ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

A polynomial of arbitrary degree

• f(x) = o A
• f(x) = x B
• f(x) = a C
• f(x) = ax + b,a ≠ 0 D

If the roots of ax²+ b = 0 are real and distinct then

• ab > 0 A
• a = 0 B
• ab < 0 C
• a > 0, b > 0 D

• 
  A
• 
  B
• 
  C
• 
  D

The roots of px2 - (p-q)x-q=0 are

• equal A
• Irrational B
• Rational C
• Imaginary 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

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

• 2 A
• 1 B
• 0 C
• -1 D

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

• 2 A
• 5 B
• 2,5 C
• 7 D

There are ______ basic techniques for solving a quadratic equation

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

Roots of the equation x²- 7x + 10 = 0 are

• {2, 5} A
• {-2, 5} B
• {2,5} C
• {-2,-5} D

The polynomial x - a is a factor of the polynomial f(x) if and only if

• f(a) is positive A
• f(a) is negative B
• f(a) = 0 C
• None of these D

The standard parabolic form of the equation f(x) = x² +4 x +1 is

• x(x+4)+1 A
• (x+2)²-3 B
• (x+4)³ + 9 C
• x(x-2)²+1 D

The roots of the equation will be irrational if b²- 4ac is

• Positive and perfect square A
• Positive but not a perfect square B
• Negative C
• Zero D

The solution set of x²- 5x + 6 = 0 is

• {1, 3} A
• {2, 3} B
• {1, 2} 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

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

• 7 A
• -2 B
• 6 C
• 1 D

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  A
• 
  B
• 
  C
• 
  D

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

• -5 A
• 5 B
• 0 C
• 1 D

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

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

• 4 A
• 3 B
• 50 C
• 7 D

If a parabola opens down, then its vertex is at the

• Right of the parabola A
• Left of parabola B
• Lowest point on the parabola C
• Highest point on the parabola D

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

• (-3,10) A
• (-3,-10) B
• (3,10) C
• (3,-10) D

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

The roots of (x - a)(x - b) = ab x2 are always

• Real A
• Depends upon a B
• Depends upon b C
• Depends upon a and b D

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

• 
  A
• 
  B
• 
  C
• 
  D

• Polynomial of degree 0 A
• Polynomial of degree 1 B
• Polynomial of degree 2 C
• Polynomial of degree n D

If the roots of ax2 + b =0 are real and distinct then

• ab > 0 A
• a = 0 B
• ab < 0 C
• a > 0,b > 0 D