Mathematics Tes...

If \(A=\left[\begin{array}{rrr}x & 3 & 2 \\ -3 & y & -7 \\ -2 & 7 & 0\end{array}\right]\) and \(A=-A^{T},\) then \(x+y\) is equal to

If \(A=\left[\begin{array}{rrr}\cos \frac{\pi}{5} & \sin \frac{\pi}{5} \\ -\sin \frac{\pi}{5} & \cos \frac{\pi}{5}\end{array}\right],\) and \(B=A+A^{2}+A^{3}+A^{4},\) which of the following statements is/are correct?

What is the circumradius of a triangle with length of sides as 6 units, 8 units and 10 units?

Let f(x) = sin x + cos x. Then,

The number of subsets of the set A = {a₁, a₂, …, a_n} which contain even number of elements is

A line 'm' is drawn as reflection of the line \({ }^{\prime} \ell^{\prime}\) on the \(\mathrm{x}\) -axis as shown in the figure given below. What will be the slope of line 'm'? (It is given that the reflection is about the x-axis.)

If \(\lim _{x \rightarrow 0}\left(1+x \log \left(1+b^{2}\right)\right)^{1 / x}=2 b \sin ^{2} \theta, b / 0\) and \(\theta \in[-\pi, \pi],\) then the value of \(\theta\) is