Mathematics Tes...

The existence of unique solution of the system of equations, 

x + y + z = β,

5x – y + αz = 10,

2x + 3y – z = 6

depends on

The value of 

The total number of shortest path from A to B is:-

If |z| = 1 then is equal to ?

A ten digit number is formed (without repetition), the probability that the difference of the digits at equal distances from the begining and the end is always 1 is ?

The coordinates of the foot of the perpendiculars from the vertices of a triangle on the opposite sides are (20,25), (8,16) and (8,9). The orthocentre of the triangle lies at the point-

The co-ordinates of the orthocentre of the triangle formed by the lines 2x² – 2y² + 3xy + 3x + y + 1 = 0 and 3x + 2y + 1 = 0 are :-

The point A on the parabola y² = 4ax for which |AC – BC| is maximum, whose B(0, a) and C(–a, 0) is :-

The distance of the point having position vectorfrom the straight line passing through the point (2, 3, –4) and parallel to the vector,

If the distance of the point P(1,–2,1) from the plane x + 2y – 2z = a, where a > 0, is 5, then the foot of the perpendicular from P to the plane is-