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
C.
7/16
P(exactly one of A or B occurs)
= P(A) + P(B) – 2P(A ∩ B) =1/4
P(Exactly one of B or C occurs)
= P(B) + P(C) – 2P(B ∩ C) =1/4
P(Exactly one of C or A occurs)
= P(C) + P(A) – 2P(C ∩ A) =1/4
Adding all, we get
2ΣP(A) – 2ΣP(A ∩ B) =3/4
∴ΣP(A) – ΣP(A ∩ B) =3/8
Now, P(A ∩ B ∩ C) =1/16
(Given)
∴ P(A ∪ B ∪ C)
= ΣP(A) – ΣP(A∩B) + P(A ∩ B ∩ C)
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