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 options given below

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 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:

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

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

If \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector, then the value of \(x\) is:

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:

The area of the parallelogram whose adjacent sides are \(\hat{i}+\hat{k}\) and \(2\hat{i}+\hat{j}+\hat{k}\) 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)…