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.)

A man looks down on a fish of length 20 cm. His eye is 2 m above the surface of the water (m = 4/3) and the fish is 2 m below the surface as shown in the figure. The ratio of angular width of the fish as seen by the man in presence of water to the in the absence of water is

The reflecting surface is represented by the equation as shown in figure. A ray travelling horizontal becomes vertical after reflection. The co-ordinates of the point of incidence can be

The rectangular box is the place of a spherical mirror. The point S is the position of an object and the point I is the position of its image. The height of the point S from the axis is two times that of point I. The horizontal separation between S and I is equal to 15 cm.

A given mass of a gas expands from the state A to the state B by three paths 1, 2 and 3 as shown in V-T indicator diagram. If respectively be the work done by the gas along the three paths, then

A point-like object of mass 2.0 kg moves along the x-axis with a velocity of + 4.0 m/s. A net horizontal force acting along the x-axis is applied to the object with the force-time profile shown. What is the total work that was done by the force?