The angle between two linear transmembrane domains is defined by following vectors $\mathrm{a} = \hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}} \mathrm{and} \mathrm{b} = \hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}$

• cos^-1 $\left(\frac{1}{3}\right)$

• cos^-1 $\left(\frac{-1}{3}\right)$

• sin^-1 $\left(\frac{-1}{3}\right)$

• sin^-1 $\left(\frac{1}{3}\right)$

The distance x (in µm) covered by a molecule starting from point A at time t = 0 and stopping at another point B in given by the equation  $\mathrm{x} = {\mathrm{t}}^2 \left(2 - \frac{\mathrm{t}}{3}\right)$ The distance between A and B ( in μm) is closed to

• 10.7

• 20.7

• 40.7

• 50.7

A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as shown in figure

If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

• $\frac{10 \mathrm{F}}{7 \mathrm{m}}$

• $\frac{\mathrm{F}}{2 \mathrm{m}}$

• $\frac{3 \mathrm{F}}{7 \mathrm{m}}$

• $\frac{7 \mathrm{F}}{2 \mathrm{m}}$

The density of a rod having length l varies as ρ = c + dx, where x is the distance from the left end. The centre of mass is     

• $\frac{3 \mathrm{cl} + 2 \mathrm{D} {\mathrm{l}}^2}{3 \left( 2\mathrm{c} + \mathrm{D} \mathrm{l} \right)}$

• $\frac{2 \mathrm{cl} + 3\mathrm{D} {\mathrm{I}}^2}{2 \left( 4\mathrm{c} + 8\mathrm{I} \right)}$

• $\frac{2 \mathrm{cl} + 3 {\mathrm{DI}}^2}{3 \left(2\mathrm{c} + \mathrm{I}\right)}$

• $\frac{\mathrm{cl} + {\mathrm{DI}}^2}{2 \left( 2 \mathrm{c} + \mathrm{DI} \right)}$

One end of a massless spring of constant 100 N /m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the mass is made to rotate at angular velocity of 2 rad/s, then elongation of spring is

• 0.1 m

• 10 cm

• 1 cm

• 0.01 cm

A block slides down on an incline of angle 30° with an acceleration g/4 . Find the kinetic 4 friction coefficient.

• 1 / 2√2

• 0.6

• 1 / 2√3

• 1 / √2

 A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass m and of equal to radius. The centre of the ring is at a distance $\sqrt{3}$a from the centre of the sphere. The gravitational force (Fl exerted by the sphere on the ring is

• $\frac{\sqrt{3} \mathrm{G} \mathrm{Mm}}{8 {\mathrm{a}}^2}$

• $\frac{2 \mathrm{G} \mathrm{M} \mathrm{m}}{3 {\mathrm{a}}^2}$

• $\frac{7 \mathrm{G} \mathrm{Mm}}{\sqrt{2} {\mathrm{a}}^2}$

• $\frac{3 \mathrm{G} \mathrm{Mm}}{{\mathrm{a}}^2}$

8.

A projectile is fired with a velocity u at angle θ with the ground surface. During the motion at any time it is making an angle a with the ground surface. The speed of particle at this time will be

• ucosθ sec$\mathrm{\alpha }$

• ucosθ tan$\mathrm{\alpha }$

• u² cos²$\mathrm{\alpha }$ sin²$\mathrm{\alpha }$

• usinθ.sin$\mathrm{\alpha }$

Water level is maintained in a cylindrical vessel upto a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?

• $\mathrm{h} = \frac{\mathrm{H}}{2}$

• $\mathrm{h} = \frac{3\mathrm{H}}{2}$

• $\mathrm{h} = \frac{2 \mathrm{H}}{3}$

• h = $\frac{3}{4}\mathrm{H}$

A pendulum having a bob of mass m is hanging in a ship sailing along the equator form east to west. When the strip is stationary with respect to water, the tension in the string is T₀, The difference between T₀ and
earth attraction on the bob, is

• $\frac{\mathrm{mg} + \mathrm{m} {\mathrm{\omega }}^2 \mathrm{R}}{2}$

• $\frac{{\mathrm{m\omega }}^2 \mathrm{R}}{3}$

• $\frac{{\mathrm{m\omega }}^2 \mathrm{R}}{2}$

• mω² R