Mathematics Tes...

If λ ∈ R is such that the sum of the cubes of the roots of the equation x² + (2 - λ) x + (10 - λ) = 0 is minimum, then the magnitude of the difference between the roots of this equation is

If tan A and tan B are the roots of the quadratic equation 3x² - 10x - 25 = 0, then the value of 3 sin² (A + B) - 10 sin (A + B) × cos (A + B) - 25 cos² (A + B) is

If the system of linear equations

x + ky + 3z = 0

3x + ky - 2z = 0

2x + 4y - 3z = 0

has a non-zero solution (x, y, z), then xz/y² is equal to

If β is one of the angles between the normals to the ellipse x² + 3y² = 9 at the points (3 cos θ, √3 sin θ) and (-3 sin θ, √3 cos θ); θ ∈ (0, π/2), then 2 cot β/sin2θ is equal to

The number of four-lettered words that can be formed using the letters of the word BARRACK is:

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws , is