Mathematics Tes...

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 ΔABC, if tan A/2 tan C/2 = 1/2, then a, b, c are in

\(\frac{1}{3 !}+\frac{2}{5 !}+\frac{3}{7 !}+\ldots \ldots \infty\) is equal to

\(\int\left[f(x) g^{*}(x)-f(x) g(x)\right] d x\) is equal to

A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are proportional to 1, –1, 1 then direction cosines of the reflected ray are

The coefficient of x in the equationx²+ px+ q = 0 was taken as 17 in place of 13, its roots were found to be -2 and -15, the roots of the original equation are

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)?