The radius of two concentric circle are 13 cm and 8 cm. AB is a diameter of the bigger circle. BD is tangent to the smaller circle touching it at D. The length AD is [Figure: two concentric circles with centre O; AB is a diameter of the bigger circle; BD is drawn from B touching the smaller circle at D and meeting the bigger circle again at E; A is joined to D and E.]

ABC is right angled triangle at C. Let BC = a, CA = b and AC = c and let p be the length of perpendicular from C on AB, then cp is equal to

The minimum value of \((2\sin^2\theta + 3\cos^2\theta)\) is

The odd term out in the series 15, 16, 34, 105, 424, 2124, 12756 is

If the \(m^{th}\) term of an arithmetic progression is \(\frac{1}{n}\) and \(n^{th}\) term is \(\frac{1}{m}\), then \((mn)^{th}\) term of the progression is

At what angle the hands of a clock are inclined at 15 minutes past 5 ?

If points \((t, 2t)\), \((-2, 6)\) and \((3, 1)\) are collinear, then t is equal to

In a flat race, A beats B by 15 m and C by 29 m. When B and C run over the same course together, B wins by 15 m. The length of the course is

One cubic meter of iron weighs 7.800 kg. The weight of iron in a pipe of length 4 m, whose interior and exterior diameters measure 10 cm and 12 cm respectively, is nearly