The numbers 1, 2, 3... n are arranged in a random order. The probability that the digits 1, 2, 3,..., k(k<n) appears as neighbours in that order is

Coefficient of x⁴ in (1+x+x²+x³)¹¹ is

The odds against an event is 5 to 2 and the odds in favour of another disjoint event are 3 to 5. Then the probability that one at least of the event will happen is

There are two groups of subjects one of which consists of 5 Science and 3 Engineering subjects and the other consists of 3 science and 5 Engineering subjects. An unbiased die is cost. If 3 or 5 turns up, a subject is selected at random from the first group, otherwise the subject is selected at random from the second group. The probability that an Engineering subjects is selected ultimately is

For k = 1, 2, 3 the box B_K contains k red balls and (k + 1) white balls. Let P(B₁) = 1/2, P(B₂) = 1/3 and P(B₃) =1/6. A box is selected at random and a hall is drawn from it.If a red ball is drawn, Then the probability that it has come from box B₂, is

The equation to the locus of point of intersection of the line y-mx=√(4m²+3), my+x = √(4+3m²) is

Three persons A, B, C in order toss a die. The persons who first throws 1 or 2wins.The ratio of the probabilities of their success is

The value of k if (1,2), (k,-1) are conjugate points with respect to the ellipse 2x²+3y²=6 is

At a selection, the probability of selection of A is 1/7 and that of B is 1/5.The probability that both of them would not be selected is

The eccentricity of the ellipse 25x²+9y²-150x-90y+225=0 is