The number of integral values of k for which the line, 3x + 4y = k intersects the circle,
x² + y² – 2x – 4y + 4 = 0 at two distinct points is ______.

If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.

Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source ($$\lambda $$ = 632.8 nm). The distance between the screen and the slits is 100 cm. If a bright fringe is observed on a screen at a distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close is

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $$\omega $$ rad s^–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :