ECAT Computer Science Entry Test With Answers

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ECAT Computer Science Entry Test

Sr. # Questions Answers Choice
1 The slope of the tangent of the circle x3 + y3 =25 at (4,3) is: -4/5 4/3 -25/4 25/3
2 The points of intersection of the line y = 2x -3 and the circle x2 + y2 - 3x =2y -3 = 0 are: two three less thean two not intersect
3 If one end of the diameter of the circle x2 + y2- 5x = 3y -22 = 0 is (3,4) the other end is: (2,7) (-2,-7) (-2,7) (2,-7)
4 If one end of the diameter of the circle 2x2 + 2y2 -8x - 4y = 2 = 0 is (2 ,3), the other end is: (2,1) (-2,1) (2,-1) (1,-1)
5 Two circle x2 + y2+2x - 8 = 0 and x2 + y2 -6 + 6x -46 =0: touch internally do not intersect touch externally None of these
6 Circle x2 + y2 - 2y -y = 0 and x2 + y2 - 8y -4 =0: Interesect touch externally touch internally do not touch
7 The point of contact of the circles x2 + y2 - 6x -6y+10 = 0 and x2 + y2 =2 is (-3 ,2) (1 , 3) ( -2 , -1) None of these
8 The radius of the circle x2 + y2 - 6 x + 4 y +13 = 0 , is 1 2 0 None of these
9 The are of the circle centred at ( 1 , 2) and passing through ( 4 , 6) is: 10π 25π 5π 25/2π
10 The equation x2 + y2 +2g +2fy + c =0 represents a circle whose centre is : (g,f) (-g,-f) (2g ,2f) (-2f ,-2g)
11 The radius of the circle 2x2 + 2y2 - 4x + 12 y+11=0 is: √4.5 √11 √29 √15
12 Parametric equation of circle : x2+y2+r2, are r1 = x cos𝜽 r<sup>2</sup> = y sin𝜽 x = r cos𝜽 y = r sin𝜽 x = r sin𝜽1 y = r sin𝜽2 x = r<sub>1</sub> cos𝜽 y = r<sub>2 sin𝜽</sub>
13 The general equation of circle x3 + y3 + 2gx + 2fy + c = 0 , contains: Three independent variables Two independent conntants Three indepentent parameters Three independent constants
14 The three noncollinear points through which a circle passe are known, then we can find the: Variables x and y Value of x and c three constants f,g and c inverse of the circle
15 A second degree equation in which coefficients of x2and y2 are equal and there is no product therm xy represents: a parabola a circle an ellipse a pair of lines
16 Apollonius was a: Rocket Muslims scientist Greek mathematicians Method of finding conics
17 The study conics, pappus used the method of: analytic geometry Euclidean solid geometry Greek mathmaticians None of these
18 The familiar plane curves, namely circle, ellipse, parabola and hyperbola are called: cones conics nappes apex
19 If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is: an ellipse a circle a parabols a hyperbola
20 The exact value of cos-1 (-1) + cos -1 (1) = π -π π/2 π/3
21 The exact value of cos-1 (0) is π/2 -π/2 3π π-π/6
22 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
23 cos-1(cos x) = x cos x x = 1/x cos<sup>-2</sup> x
24 Cos-1(x)= cos x x tan-1(-x) Sec-1 (1/x)
25 Cos-1 (-x) = -x 1/x tan-1 x π-cos-1 x
26 Ifπ≤x≤2π, then cos-1 (cos x)= cos x -x 1/x -x
27 If cos (2 sin-1 x) = 1/9 , then what is the value of x? 1/3 -2/3 2/3 2/3 , -2/3
28 Cos (cos4π/3)= π/2 π/3 2π/3 -π/3
29 The exact degree value of the function sin-1( -√3/2) is 70<sup>ο</sup> 50<sup>ο</sup> 90<sup>ο</sup> 60<sup>ο</sup>
30 What is the value of cos (cos-1 2) ? √2 1/2 undefine 0
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