Maths

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an off number of times is:

A scientific committee is to be formed form 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways the committee and be formed is

Rakshit is allowed to select 1 or more books out of (2n + 1) distinct books. If the number of ways in which he may not select all of them is 126, then value of n is __________

Let g(x) = x + 2| - 3|. If a denotes the number of relative minima, b denotes the number of relative maxima and c denotes the product of the zeros. Then the value of (a + 2b - c) is __________

In a geometric progression the ratio of the sum of the first 5 terms to the sum of their reciprocals is 49 and sum of the first and the third term is 35. The fifth term of the G.P. is p, the value of 4p is __________

A circle passes through the points (2, 2) and (9, 9) and touches the x-axis. The absolute value of the difference of possible x-coordinate of the point of contact is __________

Number of ways in which three distinct numbers can be selected between 1 and 20 both inclusive, whose sum is even is __________

If the co-efficient of variation of a distribution is 60 and its standard deviation is 24, then its arithmetic mean is __________

The value of cot^-1(2² + 1/2) + cot^-1(2³ + 1/2²) + ……∞ is equal to tan^-1 λ, then the value of λ is equal to __________

If two of the straight lines given by 3x³ + 3x²y – 3xy² + dy³ = 0, are at right angles, then d is equal to __________