Maths

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 __________

The value of 2 cos 20º cos 40° cos 80° is equal to __________

f(1) = 2, g(1) = 2, f'(x), g'(x) exist, then the value of lim(x→1) [f(1)g(x)-f(1)-g(1)f(x)+g(1)] / [f(1)g(x)-f(x)g(1)] is __________