Mathematics Test - 5

If P(1, 0), Q(– 1, 0) and R(2, 0) are three given points, then the locus of point S, which satisfies the relation (SQ)² + (SR)² = 2(SP)², is (where SQ, SR and SP are line segments)

The orthocenter of the triangle with vertices

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is

The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x - 2y = 7. Then PQRS must be a

If the vertices P, Q, R of a triangle PQR are rational points, then which of the following points of the triangle PQR is not always a rational point?

If f(x) = x^a + a^x and g(x) = x^a – a^x, find the value of f(x) + g(x).

Find the period of the given function:

f(x) = tan(x/3) + sin(2x)

If

L(X, Y) = Square of the larger number,

S(X, Y) = Square of the smaller number,

MODD (X, Y) = Absolute value of the difference (X - Y) and

X * Y = Product of X and Y,

then the value of MODD [{L (1, 2) * S(1, - 3)}, {S(0, 2) * MODD (3, - 4)}] *MODD[{S(3, -1) * L(1, - 2)}, { MODD (1, 2) * L(1, 2)}] will be

If f(x) = log (1 + x) - log (1 - x) and log (g(x)) = log (3x + x3) - log (1 + 3x2), then what is the value of f(g(x))?

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)?