ECAT Mathematics Online Test With Answers

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ECAT Mathematics Online Test

Sr. # Questions Answers Choice
1 Geometrically the modulus of a complex number represents its distance from the Point (1,0) Point (0,1) Point (1,1) Point (0,0)
2 The square root of 2i - 20i is ±(5 - 2i) ±(5+ 2i) (5 - 2i) None of these
3 The value of i4n+1 1 -1 i i<sup>2</sup>
4 What is the conjugate of -7 -2i ? -7 + 2i 7 +2i 7 -2i √53
5 The equation |x +4| = x has solution x = -2 x = 2 x = -4 x = 4
6 If z1 =√-36 ,z2 =√-25,z3 =√-16 then 15 15i -15i -15
7 if Z1 = 1+i, Z2= 2+3i, then |Z2 -Z1| = √3 i √7 -2-i √5
8 If Z = (1,2), then Z-1 =? (0.2, 0.4) (-0.2 ,0.4) (0.2,-0.4) (-0.2,-0.4)
9 The value of x and y when (x + iy)2 = 5 - 4i x = 2, y = -1 x = -2, y = 1 x = 2, y = -i x = 2, y = 2
10 Every prime number is also Rational number Even number Irrational number Multiple of two numbers
11 √23 is A rational number A irrational number An even integer A factor of 36
12 6 is A prime integar An irrational number A rational number An odd integer
13 0 (zero) is An irrational number A rational number A negative integer A positive number
14 The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if A = B≠ 0 A≠ B and both are of same sign A≠ B both are of opposite sign Either A = 0 or B =0
15 If the distance of any point on the curve from any of the two lines approaches zero then it is called Axis Directrices Asymptotes None
16 The ellipse and hyperbola are called Concentric conics Central conics Both a b None
17 The directrix of y2 =-4ax is y =-a y = a x = a x = -a
18 A line joining two distinct points on a parabola is called Axis Directrix Chord Tangent
19 For the parabola the line through focus and perpendicular to the directrix is called Tangent Vertex Axis None
20 The eccentricity e of an ellipse is always Rational Real Irrational Integer
21 The line y= 4x +c touches the hyperbola x2- y2 =1 if and only if c =±√2 c =0 c=±√17 c=±√15
22 If e,e′ be the eccentricities of two conics S=0 and S′ =0 and if e2 +e′2 =3 then both S and S′ can be Hyperbola Parabolas Ellipses None of these
23 The line 2x +√6y =2 is a tangent to the curve x2 -2y2 =4 The point of contact is (√6,1) (2,3) (7,-2√6) (4,-√6)
24 If eccentricity of ellipse becomes zero then it takes the form of A parabola A circle A straight line None of these
25 The sum of the focal distance from any point on the ellipse 9x2 +16y2 =144 is 32 16 18 8
26 The centre of the conic x2 +16x +4y2 -16y +76 =0 is (0,10) (-8,4) (-8,-2) (1,1)
27 Intersection of two parabolas parabola Two points Four points Hyperobla
28 If either A = 0 or B =0,then Ax2 +By2 +2Gx +2Fy +c =0 represents a Circle Hyperbola Ellipse Parabola
29 ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if h2 -ab &lt;0 h2 -ab≠ 0 h2 -ab =0 h2 -ab &gt;0
30 The remove the term involving xy, from 7x2 -6√3xy+ 13y2 -16 =0 the angel of rotation is θ = 30° θ = 45° θ = 60° θ = 75°
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