Mathematics Tes...

If \(\alpha\) is a root of \(x^{4}=1\) with negative principal argument, then principal argument of \(\omega\) where

The integrating factor of the differential equation  is given by

If \(x, y, z\) are integers in \(A . P,\) lying between 1 and \(9,\) and \(x 51, y 41\) and \(z 31\) are three digit numbers then the value of \(\left|\begin{array}{lll}5 & 4 & 3 \\ x 51 & y 41 & z 31 \\ x & y & z\end{array}\right|\) is

\(A\) and \(B\) are two independent events such that \(\mathrm{PA} \cup \mathrm{B}^{\prime}=0.8\) and \(\mathrm{PA}=0.3 .\) Then, \(P(B)\) is

Assertion [A]: From 0 to π, area of region bounded by y = sin⁡x and x -axis is greater then the area bounded by y = sin²⁡x, x -axis.

Let \(A\) and \(B\) be two fixed points and \(P\), another point in the plane, moves in such a way that \(k_{1} P A+k_{2} P B=k_{3}\) where \(k_{1}, k_{2}\) and \(k_{3}\) are real constants. Then which one of the following is not the locus of \(P\) -