ECAT Pre General Science Mathematics Online Test With Answers

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ECAT Pre General Science Mathematics Online Test

Sr. # Questions Answers Choice
1 The straight line passing through the focus and perpendicular to the directrix of the conic is known as its Tangent axis Focal chord major or manor axis
2 If a,b = 0 then a |b a||b a = b None
3 If a,b,c are three non-coplanar vector then [a +b,b +c,c +a] = _____ [a.b.c] 2[a,b,c] [abc]-2 2[abc]2
4 If a +b +c =0 then which of the following is true a =b =c =0 a,b =b,c =c,a a xb=b xc =c xa None
5 If |a x b|2 + (a,b)2 = _____ |a|2 + |b|2 |a|2- |b|2 |a|2|b|2 None
6 Three points whose position vector a,b,c are collinear axb +b x c+ c x a = 0 a,b +b,c +c,a =0 a,|a xc| =0 a+b+c =0
7 If a2 = b2 then a = b a+b= 1 |a+b| =0 None
8 The zero vector is regarded to be parallel to Every vector Is some cases Both a,b None
9 Projection of vector u along v is |v| cosθ |u| cosθ |v| sinθ |u| sinθ
10 The null vector is regarded to be perpendicular to Every vector In some cases Both a b None
11 For two vector a and b, a+b = _______ a b b+a b-a None
12 The point (1,3) is one solution of 3x + 5y > 29 3x + 5y < 7 x + 2y < 4 x + 4y > 3
13 Optimal solution is found by evaluation the objective function at All point of feasible region Corner point Origin None
14 A function which is to be maximized or minimized is called an Explicit function Implicit function Objective function None
15 Each point of the feasible region is called Solution feasible solution Both a & b None
16 A point (x,y) which satisfy a linear inequality in two variables form its Solution Domain Range None
17 If |αi + (α+1)j +2k| =3 then value of α is 1,2 -1,-2 1,-2 -1,2
18 [i,j,k] 0 2 1 -2
19 If a,b c are sides of a triangle taken in order then a x b = b x c b x a cxa Both a & b
20 The number z so that the triangle with vertices A(1,-1,0),B(-2,2,1)and C(0,2,z) is a right triangle with right angle at vertex C 1,2 -1,-2 2,-1 -2,1
21 If θ be angle between u,v and u,v determine the sides of a triangle then the third side opposite to angle θ has length |u+v| |u|+|v| |u-v| |u|-|v|
22 If a,b,c are unit vectors then |a + b|2 +|a - b|2 4 8ab 9cos 4(a,b)
23 A point where two of its boundary lines intersect is called Corner point Feasible point Vertex Feasible solution
24 Corner point of the system x - y≤ 2,x + y≤ 4,2x -y≤ 6,x≥ 0,y≥ 0 (1,4) (4,2) (3,1) (4,1)
25 Which of the following is not a solution of system of inequalities 2x- 3y ≤6,2x +y≥ 2,x +2y≤ 8, x≥ 0,y ≥ 0 (1,0) (0,4) (3,0) (8,0)
26 Sum of two quantities is at least 20 is denoted by x +y =20 x +y≥ 20 x +y≠ 20 x +y≤20
27 Maximum value of z =15x +20y subject to 3x+ 4y≤ 12,x,y≥ 0 is given by 46 60 50 70
28 The maximum value of Z = 3x+ 4y subjected to the constrains x+ y≤ 40,x+ 2y≤ 60, x≥ 0 and y≥ 0 is 120 100 140 160
29 If a force F = 2i + j +3k acts at point (1,-2,2) of a body then the moment of F about a pint lying on the line of action of the force is 5 Equal to the moment of the force about origin 0 Cannot be found
30 u,v,wand u x (v.w) are Equal Parallel Additive immense of each other Meaningless
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