KVPY Government Jobs Exams

Suppose two perpendicular tangents can be drawn from the origin to the circle x2 + y2 – 6x –2py + 17 = 0, for
some real p. then |p| =

Read Solution (Total 1)

Director circle passes through origin so
Radius of director circle = 2 radius of circle

2 2 3 p + =
2 2 2 3 P 17 + −
32
+ p2
= 2(32
+ P2
– 17)
0 = 32
+ p2
– 34
| P | = 5
10 years agoHelpfull: Yes(1) No(2)

KVPY Other Question

The maximum value M of 3^x + 5^x – 9^x + 15^x –25^x, as x varies over reals, satisfies –
(A) 3 < M < 5 (B) 0 < M < 2 (C) 9 < M < 25 (D) 5 < M < 9 Let a, b, c, d be numbers in the set {1, 2, 3, 4, 5, 6} such that the curves y = 2x^3 + ax + b and y = 2x^3 + cx + d have no point in common. The maximum possible value of (a - c)^2 + b d is