Evaluate $\int{{{\sec }^{2}}\theta }d\theta $

The distance travelled by a particle from a fixed point is given as $s={{t}^{3}}-{{t}^{2}}-t+5$find the minimum distance that the particle can cover from the fixed point.

What is the value of x will make the function $x(4-x)$ a maximum?

If $s=(2+3t)(5t-4),\text{ find }\frac{ds}{dt}$ when t = $\tfrac{4}{5}$secs.

If $y=3\cos 4x,\text{ }\frac{dy}{dx}$ equals

A cliff on the bank of a river is 300 metres high. If the angles of depression of a point on the opposite side of the river is 60^o. Find  the width of the river.

Find the value of sin45^o – cos 30^o

What is the value of r, if the distance between the point(4, 2) and (1,r) is 3 units

What is the value of P if the gradient of the line joining ( – 1,p) and (p, 4) is $\tfrac{2}{3}$

What is the locus of the mid-point of all chords of length 6cm with a circle of radius 5cm and with centre O