ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 22

If a plane passes through the vertex of the cone, then the intersection is

• an ellipse A
• a parabola B
• a hyperbola C
• a point circle D

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

• an ellipse A
• a circle B
• a parabola C
• a hyperbola D

If the centre of the circle is the origin, then equation of the cirlce is

• x²+ y²= 0 A
• 2gx + 2fy - c = 0 B
• x²+ y²= r² C
• gx + fy - c/2 = 0 D

To study conics, Pappus used the method of

• analytic geometry A
• solid geometry B
• Euclidean geometry C
• none of these D

A second degree equation in which coefficients of x²and y²are equal and there is no product term xy represents

• a parabola A
• a circle B
• an ellipse C
• a pair of lines D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The vertex of the cone is also called

• nappes A
• axis B
• rulings C
• apex D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• a = b , h = 0 B
• f = g, h = 0 C
• h = h, c = 0 D

A cone is generated by all lines through a fixed point and the circumference of

• a circle A
• an ellipse B
• a hyperbola C
• none of these D

• Three Independent Variables A
• Two independent constant B
• Three independent parameters C
• Three independent constant D

The fixed point which lies on the axis of the cone is called its

• axis A
• apex B
• nappes C
• axis D

The area of the circle centred at (1, 2) and passing through (4, 6) is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If three non-collinear points through which a circle passes are known, then we can find the

• variables x and y A
• value of x and c B
• three constant f, g and c C
• inverse of the circle D

If the cutting plane is slightly tilted and cuts only one nappe of the cone, the resulting section is

• an ellipse A
• a circle B
• a hyperbola C
• a parabola D

The equation: x²+ y²+ 2gx + 2fy + c = 0, represents

• pair of lines A
• a circle B
• a general second degree equation C
• a hyperbola D

• 
  A
• 
  B
• 
  C
• None of these D

The set of all points in the plane that are equally distant from a fixed point is called a

• parabola A
• ellipse B
• hyperbola C
• circle D

The generators of a cone are also called

• rulings A
• apex B
• nappes C
• ellipse D

Apollonius was a

• rocket A
• Muslim scientist B
• Greek mathematicians C
• method of finding conics D

The equation of the circle whose centre is (-3, 5) and having radius 7 is

• (x-3)²+ (y+5)²= 7² A
• (x-3)²+ (y+5)²= 7² B
• (x-3)²+ (y-5)²= 7² C
• x²+y²+6x-10y-15=0 D

IF the cone is cut by a plane perpendicular to the axis of the cone, then the section is a

• circle A
• ellipse B
• hyperbola C
• parabola D

• 1 A
• 2 B
• 0 C
• None of these D

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

• an ellipse A
• a circle B
• a parabola C
• a hyperbola D

• 
  A
• 
  B
• 
  C
• 
  D

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve of intersection is

• a circle A
• an ellipse B
• a parabola C
• a hyperbola D

The equation of the circle with centre at (5, -2) and radius 4 is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D