Mathematics Tes...

If X = {8ⁿ - 7n - 1 : n ∈ N} and Y = {49(n - 1) : n ∈ N}, then

If x² + b₁x + c₁ = 0 has two real roots α, β and x² + b²x + c² = 0 has two real roots α + 2 , β + 2 where b₁, b₂, c₁, c₂ are real numbers, then  is equal to which of the following?

The value of the determinant  is equal to

Coefficient of t²⁴ in (1 + t²)¹²(1 + t¹²)(1 + t²⁴) is

Let there exist a function f such that f'(a) = f²(a) = ... = f²ⁿ (a) = 0, where fn(x) stands for the n^th derivative of the function, f^{2n + 2}(a) = -ve and f has a local maximum value b at x = a. Find f(x).

The three lines px + qy + r = 0, qx + ry + p = 0 and rx + py + q = 0 are concurrent, if

If α and β are the roots of the quadratic equation ax² + bx + c = 0 and the plane βx + αy = z is passing through the line of intersection of the two planes x + αz = y and y + βz = x, then the value of b

A problem of mathematics is given to three students A, B and C, and their respective probabilities of solving the problem is 1/2, 1/3 and 1/4. The probability that the problem is solved is

The trigonometric equation sin^-1 x = 2 sin^-1 a has a solution for