(Download) Special Class Railway Apprentices (SCRA) Practice Paper (SET - 2) : Mathematics

Two circles each of radius 5 units touch each other at (1, 2). If the equation of their common tangent is 4x + 3y = 10, then the centres of the two circles are:
(a) (3, 4), (–1, 0)
(b) (5, 7), (–3, – 3)
(c) (5, 5), (–3, –1)
(d) None of the above

If the curves y2 = 16x and 9x2 + by2 = 16 cut each other at right angles, then the value of b is:
(a) 2
(b) 4
(c) 9/2
(d) none of these

The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 144 sq units. Then the equation of this circle is:
(a) x2 + y2 + 2x – 2y = 62
(b) x2 = y2 + 2x – 2y = 47
(c) x2 + y2 – 2x + 2y = 47
(d) x2 + y2 – 2x + 2y = 62

Two vertices of a triangle are (5 – 1) and (–2, 3). If the orthocentre of the triangle is the origin, then co-ordinates of the third vertex are:
(a) (4, 7)
(b) (–4, –7)
(c) (–4, 7)
(d) none of these

A circle is given by x² + y² – 6x + 8y – 11 = 0 and are two points (0, 0) and (1,
8). These points lie:
(a) both inside the circle
(b) both outside and one inside the circle
(c) both outside the cirlce
(d) one on and other inside the circle