If a leaf of a book is folded so that one corner moves along an opposite side, then prove that the line of crease will always touch parabola.

The lower corner of a leaf in a book is folded over so as to reach the inner edge of the page. Show that the fraction of the width folded over when the area of the folded part is minimum is 2//3.

If a vertex of a square is at the origin and its one side lies along the line 4x+3y-20=0, then the area of the square is

If a triangle is inscribed in a n ellipse and two of its sides are parallel to the given straight lines, then prove that the third side touches the fixed ellipse.

Prove that for thetainR , the line y=(x-11)costheta-cos3theta is always normal to the parabola y^(2)=16x .

If two consecutive angles of cyclic quadrilateral are congruent, then prove that one pair of opposite sides is congruent and other is parallel.

Read the following paragraph carefully and answer the following: Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are appliying a force towards it. The force stops acting on it if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that the directionn of its velocity at that instant of time. You may recall a similar activity in which a 5 rupee coin kept on a rotating circular disc flies off the disc along the tangent to the disc. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. The impressed force on the same is in which direction?

Read the following paragraph carefully and answer the following: Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are appliying a force towards it. The force stops acting on it if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that the directionn of its velocity at that instant of time. You may recall a similar activity in which a 5 rupee coin kept on a rotating circular disc flies off the disc along the tangent to the disc. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. What happens if the string is released?

Read the following paragraph carefully and answer the following: Tie a stone to one end of a string. Take the other end in your hand and rotate the string so that the stone moves along a circle. As long as we are holding the string, we are pulling the stone towards us i.e. towards the centre of the circle and are appliying a force towards it. The force stops acting on it if we release the string. In this case, the stone will fly off along a straight line which is the tangent to the circle at the position of the stone when the string is released, because that the directionn of its velocity at that instant of time. You may recall a similar activity in which a 5 rupee coin kept on a rotating circular disc flies off the disc along the tangent to the disc. Thus, a force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force. What is centripetal force?

Two concave mirrors of equal radii of curvature R are fixed on a stand facing opposite directions. The whole system has a mass m and is kept on a frictionless horizonal table. Two blocks A and B, each of mass m, are placed on the two side of the stand. At t=0, the separation between A and the mirrors is 2R and also the separation between B and the mirrors is 2R. The block B moves towards the mirror at a speed v. All collisions which take place are elastic. Taking the original position of the mirrors stand system to be x=0 and X -axis along AB, find the position of the image of A and B at t= a.) R/(upsilon) , b.) (3R)/(upsilon) c.) (5R)/(upsilon)