ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

A quadratic equation has two

• roots A
• degree B
• variables C
• constants D

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

• Opens up A
• Opens down B
• close up C
• symmetric w.r.t.x.axis D

• 
  A
• 
  B
• 
  C
• 
  D

If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is

• 0 A
• ±1 B
• ±5 C
• ±7 D

• (-1, 2) A
• (-1, 1) B
• (1, 2) C
• {-1} D

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D

The roots of the equation ax²+ bx + x = 0 are real and distinct if

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

• Two real roots A
• Two positive roots B
• Two negative roots C
• One positive and one negative root D

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

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

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• equal A
• Irrational B
• Rational C
• Imaginary 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

If f(x) = ax², and a>0, then the lowest point on the parabola is called.

• Vertex of parabola A
• Co-ordinates of parabola B
• Roots of the equation C
• Coefficient of the equation D

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² 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

If b²- 4ac = 0 then the roots of the equation are

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

w^-1= ______

• 0 A
• 1 B
• w C
• w² D

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

• 3 A
• 5 B
• -3 C
• -5 D

If a polynomial P(x) is divided by x + a, then the remiander is

• P(a) A
• P(-a) B
• P(0) C
• None of these D

The sum of the roots of the equation x2 -6x +2 = 0 is

• -6 A
• 2 B
• -2 C
• 6 D

If 2x^1/3+ 2x^-1/3= 5, then x is equal to

• 1 or -1 A
• 2 or 1/2 B
• 8 or 1/8 C
• 4 or 1/4 D

• 
  A
• 
  B
• 
  C
• 
  D

• Polynomial of degree 0 A
• Polynomial of degree 2 B
• Quadratic equation C
• None of these D

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

If x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

• -7 A
• 7 B
• 0 C
• None of these D

The quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

• Infinitely many roots A
• Exactly two roots B
• Exactly four roots C
• No roots 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