Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents Circle Hyperbola Ellipse Pair of straight lines
2 If the line 2x -y +k =0 is a diameter of the circle x2 +y2 +6x -6y +5 =0 then k is equal to 12 9 6 3
3 The area of the circle centred at (1,2) and passing through (4,6) is 30 πsq.units 5π sq.units 15π sq.units 25π sq.units
4 The number of tangents to the circle x2+ y2 -8x -6y +9 =0 which pass through the point (3,-2) is 2 1 0 None of these
5 The slope of the tangent at the point (h,h) of the circle x2 +y2 =a2 is 0 1 -1 h
6 The equation x2+ y2- 8x+ 6y+ 25= 0 represents A circle A pair of straight lines A point None of these
7 Two circle s1: x2+ y2 +2x- 2y- 7= 0: s2: x2+ y2- 6x+ 4y+ 9= 0 Touch externally Touch internally Intersects each other Do not intersects
8 The tangent to the parabola y2 =4ax and perpendicular line from the focus on it meet x =0 y =0 x =-9 y = -a
9 If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____ 12 8 24 -24
10 The line y =mx +1 is tangent to the parabola y2 =4x if m=1 m=2 m=3 m=4
11 If (2,0) is the vertex and y-axis is directrix of parabola then focus is (2,0) (-2,0) (4,0) (-4,0)
12 Number of conics is 1 3 2 4
13 The vertex of the parabola (xsin a -ycos a)2 =4a(xcos a +ysin a) lies at (acos a,asin a) (a,0) (cos a,sin a) (0,0)
14 The number of standard parabolic functions are is 4 2 3 1
15 The parabolay2=4ax open up if a<0 a≠0 a>0 All are incorrect
16 y=-a is the equation of the directrix of y2 =4ax x2=-4ay x2=4ay y2=-4ax
17 Equation of normal to the circle x2 + y2 =25 at (5cosθ,5sinθ) xcosθ+ysinθ =5 xcosθ -ysinθ =0 xsinθ -ycosθ =0 None of these
18 For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0 k=0 k=0 or 26 k = 26 k=-13
19 Two circles x2 +y2 +8x -9= 0 and x2+y2+6y +k =0 touchinternallyif the value of k is k = 9 k = ±9 k=-9 k=11
20 The line joining the center of a circle to the midpoint of the chord is Perpendicular to the tnagent Perpendicular to the normal Perpendicular to the chord Perpendicular to the chord
21 Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21 -3x + 4y =21 4x - 3x = 0 -3x + 4y = 25 None of these
22 Area of the circle with ends of a diameter at (-3,2) and (5,-6) 128π sq. units 64π sq. units 32π sq.units None of these
23 Two tangents drawn from (2,3) to the circle x2+y2 =9 are Real and distinct Imaginary Real and coincident None of these
24 The centre of the circle x2+y2 -2fx-2gy+x=0 is (-g,-f) (g,f) (f,g) (-f,-g)
25 x =r cosθ,y= sinθ are the parametric equations of Circle Ellipse Parabola Hyoerbola
26 The common point to four standard parabolas Focus Centre Vertex P(x,y)
27 Equation of parabola with focus F(-3,1) directrix x=3 is (y -1)2 =-12x (y-1)2 =4x (x+3)2 =4a(y-1) y2 =-12(x-1)
28 The span of a standard parabola depends upon x a y y2
29 If a > 0 they parabola y2 =-4ax lies in I and iv quadrant I quadrant II and III quadrant All are incorrect
30 The conic ax2+2hxy+by2+2gx+2fy+c= 0 never represent a circle if a≠ b,h≠0 a=b h≠0 h=0
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