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

The corner points of the feasible region for an L.P.P. are \((2,0)\), \((7,0)\), \((4,5)\) and \((0,3)\), and \(z = 2x+3y\) is the objective function. The difference of the maximum and minimum values of \(z\) is:

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

The value of \(\hat{i}\cdot(\hat{j}\times\hat{k})+\hat{j}\cdot(\hat{i}\times\hat{k})+\hat{k}\cdot(\hat{i}\times\hat{j})\) 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 \(\cos\alpha, \cos\beta, \cos\gamma\) are the direction cosines of a vector \(\vec{a}\), then the value of \(\cos2\alpha+\cos2\beta+\cos2\gamma\) is equal to:

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

\(\int\tan x(\sec x-\tan x)\,dx =\)

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…