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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• axis A
• apex B
• nappes C
• axis D

Apollonius was a

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

• 
  A
• 
  B
• 
  C
• None of these D

• 1 A
• 2 B
• 0 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  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 generators of a cone are also called

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

• 
  A
• 
  B
• 
  C
• 
  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
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  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

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

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

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 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 vertex of the cone is also called

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

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

• 
  A
• 
  B
• 
  C
• 
  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

To study conics, Pappus used the method of

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