Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 Which of the vectors have opposite direction?
2
3 The magnitude of a vector can never be Zero Negative Positive None of these
4 A vector of magnitude zero is called Position vector Null vector Free vector None of these
5 Unit vector in the positive direction of x-axis is
6 Free vector Null vector Unit vector None of these
7 The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is A parabola A circle An ellipse A st. line
8 The number of real tangents that can be drawn to the ellipse 3x2+ 5y2= 32 passing thro. (3, 5) is 0 1 2 Infinite
9 The two different parts of the hyperbola are called its Vertices Directrices Nappes Branches
10 The line through the centre and perpendicular to the transverse axis is called the Major axis Minor axis Focal axis Conjugate axis
11 The vertices of the ellipse x2+ 4y2= 16 are
12 The end points of the major axis of the ellipse are called its Foci Vertices Co - vertices None of these
13 The axis of the parabola y2= 4ax is X = 0 Y = 0 X = y X = -y
14 The conic is a parabola if e < 1 e > 1 e = 1 None of these
15 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
16 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
17 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
18 The point (x1, y1) lies outside the circle x2+ y2+ 2gx + 2fy + c =0 if
19 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
20 If x + y + 1 = 0 touches the parabola y2=λx, thenλis equal to 2 4 6 8
21 The parabola y2= x is symmetric about x-axis y-axis Both x and y-axis The line y = x
22 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>
23 If t is the parameter for one end of a focal chord of the parabola y2= 4ax, then its length is
24 The point on y2 = 4ax nearest to the focus has its abciassae equal to -a a a/2 0
25 The radius of the circle (x - 1)2+ (y + 3)2= 61 is 8 4 64 None of these
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27 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
28 If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a Parabola Circle Hyperbola Ellipse
29 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
30 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
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