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ECAT Computer Science Entry Test
| Sr. # | Questions | Answers Choice |
|---|---|---|
| 1 | An ellipse slides between two lines at right angles to one another. The locus of its centre is : | a parabola an ellipse a circle a hyperbola |
| 2 | The eccentricity of ellipse becomes zero, then it takes the form of: | a parabols a straight line a circle None of these |
| 3 | 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 |
| 4 | The eccentricity of parabola is: | 1 0 Greater than 1 Less than 1 |
| 5 | Co-ordinate of a point on the parabola y2 = 8x whose focal distance is 4 are: | (2 , 4) (-2 ,-4) (-2, 4) (2,-4) |
| 6 | Coordinates of the focus of the parabola x2 - 4x -8y-4=0 are: | (0,2) (,0,1) (2,0) (1,2) |
| 7 | Which shape of the following objects are approximately parabolic ares? | Light reflectors Force Weight of the pendul None of these |
| 8 | Latus rectum = 4 x ______________ | focal distance of the vertex Chord Focus 1/2 |
| 9 | Ifᵨ> 1 , then the conic, is: | Ellipse Parabola Hyperbola None of these |
| 10 | the latus rectum of the parabola x3 = -4ay is: | x = a y = -a x = -a y = 0 |
| 11 | the curve of the parabola y2 = -4ax is symmetric with respect to | x -axis y - axis Botha x and y- axis None of thes |
| 12 | The point which is closet to the focus of a parabola is: | vertex Chord Focus Directix |
| 13 | The parabola y2 + 2y + x = 0 lie in _____ quadrant. | First Second Third Fourth |
| 14 | The axis of the parabola x2 = 4ay is: | y = 0 x = 0 x = -a y = a |
| 15 | What is the axis of the parabola y2 = 4ax? | x = 0 y = 0 x = a y = 0 |
| 16 | The conic is a parabola, when: | ᵨ > 1 ᵨ < 1 ᵨ = 1 ᵨ = 0 |
| 17 | If the vertex of the parabola is the origin and directrix is x+5 = 0 . then its latus rectum is: | 10 5 0 20 |
| 18 | The distance of point P(x,y) from focus in a parabola y2 =4ax, is: |
2a a x + a x-a |
| 19 | a chord passing through the focus of a parabola is called a: | Focal chord Latus rectum Tangent Directrix |
| 20 | y=0 of the parabola y2 = 4ax is the | equation of directirx Equatio of the tangent Equation of axis equation of latus rectum |
| 21 | 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 |
| 22 | A line joining two distinct points on a parabola is called a ______ of the parabola. | Chord Tangent Lust rectum directrix |
| 23 | 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 |
| 24 | ᵨ is a | variable Positive constant Positive variable Directrix |
| 25 | The line through the focus and perpendicular to the directrix is called ______ of the parabola | axis focal chord tangent latus rectum |
| 26 | The vertex of the equation y2 = 4ax is: | (2, -2) (1,1) (0 , 0) (2 , 2) |
| 27 | 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 |
| 28 | The point where the axis meets the parabola is called | Directrix Foucu Chord Vertix |
| 29 | The slope of the normal at (5 cos, 0, 5 sin 0) to the circle. x2+y2 = 25 is: | tan𝜽 cos𝜽 /sin𝜽 -cot𝜽 - tan𝜽 |
| 30 | The slope of the normal at (4,3) to the circle x2+y2=25 is | 3/4 -3/4 4/3 -4/3 |
