Mathematics Tes...

The equation to the directrix of a parabola if the two extremities of its latus rectum are (2, 4) and (6, 4) and the parabola passes through the point (8, 1) is

then the maximum value of  Δ is

The number of solution(s) of the equation 

(where z = x + iy, x, y ∈ R, i² = –1 and x ≠ 2)

Two circles of radii r₁ and r₂ are both touching the coordinate axes and intersecting each other orthogonally. The value of r₁/r₂ (where r₁ > r₂) equals

Let X and Y be two matrices satisfying this relations

then Tr.(X) – Tr.(Y) equals

[Note : Tr.(P) denotes trace of matrix P.]

The differential equation dx/dy = 3y/2x represents a family of hyperbolas (except when it represents a pair of lines) with eccentricity can be

Line L, perpendicular to the line with equation y = 3x – 5, contains the point (1, 4). The x-intercept of L, is

Let A = [a_ij] (1 ≤ i , j ≤ 3) be a 3 × 3 matrix and B = [b_ij] (1 ≤ i , j ≤ 3) be a 3 × 3 matrix such that

If det. A = 4, then the value of det. B is

Number of words that can be formed using all the letters of the word GARGEE if no two alike letters are together, is

If acute angle between the line  and xy plane is α and acute angle between the planes x + 2y = 0 and 2x + y = 0 is β then (cos²α + sin²β) equals