If the normal at one end of the latusrectum of an ellipse passes through the one end of the minor axis, then
e4 - e2 + 1 = 0
e2 - e + 1 = 0
e2 + e + 1 = 0
e4 + e2 - 1 = 0
The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact, is
a parabola
an ellipse
a circle
a hyperbola
D.
a hyperbola
The equation of the tangent at any point P(x, y) is
This cuts the coordinate axes at
It is given that P(x, y) is the mid point of AB.
Clearly, it represents a rectangular hyperbola.
Let E' denote the complement of an event E. Let E, F, G be pairwise independent events such that P(G) > 0 and P(E ∩ F ∩ G) = 0. Then, P(E' F' /G) equals
P(E') + P(F')
P(E') - P(F')
P(E') - P(F)
P(E) - P(F')
If the relation between direction ratios of two lines are given by a + b + c = 0 and 2ab + 2ac - bc = 0, then the angle between the lines is
If the slope of the curve at the point (1, 1) is 2, then
a = 1, b = - 2
a = - 1, b = 2
a = 1, b = 2
None of these
Let w be the complex number Then, the number of distinct complex number z satisfying
= o is equal to
1
0
2
3
If A is a square matrix such that A2 = A and B = I - A, then AB + BA + I - (I - A)2 is equal to
A
2A
- A
I - A
If A = is an orthagonal matrix, then
a = 2, b = 1
a = - 2, b = - 1
a = 2, b = - 1
a = - 2, b = 1