Mathematics Tes...

If \({x}+{iy}=\frac{3+4 {i}}{2-{i}}\) where \({i}=\sqrt{-1}\), then what is the value of y?

If the function \(f\) defined by \(f(x)=\left\{\begin{array}{cl}\lambda x, & \text { if } x \leq \frac{\pi}{2} \\ \cos 2 x, & \text { if } x>\frac{\pi}{2}\end{array}\right\}\) is continuous at \(x=\frac{\pi}{2}\), then the value of \(\lambda\) is:

If \(\frac{e^{x}}{1-x}=B_{0}+B_{1} x+B_{2} x^{2}+\ldots+B_{n} x^{n}+\ldots\), then the value of \(B_{n}-B_{n-1}\) is:

Let \(A(\vec{a}), B(\vec{b}), C(\vec{c})\) be the vertices of the triangle \(A B C\) and let \(D E F\) be the midpoints of the sides \(B C, C A, A B\) respectively. If \(P\) divides the median \(AD\) in the ratio \(2: 1\) then the position vector of \(P\) is:

The number of solutions of the equation \(\sin ^{-1} x-\cos ^{-1} x=\sin ^{-1}\left ( \frac{1}{2}\right)\) is:

A straight line with direction cosines \(\langle 0,1,0\rangle\) is:

The coefficient of of the middle term in the binomial expansion in \(x\) of \((1+\beta x)^{4}\) and of \((1-\beta x)^{6}\) is same, if \(\beta\) equals:

Find the value of\(\sin [(n+1) A] \sin [(n+2) A]+\cos [(n+1) A] \cos [(n+2) A]\)

\(ABCD\) is a quadrilateral, \(E\) is the point of intersection of the line joining the midpoints of the opposite sides. If \(O\) is any point and \(\overrightarrow{ OA }+\overrightarrow{ OB }+\overrightarrow{ OC }+\) \(\overrightarrow{ OD }=x \overrightarrow{O E}\), then \(x\) is equal to: