Mathematics Tes...

A line passes through the points (6, –7, –1) and (2, –3, 1). If the angle which the line makes with the positive direction of the x-axis is acute, then the direction cosines of the line are

The equation of the line through the point (2, 1, 1) and the intersection of the lines 2x – y – 4 = 0 = y + 2z and x + 3z – 4 = 0 = 2x + 5z – 8 is

The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through the point (1, 1, 0) is:

Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/8. If all hit at the target independently, then the probability that the target would be hit is

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is

Out of 11 consecutive natural numbers, if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:

Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?

A random variable has the following probability distribution:

The value of k is

If (1 + 3p)/3, (1 – p)/4 and (1 – 2p)/2 are the probabilities of three mutually exclusive events, then the set of all values of p is

The mean and variance of a binomial distribution are 4 and 2, respectively. What is the probability of two successes?