ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

The graph of the quadratic equation is

• Straight line A
• Circle B
• Parabola C
• elipse D

• -1 A
• 0 B
• 2 C
• 1 D

Root of the equation 3^x-1+ 3^1-x= is

• 2 A
• 1 B
• 0 C
• -1 D

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

• {-1} A
• {-3/5} B
• Empty set C
• {-1/3} D

The roots of ax2+bx+c=0 are

• Rational ⇔ b2 -4 ac ≥ 0 A
• Irrational ⇔ b2-4 ac > 0 B
• Real ⇔ b2-4 ac ≠ 0 C
• Rational⇔ b2-4 ac = 0 D

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

• (x + 2)2(x - 1) A
• (x + 2)(x - 1)2 B
• (x+2)(x2- x- 2) C
• (x + 2)2(x - 1)2 D

If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

• 8 A
• 6 B
• 4 C
• None of these D

If the roots of 3x2+kx + 12 = 0 are equal then k = ______

• 
  A
• 
  B
• 
  C
• 
  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

• 15 A
• 9 B
• 7 C
• 8 D

• 
  A
• 
  B
• 
  C
• 
  D

The expression x2 - x + 1 has

• One proper linear factor A
• No proper linear factor B
• Two proper linear factors C
• None of these D

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

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

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

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 D

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

• 0 A
• 2 B
• 18 C
• 14 D

If a > 0,b > 0, c > 0 then the roots of the equation ax2+ bx + c =0 are

• Real and negative A
• Non-real with negative real parts B
• Real and positive C
• Nothing can be said 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

The condition for polynomial equation ax²+ bx + c = 0 to be quadratic is

• 
  A
• 
  B
• 
  C
• 
  D

There are ______ basic techniques for solving a quadratic equation

• Two A
• Three B
• Four C
• None of these D

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

• 2 A
• 4 B
• 8 C
• 16 D

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

4^1+x+ 4^1-x= 10 is called

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

• 0 A
• 1 B
• 2 C
• 3 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

The maximum value of the quadratic function f(x) = -2x2+20x,is

• 4 A
• 3 B
• 50 C
• 7 D

If the roots of ax²- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is

• 
  A
• 
  B
• 
  C
• 
  D

If b²- 4ac is positive then the roots of the equation are

• Real A
• Imaginary B
• Positive C
• Negative D