Mathematics Tes...

If A = {x ϵ Z : x³ – 1 = 0} and B = {x ϵ Z: x² + x + 1= 0}, where Z is set of complex numbers, then what is A ∩ B equal to?

Let the locus of the centre \((\alpha, \beta), \beta>0\), of the circle which touches the circle \(x^2+(y-1)^2=1\) externally and also touches the \(x\)-axis be \(L\). Then the area bounded by \(L\) and the line \(y=4\) is:

Let the curve \(C\) be the mirror image of the parabola \(y^{2}=4 x\) with respect to the line \(x+y+4=0\). If \(A\) and \(B\) are the points of intersection of \(\mathrm{C}\) with the line \(\mathrm{y}=-5\), then the distance between \(\mathrm{A}\) and \(\mathrm{B}\) is:

The point of intersection of diagonals of a square \(A B C D\) is at the origin and one of its vertices is at \(A(4,2)\). What is the equation of the diagonal \(B D ?\)

If \(A =\left[\begin{array}{cc}\cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha\end{array}\right]\) then \(AA ^{T}\) is equal to: (where \(A ^{ T }\) is the transpose of \(\left.A \right)\)

The length of the perpendicular drawn from the origin to the plane \(2 x-3 y+\) \(6 z-42=0\) is:

What is the value of \(\lim _{x \rightarrow 0} \frac{\sqrt{4+x}-2}{3 x}\)?

If \(\sin ^{-1} \frac{2 p}{1+p^{2}}-\cos ^{-1} \frac{1-q^{2}}{1+q^{2}}=\tan ^{-1} \frac{2 x}{1-x^{2}},\) then what is \(x\) equal to?

What are the direction ratios of a normal to the plane?

If \(p, q\) and \(r\) are the intercepts made by the plane on the coordinate axes respectively, then what is \((p+q+r)\) equal to?