The minimum energy required to launch a satellite of mass \(m\) from the surface of earth of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2 R\) from the surface of the earth is:

If \(\theta _1\) and \(\theta_2\) be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip \(\theta\) is given by 

The angle of incidence for a ray of light at a refracting surface of a prism is \(45^o  \). The angle of prism is \(60^o \) . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are 

For a plane electromagnetic wave propagating in \(x\)-direction, which one of the following combination gives the correct possible directions for electric field \((E)\) and magnetic field \((B)\) respectively?

The bulk modulus of a spherical object is '\(B\)'. If it is subjected to uniform pressure '\(P\)', the fractional decrease in radius is

dimensions of stress are 

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If \(l\) is the current in the circuit, then in the gap between the plates:

5 moles of liquid X and 10 moles of liquid Y make a solution having a vapour pressure of 70 torr. The vapour pressures of pure X and Y are 63 torr and 78 torr respectively. Which of the following is true regarding the described solution?

Given below are two statements: Statement \(I\): Mitochondria and chloroplasts both double membranes bound organelles. Statement \(II\): Inner membrane of mitochondria is relatively less permeable, as compared chloroplast. In the light of the above statements, choose the mis appropriate answer from the options given below:

An energy of \(484\,J\) is spent in increasing the speed of a flywheel from \(60\,rpm\) to \(360\,rpm\). The moment of inertia of the flywheel is \(.............\,kg - m ^2\)

Which of the following statements is correct?

Dalton's Atomic theory could not explain which of the following?

Following solutions were prepared by mixing different volumes of \(NaOH\) and \(HCl\) of different concentrations \((a)\;\;60\; \mathrm{mL} \frac{\mathrm{M}}{10}\; \mathrm{HCl}+40 \;\mathrm{mL} \frac{\mathrm{M}}{10} \;\mathrm{NaOH}\) \((b)\;\;55\; \mathrm{mL} \frac{\mathrm{M}}{10}\; \mathrm{HCl}+45 \;\mathrm{mL} \frac{\mathrm{M}}{10} \;\mathrm{NaOH}\) \((c)\;\;75\; \mathrm{mL} \frac{\mathrm{M}}{5}\; \mathrm{HCl}+25 \;\mathrm{mL} \frac{\mathrm{M}}{5} \;\mathrm{NaOH}\) \((d)\;\;100\; \mathrm{mL} \frac{\mathrm{M}}{10}\; \mathrm{HCl}+100 \;\mathrm{mL} \frac{\mathrm{M}}{10} \;\mathrm{NaOH}\) \(pH\) of which one of them will be equal to \(1\) ?