Class 11th

An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to 1/10th of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is:

A particle of mass m with an initial velocity ui collides perfectly elastically with a mass 3m at rest. It moves with a velocity vj after collision, then v is given by

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 ω rads⁻¹. The difference in the height, h (in cm) of liquid at the centre of vessel and at the will be:

A bead of mass m stays at point P(a,b) on a wire bent in the shape of a parabola y = Cx² and rotating with angular speed ω (see figure). The value of ω is (neglect friction)

If |x| < 1, |y| < 1 and x y, then the sum to infinity of the following series (x+y) + (x+xy+y) + (x+xy+xy+y) + . is

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.

The mass density of a spherical galaxy varies as K/r over a large distance 'r' from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:

If lim(x→1) (x+x²+x³+.+xⁿ-n)/(x-1) = 820, (n∈N) then the value of n is equal to.

A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre 'O' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required 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.