ECAT Mathematics Online Test With Answers

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ECAT Mathematics Online Test

Sr. # Questions Answers Choice
1 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
2 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
3 2 b 2 a 2 ab a + b
4 A circle is a limiting case of an ellipse whose eccentricity Tends to a Tends to b Tends to 0 Tends to a + b
5 An ellipse A parabola A circle A hyperbola
6 The latus rectum of the ellipse 5x2+ 9y2= 45 is 10 / 3 5 / 3 3 / 5 3 / 10
7 The equation ax2+ 2hxy + by2 +2gx + 2fy + c =0 represents an ellipse if
8 The slope of the normal at the point (at2, 2at) of the parabola y2= 4ax is 1/t t -t -1/t
9 The line y = 2 x + c is a tangent to the parabola y2= 16 x if c equals -2 -1 0 2
10 The equation of the parabola with directirx x = 2 and the axis y = 0 is y<sup>2</sup>= 8x y<sup>2</sup>= -8x y<sup>2</sup>= 4x y<sup>2</sup>= -4x
11 The equation of the directrix of the parabola x2= 4ay is x + a = 0 x - a = 0 y + a = 0 y - a = 0
12 The eccentricity of the parabola y2= -8x is -2 2 -1 1
13 The length of the tangent from (2, 1) to the circle x2+ y2+ 4y + 3 = 0 is
14 The equation of the chord of the circle x2+ y2- 4x = 0 whose mid-point is (1, 0) is y = 2 y = 1 x = 2 x = 1
15 The line Ax + By + C = 0 will touch the circle x2+ y2=λ when C<sup>2</sup>=<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);">λ</span>(A<sup>2</sup>+ B<sup>2</sup>) A<sup>2</sup>=<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);">λ</span>(A<sup>2</sup>+ C<sup>2</sup>) B<sup>2</sup>=<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);">λ</span>(A<sup>2</sup>+ C<sup>2</sup>) None of these
16 Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is (2, 0) (3, 0) (0, 3) (3, 2)
17 The equation x2+ y2= 0 represents A circle A degenerate circle An empty set A st. line
18
19 1 5 7 9
20 A parabola An ellipse A hyperbola A circle
21 A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP2+ CQ2+ CR2+ CS2= r<sup>2</sup> 2 r<sup>2</sup> 3 r<sup>2</sup> 4 r<sup>2</sup>
22
23 The line y = 4x + c touches the hyperbola x2- y2= 1 if
24 The eccentricity of the conic 9x2- 16y2= 144 is 4/5 5/4 4/3 3/4
25 The solution set of x < 4 is -<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);"><i>∞</i></span>&lt; x &lt; 4 -<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>∞</i></span>&gt; x &gt; 4 -<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>∞</i></span>&lt; x &lt; 2 -<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>∞</i></span>&gt; x &gt; 2
26 The graph of linear equation 2x + 3y = 10 Parabola Circle Hyperbola Straight line
27 Inequalities have ______ symbol 2 3 4 1
28 There may be ______ feasible solution in the feasible region Infinite Finite Defined None of above
29 Optimize means ______ a quantity under certain constraints Minimize Maximize Maximize or minimize None of these
30 s > t then (s - t)<sup>2</sup>&gt; (t - s)<sup>2</sup> (s - t)<sup>2</sup>&lt; (t - s)<sup>2</sup> (s - t)<sup>2</sup>= (t - s)<sup>2</sup> None
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