If 3u + 4v =10 nd `S_u = 1.2`. then Var (v) = 0.81

Let a, b, c, d be real numbers in G.P. If u, v, w satisfy the system of equations u + 2v +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4 then show that the roots of the equation (1/u+1/v+1/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+(u+v+w)=0 and 20x^2+10(a-d)^2 x-9=0 are reciprocals of each other.

If (u^2+v^2) prop (x^2 +y^2 ) and uv prop xy then show that (u+v) prop (x+y) when u/v+v/u=x/y +y/x .

Let vec u , vec v and vec w be vectors such that vec u+ vec v+ vec w=0. If | vec u|=3,| vec v|=4 and | vec w|=5, then vec u. vec v+ vec v.vec w+ vec w.vec u is a. 47 b. -25 c. 0 d. 25

The sum of first m terms of the A.P. u_(1), u_(2), u_(3),… is denoted by S_(m) . If u_(m) = 4, u_(4m) = 24 and S_(4m) = 44S_(m) , find u_(1) and m.

If vec u , vec v and vec w are three non-coplanar vectors, then prove that ( vec u+ vec v- vec w) . [ [( vec u- vec v)xx( vec v- vec w)]]= vec u . (vec v xx vec w)

If u, v and w are functions of x, then show that (d)/(dx)(u.v.w) = (du)/(dx) v.w+u. (dv)/(dx).w+u.v(dw)/(dx) in two ways-first by repeated application of product rule, second by logarithmic differentiation.

Two straight lines u=0a n dv=0 pass through the origin and the angle between them is tan^(-1)(7/9) . If the ratio of the slope of v=0 and u=0 is 9/2 , then their equations are

A particle moves in a circle of radius 1.0 cm at a speed given by v = 2.0 t, where v is in cm cdot s^(-1) and t in seconds. Find the radial acceleration of the particle at t = 1 s.