The normal to the curve x = a(1 + cos $$\theta$$), $$y=a\sin \theta$$ at $${}^{\prime }{\theta }^{\prime }$$ always passes through the fixed point

The area of the region bounded by the curves $$y=\left|x-2\right|,x=1,x=3$$ and the $$x$$-axis is :

Which one of the following represents the correct dimensions of the coefficient of viscosity?

A plano convex lens of refractive index $$1.5$$ and radius of curvature $$30$$ $$cm$$. Is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of size of the object

A light ray is incident perpendicularly to one face of a $$90^{\circ }$$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $$45^{\circ }$$, we conclude that the refractive index $$n$$

The resistance of the series combination of two resistances is $$S.$$ When they are jointed in parallel the total resistance is $$P.$$ If $$S=nP$$ then the Minimum possible value of $$n$$ is

An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of {4 \over 3} and {2 \over 3}, then the ratio of the current passing through the wires will be

The total current supplied to the circuit by the battery is

In a meter bridge experiment null point is obtained at $$20$$ $$cm$$, from one end of the wire when resistance $$X$$ is balanced against another resistance $$Y.$$ If $$X<Y$$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $$4$$ $$X$$ against $$Y$$

Thermistors are usually made of

The electrochemical equivalent of a metal is $$3.35109^{-7}$$ $$kg$$ per Coulomb. The mass of the metal liberated at the cathode when a $$3A$$ current is passed for $$2$$ seconds will be

The thermo $$emf$$ of a thermocouple varies with temperature $$\theta$$ of the hot junction as $$E=a\theta +b{\theta }^2$$ in volts where the ratio $$a/b$$ is $$700^{\circ }C.$$ If the cold junction is kept at $$0^{\circ }C,$$ then the neutral temperature is

A material $${}^{\prime }{B}^{\prime }$$ has twice the specific resistance of $${}^{\prime }{A}^{\prime }.$$ A circular wire made of $${}^{\prime }{B}^{\prime }$$ has twice the diameter of a wire made of $${}^{\prime }{A}^{\prime }$$. Then for the two wires to have the same resistance, the ratio {l \over B}/{l \over A} of their respective lengths must be

The Kirchhoff's first law $$\left(\sum i=0\right)$$ and second law $$\left(\sum iR=\sum E\right),$$ where the symbols have their usual meanings, are respectively based on

A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s}^{-1}.$$ The man holding it can exert a maximum force of $$144$$ $$N$$ on the gun. How many bullets can he fire per second at the most?

A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F.$$ The work done in stretching is

Spherical balls of radius $$R$$ are falling in a viscous fluid of viscosity $$\eta$$ with a velocity $$v.$$ The retarding viscous force acting on the spherical ball is

If two soap bubbles of different radii are connected by a tube

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

A piece of copper and another of germanium are cooled from room temperature to $$77K,$$ the resistance of