The value of \(x\), for which the area of the floor of the auditorium is maximum, is:

A biased dice is thrown once. If X denotes the number appearing on it, it has the probability distribution: x | 1 | 2 | 3 | 4 | 5 | 6 P(X = x) | k | k/2 | 2k | 8k² | 1 - 5k | k/2 where k > 0. Then consider the following statements: A. P(X = 3) B. P(X ≤ 2) C. P(X ≥ 5) D. P(X = 4)…

A line \(L: \frac{x-2}{1} = \frac{y-3}{2} = \frac{z-1}{-1}\) is perpendicular to a plane \(P\) which passes through the point \((4,3,9)\). If the mirror image of the point \(S\) on the line \(L\) in the plane \(P\) is \((2,3,1)\), then the co-ordinates of the point \(S\) are:

From the passage: A ball is thrown upwards from the plane surface of the ground. Suppose...

The equation of the plane passing through the points \(A\), \(B\) and \(C\) is:

If \(A\) and \(B\) are two independent events with \(P(A) = \frac{3}{5}\) and \(P(B) = \frac{4}{9}\), then \(P(A'\cap B')\) is equal to

The equation of the plane passing through the point \((0,7,-7)\) and containing the line \(\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z+2}{1}\) is:

If events A and B are independent, then identify the correct statement (A) A and B must be mutually exclusive (B) The sum of their probabilities must be equal to 1 (C) \(P(A)\cdot P(B) = P(A\cap B)\) (D) \(A'\) and \(B'\) are also independent Choose the correct answer from the op…

The distance between the point \((3,4,5)\) and the point where the line \(\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}\) meets the plane \(x+y+z=17\) is

The point of intersection of the lines \(\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}\) and \(\frac{x-4}{5} = \frac{y-1}{2} = z\) is