Mathematics Tes...

The equation represents the equation of a circle with ω, ω² as extremities of a diameter, then λ is , (where ω, ω² are cube roots of unity)

If sin^–1x + sin^–1y + sin^–1z = π/2 then x² + y² + z² + 2xyz is equal to -

If b² > 4ac for the equation 4x⁴ + bx² + c = 0, then all the roots of the equation will be real if:

The value of the definite integral  for 0 < α < π, equal to

Coordinates of the orthocentre of the triangle whose sides are x = 3, y = 4 and 3x + 4y = 6 will be:

An equilateral triangle is inscribed in the parabola y² = 4ax whose vertex is at the vertex of the parabola. The length of its side is

The projection of the line joining the points (3,4,5) and (4,6,3) on the line joining the points (-1,2,,4) and (1,0,5) is

Consider the following statements regarding the events E, A, B and C .

(i) Event E can take place due to the occurrence of any of the events A, B, C.

(ii) Events A, B and C are equiprobable, mutually exclusive and exhaustive.

(iii) Probability of occurrence of event E is 5/12.

Considering above data the value of P(E/C) is:

(P→q) ↔ (q V ~ P) is –

The equation of the hyperbola whose foci are (6, 5), (- 4, 5) and eccentricity 5/4 is