Mathematics ECAT Pre Engineering Online Test

The roots of the equation ax²+ bx + c = 0 are real and equal if

• b²- 4ac < 0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 C
• None of these D

If A and B are two matrices such that AB = B and BA = A then A2 + B2 =

• 2 AB A
• 2 BA B
• A + B C
• AB D

The maximum value of 12 sinθ-9 sin²θis x

• 3 A
• 4 B
• 5 C
• None of these D

Identity w.r.t intersection in a power set of any set is

• ∅ A
• Set itself B
• Singleton set C
• {0} D

In set builder notation the set {0,1,2,........100} can be written as

• {x / xε B ∧ x ≤ 100} A
• {x / x ∈ W ∧ x < 101} B
• {x / x ∈ Z ∧ x < 101} C
• The set of first 100 whole numbers D

• Parallel to the plane A
• At right angles to the plane B
• Lies in the plane C
• Meet the plane obliquely D

A function from X to Y is written as

• 
  A
• f : X to Y B
• 
  C
• f : Y to Y D

Find the next two terms of 7, 9, 12, 16,...

• 18, 20 A
• 19, 22 B
• 20, 25 C
• 21, 27 D

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 20 B
• 90 C
• 80 D

The 60th part of one minute is called

• Degree A
• Second B
• Radiam C
• None of these D

• Diagonal matrix A
• Scalar matrix B
• Triangular matrix C
• Identity matrix D

The set { {a,b} } is

• Infinite set A
• Singleton set B
• Two points set C
• Empty set D

• 
  A
• a f(x) + c B
• f(x) + a C
• 
  D

• 2x + 3 A
• x²+ 3 + c B
• 
  C
• 
  D

If 4 ⁶P_r= ⁶P_r+1, then r is equal to

• 4 A
• 3 B
• 2 C
• 1 D

Find a if 1 is a root of the equation x²+ ax + 2 = 0

• 3 A
• -3 B
• 2 C
• 0 D

6 is

• A prime integer A
• An irrational number B
• A rational number C
• An odd integer D

The sum of even coefficient in the binomial expansion is

• 2ⁿ⁺¹ A
• 2ⁿ B
• 2^n-1 C
• 2n D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

If Z₁ = 1+ i, Z₂ = 2+3i , then |Z₁ -Z₂| =?

• √5 A
• √7 B
• -1-2i C
• √3 D

22.5°=______

• 
  A
• 
  B
• 
  C
• 
  D

The largest possible domain of the function:

y=√(x ) is:

• (0 ,∞) A
• 12 B
• (3 , 12) C
• ( 3 ,∞) D

If eccentricity of ellipse becomes zero then it takes the form of

• A parabola A
• A circle B
• A straight line C
• None of these D

• trigonometric equation A
• conditional equation B
• identity C
• None D

The solution of the quadratic equation x2 -7x + 10=0, is

• 2 A
• 5 B
• 2,5 C
• 7 D

A circle which touches one side of a triangle extermally and the other two sides produced is called

• In-circle A
• Circumcircle B
• e-circle C
• Point circle D

• 1 A
• -1 B
• 0 C
• I D

Optimal solution is found by evaluation the objective function at

• All point of feasible region A
• Corner point B
• Origin C
• None D

• 
  A
• 
  B
• 
  C
• 
  D