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Let a,b,c be non-zero real numbers such that a+b+c = 0; let $q=a^2+b^2+c^{2}andr=a^4+b^4+c^4$ Then

Gravitational constant (G), Rydberg constant (R) and speed of light (C) are three constants. Which of the following has dimension of time?

In the circuit shown in figure. The reading of ammeter A is

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

A particle of mass $m=4\text{kg}$ is projected with a speed of $u=10\text{m/s}$ at an angle of ${45}^{\circ }$ with the horizontal. The particle explodes in mid air when it is at the maximum height. One component weighing $1\text{kg}$ comes to rest after the explosion and the other component of mass $3\text{kg}$ moves away. Find the distance where the $3\text{kg}$ mass component strikes the ground from the initial position (projection point). [Take $g=10{\text{m/s}}^2$]

The forces acting on the blocks are shown. What is the displacement of centre of mass in time t? The initial velocity of each is zero.

Radio station broadcasts on a frequency of 1368kHz. Calculate the wavelength and wave number of the electromagnetic radiation emitted by the transmitter

Water enters a pipe with inlet diameter of $1.5\text{cm}$ at an absolute pressure of $5\times {10}^5\text{Pa}$. The outlet of the pipe is $1\text{cm}$ in diameter and is at height of $6\text{m}$ above the inlet. When the flow speed at the inlet pipe is $2\text{m/s}$. Find the flow speed $\left(\text{m/s}\right)$ and pressure $\left(\text{Bar}\right)$ at the outlet of the pipe. (Take $g=10{\text{m/s}}^2$)

Is motion of charge, without acceleration only? And why

According to the principle of conservation of momentum

What will be the length of Hg column in a barometer tube, when the atmospheric pressure is 75 cm of Hg & the tube is inclined at an angle of 60° with the horizontal direction?

A rectangular film of liquid is extended from $(4\text{cm}\times 2\text{cm})$ to $(5\text{cm}\times 4\text{cm})$. If the work done is $3\times {10}^{-4}\text{J}$, then value of the surface tension of the liquid is

For two resistors R1 and R2 connected in parallel find the relative error in their equivalent resistance, if R1=(50+- 2)ohm and R2 = ( 100+-3)

A dart is thrown horizontally with an initial speed of 10 m/s towards point P, the bull's eye on a dart board. It hits at the point Q on the rim, vertically below P, 0.2 seconds later, what is distance PQ?

Why is it not possible to achieve speed more than that of light?

Four charges q, 2q, 3q and 4q are placed at corners A, B, C and D of a square as shown in the figure below. Find the direction of electric field at the centre P of the square.

The ---------- across a Zener diode remains constant.

The magnifying power of a microscope with an objective of 5 mm focal length is 400. The length of its tube is 20 cm. Then the focal length of the eye-piece is [MP PMT 1991]

The position x of a particle varies with time (t) as

x = 3t² – 2t³

The acceleration of the particle will be zero at time

The frequency of a wave of light is $12\times {10}^{14}{S}^{-1}$ The wave number associated with this ligh

A diminished image of an object is to be obtained on a screen 1.0 m from it. This can be achieved by appropriately placing :

The lower end of a capillary tube of radius 1 mm is dipped vertically into mercury. (a) Find the depression of mercury column in the capillary. If the length dipped inside is half the answer of part (a), find the angle made by the mercury surface at the end of the capillary with the vertical. Surface tension of mercury = $0.465N{m}^{-1}$ and the contact angle of mercury with glass= ${135}^{\circ }$.

A pulley fixed to the ceiling carried a thread with bodies of masses $m_1$ and $m_2$ attached to its ends. The masses of the pulley and the thread are negligible and friction is absent. Find the acceleration of the center of mass of this system.

A cylindrical tank has a hole of 1 $c{m}^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 70 $c{m}^3$/sec. then the maximum height up to which water can rise in the tank is

Calculate the minimum energy needed to separate a neutron from a nucleus with Z protons and N neutrons in terms of the masses $M_{Z.N},M_{Z,Z-1}$ and the mass of the neutron.

The radius of a ring is R and its coefficient of liner expansion is $\alpha$. If the temperature of ring increases by $\theta$, then its circumference will increases by

Two parallel rail tracks run north-south. Train A moves north with a speed of 54 km/h and train B moves south with a speed of 90 km/hr. What is the velocity of a monkey running on the roof of the train A against its motion (with its velocity of 18 km/h with respect to the train A) as observed by a man standing on the ground?

The coefficient of static friction between the block of 2 kg and the table shown in figure is $\mu$s = 0.2. what should be the maximum value of m so that the blocks do not move? Take g = 10 $m/s^2$. The string and the pulley are light and smooth.

A resistance thermometer reads R = 20.0 $\Omega$, 27.5 $\Omega$, and 50.0 $\Omega$ at the ice point ($0^{\circ }C$), the steam point (${100}^{\circ }C$) and the zinc point (${420}^{\circ }C$) respectively. Assuming that the resistance varies with temperature as $R_{\theta }=R_0(1+\alpha \theta +\beta {\theta }^2)$, find the values of $R_0,\alpha$ and $\beta$. Here $\theta$ represents the temperature on Celsius scale.

Difference between ideal and non ideal gas.

A spherical drop of capacitance$1\mu F$ is broken into eight drops of equal radius. Then, the capacitance of each small drop is ......

I want to play a prank on my friend and turn his world upside down, at what acceleration must his lift move to make it seem that the world is upside down to him

Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120${}^{\circ }$. The resultant amplitude will be

Point $A$ of rod $AB$ $(l=2\text{m})$ is moving upwards against a wall with velocity $v=2\text{m/s}$. Find angular speed of the rod at an instant when $\theta ={60}^{\circ }$

The macroelement, _______________, is needed for the formation of coenzyme A.

A rod of weight W is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance d from each other. The centre of mass of the rod is at distance x from A. The normal reaction on A is :

A small block of mass ‘m’ is rigidly attached at ‘P to a ring of mass ‘3m’ and radius ‘r’. The system is released from rest at $\theta ={90}^{\circ }$ and rolls without sliding. The angular acceleration of hoop about the center of the ring, just after release is

The focal length of an equiconvex lens is equal to half the radius of curvature of either face. What is the refractive index of the material of the lens?