The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

• ellipse

• parabola

• circle

• circle

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

• 4

• 10

• 6

• 6

For the Hyperbola  which of the following remains constant when α varies?

• Eccentricity

• Directrix

• Abscissae of vertices

• Abscissae of vertices

A value of C for which the conclusion of Mean Value Theorem holds for the function f(x) = log_ex on the interval [1, 3] is

• 2log₃e

• log_e3/2

• log₃e

• log₃e

The sum of the series 

• e^-2

• e^–1

• e^-1/2

• e^-1/2

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

• 40

• 20

• 80

• 80

The equation of a tangent to the parabola y² = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

• (−1, 1)

• (0, 2)

• (2, 4)

• (2, 4)

If the difference between the roots of the equation x² + ax + 1 = 0 is less than 5 , then the set of possible values of a is

•  (−3, 3)

• (−3, ∞)

• (3, ∞)

• (3, ∞)

19.

The largest interval lying in  for which the function  is defined, is

• [0, π]

• 

• [-π/4, π/2)

• [-π/4, π/2)

If D = for x ≠ 0, y ≠ 0 then D is

• divisible by neither x nor y

• divisible by both x and y

• divisible by x but not y

• divisible by x but not y