In a group of children, 35 play football out of which 20 play footballs only, 22 play hockey; 25 play cricket out of which 11 play cricket only. Out of these 7 play cricket and football but bot hockey, 3 play football and hockey but not cricket and 12 play football and cricket both.
How many plays hockey only ?

In the evaporation of water, the entropy:

The enthalpy changes at 298 K in successive breaking of O-H bonds of water are
and The bond enthalpy of O-H bond is:

Energy required to dissociate 4 g of gaseous hydrogen into free gaseous atoms is 208 kcal at '250 C The bond energy of H-H bond will be:

A vector of magnitude 10 and perpendicular to and is

The vectors and have their initial points at (1, 1). The value of so that the vectors terminate on one straight line is

The adjacent sides of a parallelogram are and where and are the usual unit vectors along the positive directions of x and y-axes respectively. Then the angle between the diagonals is

If vector and are the sides of a triangle ABC, then the length of the median AM, is

____________ pairs of parallel lines are there in regular hexagon?

Hexagon is a closed figure which has six sides and six corners. Given is a regular hexagon, which means it has equal interior angles and equal side lengths. So, there will be 3 pairs of parallel lines in a regular hexagon.
>>>Hence, we can say that the Hexagon has 3 parallel pairs.

Statement–I : In gravity free space, the liquid in a capillary tube will rise to infinite height
Statement–II : In the absence of gravity , there will be no force to prevent the rise of liquid due to surface tension

Statement–I : The velocity of horizontal flow of a ideal liquid is smaller where pressure is large and vice versa. Statement–II : According to Barnoullis theorem for the stream line flow of an ideal liquid, the total energy per unit mass remains constant

A concave mirror of focal length 2 cm is placed on a glass slab as shown in the figure. Then the image of object O formed due to reflection at mirror and then refraction by the slab :

In the figure shown a point object O is placed in air. A spherical boundary separates various media of radius of curvature 1.0 m. AB is principal axis. The refractive index above AB is 1.6 and below AB is 2.0. The separation between the images formed due to refraction at spherical surface is:

A wooden block with mass 2.0 kg is moving up an inclined surface At point S it has a speed of 8 m/sec; the block comes to a halt at point P (see the figure which is a vertical cross-section). The friction coefficient m between the block and the inclined surface is 0.25 (assume that g = 10 and that the kinetic and the static friction coefficients are the same).

A fish, F in the pond, is at a depth of 0.8 m from water surface and is moving vertically upwards with velocity At the same instant, a bird B is a height of 6m from water surface and is moving downwards with velocity At this instant both are on the same vertical lines as shown in the Figure. Which of the following statement(s) is(are) correct?
i) Height of B, observed by F (from itself) is equal to 5.30 m.
ii) Depth of F, observed by B (from itself) is equal to 6.60 m.
iii) Velocity of B, observed by F (relative to itself) is equal to
iv) Velocity of F, observed by B (relative to itself) is equal to

What is the length of the image of the rod in mirror, according to the observer in air? (The refractive index of liquid is m.)