Mathematics Tes...

The orthocenter of the triangle with vertices

The order of a differential equation whose solution is y = a cos x + b sin x, where a and b are arbitrary constants, is

Directions: Refer to the following functions:

A(x, y, z) = Max {max (x, y), min (y, z), min (x, z)}

B(x, y, z) = Max {max (x, y), min (y, z), max (x, z)}

C(x, y, z) = Max {min (x, y), min (y, z), min (x, z)}

D(x, y, z) = Min {max (x, y), max (y, z), max (x, z)}

Max (x, y, z) = Maximum of x, y and z.

Min (x, y, z) = Minimum of x, y and z.

Assume x, y and z as distinct integers.

For what condition, will A(x, y, z) be equal to Max (x, y, z)?

The eccentricity of an ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then the equation of the ellipse is

The greatest value of λ ≥ 0 for which both the equations 2x² + ( λ − 1)x + 8 = 0 and x² − 8x + λ + 4 = 0 have real roots is

In a triangle, the lengths of the two larger sides are 10 cm and 9 cm respectively. If the angles of the triangle are in A.P, then the length of the third side (in cm) can be