ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D

• Only one real solution A
• Exactly three real solution B
• Exactly one rational solution C
• Non-real roots D

If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

• -5 A
• 5 B
• 0 C
• 1 D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

• 0 A
• 1 B
• 2 C
• None of these D

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

• x+1 A
• 2x+1 B
• 3x+1 C
• 2x-1 D

Roots of the equation 9x²- 12x + 4 = 0 are

• Real and equal A
• Real and distinct B
• Complex C
• None of these D

In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are

• 6, 10 A
• -6, -10 B
• 8, 8 C
• -8, -8 D

If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

• a = 0 A
• b = 0 B
• c = 0 C
• None of these D

In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is

• Straight line A
• Circle B
• Hyperbola C
• Symmetric w.r.t.0 D

• Rational A
• Irrational B
• Non-real C
• Zero D

The roots of the equation ax²+ bx + c = 0 are complex/imaginary if

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

2x³+ 3x + 9 is a ______

• Polynomial of degree 3 A
• Quadratic equation B
• Cubic equation C
• Polynomial of degree 2 D

The roots of ax2 + bx + c = 0 are always unequal if

• b2 - 4ac = 0 A
• b2- 4ac ≠ 0 B
• b2- 4ac > 0 C
• b2- 4ac ≥ 0 D

If one root of the equation ix²- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is

• -i A
• 2 + i B
• i C
• 2 - i D

The graph of a quadratic function is

• Circle A
• Ellipse B
• Parabola C
• Hexagon D

Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then

• α = β A
• αβ = 1 B
• α = β C
• α = 1 D

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is

• 0 A
• 2 B
• 1 C
• 5 D

• 
  A
• 
  B
• 
  C
• 
  D

The maximum value of the quadratic function f(x) = 2x2-4x+7,is

• 3 A
• 5 B
• -3 C
• -5 D

Roots of the equation x²+ 7x + 12 = 0 are

• {3, -4} A
• {-3, 4} B
• {3, 4} C
• {-3, -4} D

If ax + bx + c =0 is satisfied by every value of x,then

• b = 0,c = 0 A
• c = 0 B
• b = 0 C
• a = b = c = 0 D

If a polynomial P(x) is divided by x - a, then the remainder is

• P(o) A
• P(-a) B
• P(a) C
• None of these D

If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is

• ay2 +2by+c=0 A
• ay2+2by+4c=0 B
• ay2+2by+c=0 C
• ay2+by+4c=0 D

• 
  A
• 
  B
• 
  C
• 
  D

• Reciprocal equation A
• Exponential equation B
• Radical equation C
• None of these D

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

• 8 A
• -16 B
• -64 C
• 16 D

The discriminant of the quadratic equation ax²+ bx + c = 0 is

• b²+ 4ac A
• b²- 4ac B
• 4ac - b² C
• a²- 4ac D

Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

• Positive A
• Negative B
• Real C
• None of these D