ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test With Answers

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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test

Sr. # Questions Answers Choice
1 The number of real tangents that can be drawn to the ellipse 3x2+ 5y2= 32 passing thro. (3, 5) is 0 1 2 Infinite
2 The two different parts of the hyperbola are called its Vertices Directrices Nappes Branches
3 The line through the centre and perpendicular to the transverse axis is called the Major axis Minor axis Focal axis Conjugate axis
4 The vertices of the ellipse x2+ 4y2= 16 are
5 The end points of the major axis of the ellipse are called its Foci Vertices Co - vertices None of these
6 The axis of the parabola y2= 4ax is X = 0 Y = 0 X = y X = -y
7 The conic is a parabola if e < 1 e > 1 e = 1 None of these
8 The perpendicular bisector of any chord of a circle Passes through the centre of the circle Does not pass through the centre of the circle May or may not pass through the centre of the circle None of these
9 A line segment whose end points lie on a circle is called The secant of the circle The arc of the circle The chord of the circle The circumference of the circle
10 The equation of the normal to the circle x2+ y2= 25 at (4, 3) is 3x - 4y =0 3x - 4y =5 4x + 3y = 5 4x + 3y = 25
11 The point (x1, y1) lies outside the circle x2+ y2+ 2gx + 2fy + c =0 if
12 The circle (x - 2)2+ (y + 3)2= 4 is not concentric with the circle (x - 2)<sup>2</sup>+ (y + 3)<sup>2</sup>= 9 (x + 2)<sup>2</sup>+ (y - 3)<sup>2</sup>= 4 (x + 2)<sup>2</sup>+ (y - 3)<sup>2</sup>= 8 (x - 2)<sup>2</sup>+ (y + 3)<sup>2</sup>= 5
13 If x + y + 1 = 0 touches the parabola y2=λx, thenλis equal to 2 4 6 8
14 The parabola y2= x is symmetric about x-axis y-axis Both x and y-axis The line y = x
15 If (a, b) is the mid-point of a chord passing thro' the vertex of the parabola y2= 4x, then a = 2b 2a = b a<sup>2</sup>= 2b 2a = b<sup>2</sup>
16 If t is the parameter for one end of a focal chord of the parabola y2= 4ax, then its length is
17 The point on y2 = 4ax nearest to the focus has its abciassae equal to -a a a/2 0
18 The radius of the circle (x - 1)2+ (y + 3)2= 61 is 8 4 64 None of these
19
20 The constant distance of all points of the circle from its centre is called the Radius of the circle Secant of the circle Chord of the circle Diameter of the circle
21 If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a Parabola Circle Hyperbola Ellipse
22 If the st. line 3x + 4y = K touches the circle x2+ y2- 10x = 0 then the value of K is -1 or 20 -10 or 40 -2 or 20 2 or 20
23 A square is inscribed in the circle x2+ y2- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is
24 The equation of a line parallel to the tangent to the circle x2+ y2= 16 at the point (2, 3) and passing thro' the origin is 2x + 3y = 0 2x - 3y = 0 3x + 2y = 0 3x - 2y = 0
25 The line 3x - 4y = 0 Is a tangent to the circle x<sup>2</sup>+ y<sup>2</sup>= 25 Is a normal to the circle x<sup>2</sup>+ y<sup>2 </sup>=25 Does not meet the circle x<sup>2</sup>+ y<sup>2</sup>= 25 Does not pass thro' the origin
26 2 b 2 a 2 ab a + b
27 A circle is a limiting case of an ellipse whose eccentricity Tends to a Tends to b Tends to 0 Tends to a + b
28 An ellipse A parabola A circle A hyperbola
29 The latus rectum of the ellipse 5x2+ 9y2= 45 is 10 / 3 5 / 3 3 / 5 3 / 10
30 The equation ax2+ 2hxy + by2 +2gx + 2fy + c =0 represents an ellipse if
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