If the locus of the mid points of the chords of the ellipse , drawn parallel to is then

If ⁿC_r denotes the number of combinations of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_{r –1} + 2 × ⁿC_r equals-

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is .

The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -

An intense stream of water of cross-sectional area strikes a wall at an angle with the normal to the wall and returns back elastically. If the density of water is and its velocity is ,then the force exerted in the wall will be

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line will

Two small particles of equal masses start moving in opposite directions from a point in a horizontal circular orbit. Their tangential velocities are and , respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at , these two particles will again reach the point

In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is

The number of non-negative integral solutions of x + y + z  n, where n  N is -

Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -

If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

The number of rectangles in the adjoining figure is –

Assertion :this equilibrium favours backward direction.
Reason :is stronger base than

A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at is

Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at ,these two particles will again reach The point

The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position are The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are