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

Answer any one : If in a triangle, the area of the square drawn on one side is equal to the sum of the areas of the squares drawn on other two sides, then prove that the angle opposite to the first side will be a right angle.

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

A charged particle is free to move in an electric field. Will it always move along the line of force?

For the parabola y^(2)=16x prove that whatever be the value of theta , the line y = (x-11) cos theta - cos 3 theta is always normal to the parabola

A line segment of length (a+b) units moves on a plane in such a way that its end points always lie on the coordinates axes. Suppose that P is a point on the line segment it in the ratio a:b. Prove that the locus of P is an ellipse.

A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the locus of a point, which divides the line into two portions of lenghts a unit and b units, is an ellipse. State the situation when the locus will be a circle.

A perpendicular AD is drawn on BC from the vertex A of the acute Delta ABC . Prove that AC^(2) = AB^(2) +BC^(2) -2BC.BD OR Prove that the square drawn on the opposite side of theacute angle of an acute triangle is equal to the areas of the sum of the squares drawn on its other two sides being subtracted by twice the area of the rectangle formed by one of its sides and the projection of the other side to this side.

A bridge is situted at right-angle to the bank of a river. If one moves away a certain distance from the bridge along this side of the river, the other of the bridge is seen at an angle of 45^(@) and if someone moves a further distance of 400 metres in the same direction, the other end is seen at an angle of 30^(@) . Find the length of the bridge.