Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :

A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the distance of the point (2, $$-$$3) from the line 3x + 4y = 5, is given by :

If two tangents drawn from a point P to the
parabola y² = 16(x $$-$$ 3) are at right angles, then the locus of point P is :

The equation of the plane passing through the line of intersection of the planes $$\overrightarrow r .\left( {\widehat i + \widehat j + \widehat k} \right) = 1$$ and $$\overrightarrow r .\left( {2\widehat i + 3\widehat j - \widehat k} \right) + 4 = 0$$ and parallel to the x-axis is :