Class 11th

A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labeled as A → B, A → C and A → D. The change in internal energies during these process are taken as EAB, EAC and EAD and the work done by WAB, WAC and WAD. The correct relation between these parameters are:

A physical quantity z depends on four observables a, c, c and d, as z = (a²b³)/(√cd³). The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h₁, a girl standing at a distance d (point B) from A (see figure) sees it at the angle 45° with respect to the vertical. When the balloon climbs up a future height h₂, it is seen at the angle 60° with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height h₂ is (given tan 30° = 0.5774) :

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is 27/8 w.r.t water, the value of r is.

Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, –4) in this line is:

For all twice differentiable functions f: R → R, with f(0) = f(1) = f'(0) = 0,

If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to:

If the solubility product of AB₂ is 3.20 * 10⁻¹¹ M³, then the solubility of AB₂ in pure water is _____ * 10⁻⁴ mol L⁻¹. [Assuming that neither kind of ion reacts with water]

The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km ) of the summit from the ground is: