The point to which the origin is to be shifted to remove the first degree terms from the equation 2x2 + 4xy - 6y2 + 2x + 8y + 1 = 0 is
If lx + my = 1 is a normal to the hyperbola , then a2m2 - b2l2 = ?
l2 + m2(a2 + b2)2
l2m2(a2 + b2)2
There are 10 intermediate stations on a railway line between two particular stations. The number ofways that a train can be made to stop at 3 of these intermediate stations so that no two of these halting stations are consecutive is
56
20
126
120
A.
56
(a) We have 10 mtermed1ate stations between A and B There are 7 stations where the tram does not stop and the three stations where the train stops should be any three of the 8 places
:. Total number of ways =
= 56
The figure formed by the pairs of lines
and
6x2 + 13xy + 6y + 10x + 10y + 4 = 0, is a
Square
Parallelogram
Rhombus
Rectangle
If the point of intersection of the tangents drawn at the points where the line 5x + y + 1 = 0 cuts the circle x2 + y2 - zx - 6y - 8 = 0 is (a, b), then 5a + b =
3
- 44
- 1
4
The number of different ways of preparing a garland using 6 distinct white roses and 5 distinct red roses such that no two red roses come together is
21600
43200
86400
151200