Mathematics Tes...

If the probability that exactly one of the three event occurs is given by S 1 - α S 2 + β S 3, then the value of α 2 + β 2 is _____.

Tangent drawn to the circle at \(P(1, \sqrt{3})\) on the circle \(x^{2}+y^{2}=4,\) which meets the transverse axis of hyperbola \(\frac{x^{2}}{4}-\frac{y^{2}}{1}=1\) at \(Q .\) From \(Q\) a line is drawn parallel to conjugate axis, which cuts the hyperbola at \(R\) above the \(x\) axis, then \(P R\) equals -

The point on the curve \(y^{2}=x,\) the tangent at which makes an angle \(b\) with \(x\) -axis is

Let \(f\) be a non-negative function defined on the interval [0,1] , If \(\int 0 \times 1-(f(t)) 2 d t=\int 0 x f(t) d t, 0 \leq x \leq 1\), and \(f(0)=0,\) then:

If the foci and vertices of an ellipse be $\left(\pm 1,0\right)$ and $\left(\pm 2,0\right)$ then the minor axis of the ellipse is

Negation of "Paris is in France and London is in England" is