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

If for  x ∈ (0, 1/4)  the derivatives  then g(x) is equals to 

18.

The radius of a circle, having minimum area, which touches the curve y = 4 – x² and the lines, y = |x| is

• 
• 
• 
• 

If A, then adj (3A2 + 12A) is equal to

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