ECAT Mathematics Online Test With Answers

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ECAT Mathematics Online Test

Sr. # Questions Answers Choice
1 The eccentricity of ellipse becomes zero, then it takes the form of: a parabols a straight line a circle None of these
2 The lotus of intersection of perpendicular tangents to the parabola y2 = 4ax is: Axis of the parabola Focal chord of the parabos The tangent at vertex of the parabola a directrix of the parabola
3 The eccentricity of parabola is: 1 0 Greater than 1 Less than 1
4 Co-ordinate of a point on the parabola y2 = 8x whose focal distance is 4 are: (2 , 4) (-2 ,-4) (-2, 4) (2,-4)
5 Coordinates of the focus of the parabola x2 - 4x -8y-4=0 are: (0,2) (,0,1) (2,0) (1,2)
6 Which shape of the following objects are approximately parabolic ares? Light reflectors Force Weight of the pendul None of these
7 Latus rectum = 4 x ______________ focal distance of the vertex Chord Focus 1/2
8 Ifᵨ> 1 , then the conic, is: Ellipse Parabola Hyperbola None of these
9 the latus rectum of the parabola x3 = -4ay is: x = a y = -a x = -a y = 0
10 the curve of the parabola y2 = -4ax is symmetric with respect to x -axis y - axis Botha x and y- axis None of thes
11 The point which is closet to the focus of a parabola is: vertex Chord Focus Directix
12 The parabola y2 + 2y + x = 0 lie in _____ quadrant. First Second Third Fourth
13 The axis of the parabola x2 = 4ay is: y = 0 x = 0 x = -a y = a
14 What is the axis of the parabola y2 = 4ax? x = 0 y = 0 x = a y = 0
15 The conic is a parabola, when: ᵨ > 1 ᵨ < 1 ᵨ = 1 ᵨ = 0
16 If the vertex of the parabola is the origin and directrix is x+5 = 0 . then its latus rectum is: 10 5 0 20
17 The distance of point P(x,y) from focus in a parabola
y2 =4ax, is:
 2a a x + a x-a
18 a chord passing through the focus of a parabola is called a: Focal chord Latus rectum Tangent Directrix
19 y=0 of the parabola y2 = 4ax is the equation of directirx Equatio of the tangent Equation of axis equation of latus rectum
20 I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is: x<sup>2</sup> = 4ay y<sup>2</sup> = 4ax y<sup>2</sup> = -4ax x<sup>2</sup> = 4ax
21 A line joining two distinct points on a parabola is called a ______ of the parabola. Chord Tangent Lust rectum directrix
22 If the focus lies on the y-axis with coordinates f(0,a) and directrix of the parabola is y = -a, the equation of parabola is: y<sup>2</sup> = -4 ax x<sup>2</sup> = 4ay x<sup>2</sup> = -4ay y<sup>2</sup> = 4ax
23 ᵨ is a variable Positive constant Positive variable Directrix
24 The line through the focus and perpendicular to the directrix is called ______ of the parabola axis focal chord tangent latus rectum
25 The vertex of the equation y2 = 4ax is: (2, -2) (1,1) (0 , 0) (2 , 2)
26 If (0,4) and (0,2) are vertex and focus of the parabola respectively, the the equation of the parabola is: x<sup>2</sup> = 4y -32 x<sup>2</sup> =8y -32 y<sup>3</sup> = 16 x x2 + 8y =32
27 The point where the axis meets the parabola is called Directrix Foucu Chord Vertix
28 The exact value of cos-1 (-1) + cos -1 (1) = π -π π/2 π/3
29 The exact value of cos-1 (0) is π/2 -π/2 3π π-π/6
30 Cos-1 12/13 = tan<sup>-1</sup> 3/5 cot<sup>-1</sup> 13/12 Sec<sup>-1</sup> 13/12 sin<sup>-1</sup> 5/13
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