ECAT Pre Engineering MCQ Test With Answer for Chapter 24 Mathematics

If |a x b|2 + (a,b)2 = _____

• |a|2 + |b|2 A
• |a|2- |b|2 B
• |a|2|b|2 C
• None D

Which of the following is a vector.

• distance A
• temperature B
• energy C
• acceleration D

Three points whose position vector a,b,c are collinear

• axb +b x c+ c x a = 0 A
• a,b +b,c +c,a =0 B
• a,|a xc| =0 C
• a+b+c =0 D

• 
  A
• 
  B
• 
  C
• none of these D

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| A
• |u|+|v| B
• |u-v| C
• |u|-|v| D

• 
  A
• 
  B
• 
  C
• 
  D

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 A
• -1,-2 B
• 2,-1 C
• -2,1 D

• 
  A
• 
  B
• 
  C
• 
  D

If a +b +c =0 then which of the following is true

• a =b =c =0 A
• a,b =b,c =c,a B
• a xb=b xc =c xa C
• None D

• [0, 0, 0] A
• [1, 0, 0] B
• [0, 1, 0] C
• [0, 0, 1] D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If a,b,c are unit vectors then |a + b|2 +|a - b|2

• 4 A
• 8ab B
• 9cos C
• 4(a,b) D

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

• A,. B, C are coincident A
• A, B, C are collinear B
• Both A and B C
• None of these D

Which of the following represents a vector

• 
  A
• 
  B
• 
  C
• (x, y) D

Projection of vector u along v is

• |v| cosθ A
• |u| cosθ B
• |v| sinθ C
• |u| sinθ D

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• none of these D

• 12 A
• 6 B
• 8 C
• none of these D

• 
  A
• 
  B
• 0 C
• 1 D

• 
  A
• 
  B
• 
  C
• 
  D

The position vector of the point P(a, b, c) is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• none of these D

If a2 = b2 then

• a = b A
• a+b= 1 B
• |a+b| =0 C
• None D

• 1 A
• 0 B
• 
  C
• 
  D

If C is the mid point of AB and P is any point outside AB, then

• 
  A
• 
  B
• 
  C
• 
  D