2 convergent GP, P and Q have similar sum to infinity. The first and second terms of P are 6 and 6r respectively. The first and second terms of Q are 12 and -12r respectively. Find sum to infinity for both GP.

Given the position vectors,

OA=2i-2j-k, OB= - 2i+3j+6k and OC=2i+6j+5k. Find the value of constant p for which pOA+OC is perpendicular to OB.

Part BCD is a semicircle and part DAB is a segment of a circle with centre O and radius 10cm. Angle BOD is 1.2 radians. Find the perimeter of the metal plate.

Find the term independent of x in the expansion of (2x+1/2x³)⁸

Functions f and g are defined by f:x -->3x+2, g:x-->4x-12. Solve the equation f^-1(x)=gf(x)

The function f is such that f'(x)=3x²-7 and f(3)=5. Find f(x).

The function f is defined for x>0 and is such that f'(x)=2x-2/x². The curve y=f(x) passes through the point P(2,6). Find the equation of the normal to the curve at P.

Solve the following equation for 0^o<Ø<180^o

The curve defined by y=x³-6x²+9x for x greater than or equal 0. A is a max. point and B is the min. point. The normal to the curve at C(2,2) meets the normal to the curve at B at the point D. Find the area of shaded region.