Mathematics Tes...

If \(\mathrm{i} \mathrm{z}^{3}+\mathrm{z}^{2}-\mathrm{z}+\mathrm{i}=0\) then \(|\mathrm{z}|\) equal to:

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:

If \(A=\left[\begin{array}{ll}0 & 5 \\ 0 & 0\end{array}\right]\) and \(f(X)=1+x+x^2+\ldots .+x^{16}\), then \(f(A)=?\)

In An A.P. twenty fifth term is 70 more than to fifteen term. Find the common differences.

If \(a, b, c\) are real numbers, then the value of the determinant

\(\left|\begin{array}{lll}1-a & a-b-c & b+c \\ 1-b & b-c-a & c+a \\ 1-c & c-a-b & a+b\end{array}\right|\)

Let \(\vec{b}=4 \hat{i}+3 \hat{j}\) and \(\vec{c}\) be two vector perpendicular to each other in the \(x y-\) plane. Then a vector in the same plane having projections 1 and 2 along \(\vec{b}\) and \(\vec{c}\), respectively, is:

Which one of the following is correct in respect of the function f : R → R⁺ defined as f(x) = |x+1|?

If \((1+i)(1+2 i)(1+3 i) \ldots(1+n i)=\alpha+i \beta\) then \(2.5 .10 \ldots\left(1+n^{2}\right)\):

A _________ is a simple closed curve all of whose points are at the same distance from a fixed point.