A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by y(x, t) = 0.5 sin \left( {{{5\pi } \over 4}x} \right)\, cos(200 $$\pi$$t). What is the speed of the travelling wave moving in the positive x direction ? (x and t are in meter and second, respectively.)

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

In a certain region static electric and magnetic fields exist. The magnetic field is given by $$\overrightarrow{B}=B_0\left(\hat{i}+2\hat{j}-4\hat{k}\right)$$ . If a test charge moving with a velocity $$\overrightarrow{\upsilon }={\upsilon }_0\left(3\hat{i}-\hat{j}+2\hat{k}\right)$$ experiences no force in that region, then the electric field in the region, in SI units, is :

A magnetic dipole in a constant magnetic field has :

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = Io cos ($$\omega$$t). The emf induced in the smaller inner loop is nearly :

A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations which one corresponds to stable equilibrium ?

In a coil of resistance 100 $$\Omega$$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

A circular hole of radius {R \over 4} is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is :

The machine as shown has 2 rods of length1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?

Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is Io as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$. What is the ratio {l \over R} such that the moment of inertia is minimum?

A slender uniform rod of mass M and length $$l$$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $$\theta$$ with the vertical is

At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen (N2 ) at 4 bar. The molar mass of gaseous molecule is :

Among the following, the incorrect statement is :

The major product of the following reaction is :

On treatment of 100 mL of 0.1 M solution of CoCl3. 6H2O with excess AgNO3; 1.2 $$\times$$ 1022 ions are precipitated. The complex is :

[Co2(CO)8] displays :

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pKb of ammonia solution is 4.75, the pH of the mixture will be :