Multiple Choice QuestionsThe 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
B.
6/55
Let A ≡ {0, 1,2 ,3 ,4 ......, 10 }
n(s) = 11C2 (where 'S' denotes sample space)
Let E be the given event
∴ E ≡ {(0, 4), (0, 8), (2, 6), (2, 10), (4, 8), (6, 10)} n(E) = 6
∴ n(E) = 6 = 6/55
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
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then g(x) is equals to 
then adj (3A2 + 12A) is equal to
