The eccentricity of an ellipse whose centre is at the origin is 1/2. If one of its directives is x= –4, then the equation of the normal to it at (1,3/2) is
x + 2y = 4
2y – x = 2
4x – 2y = 1
4x – 2y = 1
If two different numbers are taken from the set {0, 1, 2, 3, ......., 10), then the probability that their sum, as well as absolute difference, are both multiple of 4, is
7/55
6/55
14/55
14/55
For three events A, B and C,
P(Exactly one of A or B occurs)
= P(Exactly one of B or C occurs)
= P(Exactly one of C or A occurs) = 1/4and P(All the three events occur simultaneously) = 1/16.Then the probability that at least one of the events occurs, is
3/16
7/32
7/16
7/16
Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB.If ∠BPC = β , then tanβ is equal to
4/9
6/7
1/4
1/4
If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is
a singleton
an empty set
an infinite set
an infinite set
Let ω be a complex number such that 2ω +1 = z where z = √-3. if
then k is equal to
1
-z
z
z
The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is
Let k be an integer such that triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point
A.
We have,
⇒ 5k2 + 13k – 46 = 0
or
5k2 + 13k + 66 = 0 (no real solution exist)
∴ k =–23/5
or k = 2
k is an integer, so k =2
As
Therefore (2, 1/2)