A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity v m/s. If it is to climb the inclined surface then v should be:

A rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle ' ' q made by the hinged upper half with the vertical is

A disc of mass M and radius R rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is v, the height to which the disc will rise will be :–

The reaction of with HBr gives

The line parallel to the x-axis and passing through the intersection of the lines  where  is

In this question, we have to find the lines where it lies and what’s its distance from x-axis. If u=ax1+by1+c1=0 and v=ax2+by2+c2=0 are two intersecting lines, then the equation u + kv =0 represents a family of lines. Remember the family of lines

Distance between the two parallel lines and is

When propionic acid is treated with aqueous sodium bicarbonate  is liberated. The ‘C’ of  CO₂ comes from

The following compound is used as

 In the reaction, product P is

The compound X in the reaction
 is

The major organic product formed from the following reaction

  The compound (X) is

The product of acid hydrolysis of P and Q can be distinguished by

 Major Product is

The appropriate reagent for the transformation

; Compound on hydrolysis gives[Kerala CET 2005]