72$ inches tall. How many centimeters tall is a six-foot person?

Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy by 75% of the total energy?

An aircraft executes a horizontal loop with a speed of 150 m/s with its, wings banked at an angle of ${120}^{\circ }$. The radius of the loop is $(g=10m/s^2)$

Two identical rods each of mass 'M' and length 'l' are joined in crossed position as shown in figure. The moment of inertia of this system about a bisector would be

The radius of gyration of a uniform circular disc of radius a, rotating about an axis perpendicular to the plane and passing through its centre of mass, is



घूर्णन करती हुई a त्रिज्या की समरूप वृत्तीय डिस्क के तल के लम्बवत् तथा इसके द्रव्यमान केन्द्र से गुजरने वाले अक्ष के सापेक्ष इसकी परिभ्रमण त्रिज्या है

The molar heat capacity of 1 mole of a diatomic gas, if it does a work of $Q/4$ in a process when heat $Q$ is supplied to it, is -

A block of mass $10kg$ is placed on a rough horizontal surface whose coefficient of friction is $0.5$. If a horizontal force of magnitude $100N$ is applied on the block, then acceleration of the block will be $[\text{Take}g=10m{s}^{-2}]$

The radius of a sphere is $(6.3\pm 0.1)\text{cm}$. The percentage error in its volume is

Find the angle between the net acceleration vector and tangential acceleration vector for a particle moving in a circle of radius $4m$ and its speed is increasing at $3m/s$ every second, when the speed of the particle is $4m/s$.

Four thin uniform rods, each of length $L$ and mass $M$ are joined to form a square. The moment of inertia of square about an axis along one of its diagonal is

Magnetic field $\overrightarrow{B}=3x\hat{i}$ exists in space. Energy stored in a cylinderical region of length 1m along x-axis with one end at origin is [Radius of the cylinder is 2m]

A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by

The potential at the surface of a planet of mass M and radius R is assumed to be zero. Choose the most appropriate option

Two blocks A and B of equal masses $m\text{kg}$ are suspended with the help of ideal pulleys and string arrangement as shown in figure. Then acceleration $\left({\text{in m/s}}^2\right)$ of mass B will be:

If $\overrightarrow{P}$ and $\overrightarrow{Q}$ are two non-zero vectors, what is the angle between $(\overrightarrow{P}+\overrightarrow{Q})$ and $(\overrightarrow{P}\times \overrightarrow{Q})$ ?

Following sets of three forces act on a body. Whose resultant cannot be zero

If force (F), pressure (P) and speed (v) are fundamental quantities, then dimensional formula of time is :

The accleration of a particle is given by $a=(3t^2+2t+2)$ ${\text{ms}}^{-2}$ where $t$ is time. If the particle starts out with an initial velocity $v=2\text{m/s}$ at $t=0$, then the velocity of the particle at the end of $2\text{s}$ is

A closed vessel contains $8\text{g}$ of oxygen and $7\text{g}$ of nitrogen. The total pressure is $10$ atm at a given temperature. If now, oxygen is absorbed by introducing a suitable absorbent, the pressure of the remaining gas in atm will be

The ratio of the energy of a photon with $\lambda =150nm$ to that with $\lambda =300nm$ is

A particle performs SHM with a period $T$ and amplitude $A$. The mean velocity of the particle over the time interval during which it travels a distance $\frac{A}{2}$ from the extreme position is

A person completes half of his journey with speed $v_1$ and rest half with speed $v_2$. The average speed ($v_{avg})$ of the person is

Surface tension of liquid is $70\text{dyne/cm}$. Its value in $\text{SI}$ is

An isosceles prism of angle ${120}^{\circ }$ has a refractive index $\sqrt{2}$. Two parallel monochromatic rays enter the prism parallel to each other in air as shown. in figure. Find the angle between the emerging rays

A rod is measured at ${10}^{\circ }\text{C}$ using a scale calibrated at that temperature. Find the percentage error in length, if thermal coefficients of linear expansion of the rod and scale are $3\times {10}^{-5}{/}^{\circ }\text{C}$ and $2\times {10}^{-5}{/}^{\circ }\text{C}$ respectively, and the rod is measured at ${50}^{\circ }\text{C}$.

Find the dimensional formulae of the capacitance C

Some of the equations containing these quantities are

Q = It, U = VIt, Q = CV and V = RI;

Where 'I' denote the electric current, 't' is time and 'U' is energy.

Energy has the dimension of Force x displacement

A body takes the following path and moves with constant speed. If $a_A$ and $a_B$ are the magnitude of its radial acceleration at A and B, then.

Figure represents a capacitor made of two circular plates each of radius $r=12\text{cm}$ and separated by $d=5.0\text{mm}$. The capacitor is being charged by an external source. The charging current is constant current, $I=0.15\text{A}$.



Calculate the rate of change of electric field between the plates.