Mathematics Tes...

Solution of the differential equation x cos x (dy/dx) + y(x sin x + cos x) = 1 is

A and B toss a die alternatively till one of them gets a six and wins the game. If A begins the game, then the probability of B winning the game is

Let X = {x : x = n³ + 2n + 1, n ∈ N} and Y = {x : x = 3n² + 7, n ∈ N} then

For integers m and n, both greater than 1, consider the following three statements:

P : m divides n

Q : m divides n²

R : m is prime

then

The mean of 5 observations is 4.4 and the variance is 8.24. If three of the five observations are 1,2 and 6, the two values are

Let a₁, a₂, ... a_n be a given A.P. whose common difference is an integer and S_n = a₁ + a₂ + ... + a_n. If a₁ = 1, a_n = 300 and 15 ≤ n ≤ 50, then the ordered pair (S_{n - 4}, a_{n - 4}) is equal to

Let S₁ be the sum of first 2n terms of an arithmetic progression. Let S₂ be the sum of first 4n terms of the same arithmetic progression. If (S₂ - S₁) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to:

 then the remainder when K is divided by 6 is

The greatest positive integer k, for which 49^k + 1 is a factor of the sum 49¹²⁵ + 49¹²⁴ + ... + 49² + 49 + 1, is