D.
If x and y are acute angles such that cos(x) + cos(y) = sin(x) + sin(y) = , then sin(x + y) equals to
If the point P(1, 3) undergoes the following transformations successively.
(i) Reflection with respect to the line y = x.
(ii) Translation through 3 units along the positive direction of the X-axis.
(iii) Rotation through an angle of about the origin in the clockwise direction.Then, the final position of the point P is
If the mean and variance of a binomial variate X are 8 and 4 respectively, then P(X < 3) equals to
A random variable X has the probability distribution given below.
X | 1 | 2 | 3 | 4 | 5 |
P(X = x) | K | 2K | 3K | 2K | K |
Its variance is
A candidate takes three tests in succession and the probability of passing the first test is p. The probability of passing each succeeding test is p or according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, is
p2(2 - p)
p(2 - p)
p + p2 + p3
p2(1 - p)
A six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be 7. The probability that the number 3 has appeared atleast once, is