The area enclosed between the curves $$y^2=x$$ and $$y=\left|x\right|$$ is :

Two lenses of power $$-15$$ $$D$$ and $$+5$$ $$D$$ are in contact with each other. The focal length of the combination is

The resistance of a wire is $$5$$ ohm at $$50^{\circ }C$$ and $$6$$ ohm at $$100^{\circ }C.$$ The resistance of the wire at $$0^{\circ }C$$ will be

A circular disc of radius $$R$$ is removed from a bigger circular disc of radius $$2R$$ such that the circumferences of the discs coincide. The center of mass of the new disc is $$\alpha R$$ form the center of the bigger disc. The value of $$\alpha$$ is

Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate ?

If in a $$p$$-$$n$$ junction diode, a square input signal of $$10$$ $$V$$ is applied as shown Then the output signal across $$R_L$$ will be

Two springs, of force constant $$k_1$$ and $$k_2$$ are connected to a mass $$m$$ as shown. The frequency of oscillation of the mass is $$f.$$ If both $$k_1$$ and $$k_2$$ are made four times their original values, the frequency of oscillation becomes

A particle of mass $$m$$ executes simple harmonic motion with amplitude a and frequency $$v.$$ The average kinetic energy during its motion from the position of equilibrium to the end is

A point mass oscillates along the $$x$$-axis according to the law $$x=x_0\cos \left(\omega t-\pi /4\right).$$ If the acceleration of the particle is written as $$a=A\cos \left(\omega t+\delta \right),$$ then

The displacement of an object attached to a spring and executing simple harmonic motion is given by $$x=2\times 10^{-2}$$ $$cos$$ $$\pi t$$ metre. The time at which the maximum speed first occurs is

A particle is projected at $$60^{\circ }$$ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

A $$2$$ $$kg$$ block slides on a horizontal floor with a speed of $$4m/s.$$ It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is $$15N$$ and spring constant is $$10,000$$ $$N/m.$$ The spring compresses by

In an $$a.c.$$ circuit the voltage applied is $$E=E_0\sin \omega t.$$ The resulting current in the circuit is I = {I_0}\sin \left( {\omega t - {\pi \over 2}} \right). The power consumption in the circuit is given by

If $$M_O$$ is the mass of an oxygen isotope $${}_8{O}^{17}$$ , $$M_p$$ and $$M_N$$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is

In gamma ray emission from a nucleus

The half-life period of a ratio-active element $$X$$ is same as the mean life time of another ratio-active element $$Y.$$ Initially they have the same number of atoms. Then

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

If $$C_p$$ and $$C_v$$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

One end of a thermally insulated rod is kept at a temperature $$T_1$$ and the other at $$T_2$$. The rod is composed of two sections of length $$L_1$$ and $$L_2$$ and thermal conductivities $$K_1$$ and $$K_2$$ respectively. The temperature at the interface of the two section is

When a system is taken from state $$i$$ to state $$f$$ along the path iaf, it is found that $$Q=50$$ cal and $$W=20$$ $$cal$$. Along the path $$ibf$$ $$Q=36$$ $$cal.$$ $$W$$ along the path $$ibf$$ is