Mathematics Tes...

Let \(f(x)\) be a continuous and differentiable function satisfying \(f(x+y)=f x f(y)\) for all \(x, y \in R\). If \(f(x)\) can be expressed as \(f(x)=1+x p(x)+x^{2} q(x)\) where \(\lim x \rightarrow 0 p x=a\) and \(\lim x \rightarrow 0 q x=b,\) then \(b\) is

The plane \(x+2 y-z=4\) cuts the sphere \(x^{2}+y^{2}+z^{2}-x+z-2=0\) in a circle of radius

Forces acting on a particle have magnitude 5,3 and 1 unit and act in the direction of the vectors \(6 \hat{i}+2 \hat{j}+3 \hat{k}, 3 \hat{i}-2 \hat{j}+6 \hat{k}, 3 \hat{i}-2 \hat{j}+6 \hat{k}\) and \(2 \hat{i}-3 \hat{j}-6 \hat{k}\) respectively. They remain constant while theparticle is displaced from the points \(A(2,-1,-3)\) to \(B(5,-1,1)\). The work done is

The value of \(\sin \left[2 \cos ^{-1} \frac{\sqrt{5}}{3}\right]\) is

The equation of the sphere concentric with the sphere \(2 x^{2}+2 y^{2}+2 z^{2}-6 x+2 y-4 z=1\) and double its radius is

Find the first derivative of \(\frac{2}{x+1}-\frac{x^{2}}{3 x-1}\)

The argument of the complex number\(\frac{13-5 i}{4-9 i}\) is