ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

The minimum value of the quadratic function f(x) = 5 x 2-11,is

• -11 A
• 6 B
• -7 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

A polynomial of arbitrary degree

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

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

• 3 A
• -3 B
• 2 C
• 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 condition for polynomial equation ax2 + bx + c = 0 to be quadratic is

• a > 0 A
• a < 0 B
• a≠ 0 C
• a≠ 0,b ≠ 0 D

Another name of quadratic equation is

• Polynomial A
• 2nd degree polynomial B
• Linear equation C
• simaltaneous equations D

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

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

If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is

• 1 A
• 3 B
• 2 C
• 4 D

The product of cube roots of unity is

• Zero A
• 1 B
• -1 C
• None of these D

• Lies between 4 and 7 A
• Lies between 5 and 9 B
• Has no value between 4 and 7 C
• Has no value between 5 and 9 D

Roots of the equation 2x²- 7x + 3 = 0 are

• Rational A
• Irrational B
• Complex C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

For any integer k, wⁿ= ______ when n = 3k

• 1 A
• 2 B
• 0 C
• -4 D

• 1 A
• -1 B
• 5 C
• 2 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

A polynomial P(x)has a factor (x-a)if P(a) =

• a A
• x B
• 1 C
• 0 D

The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

• 2 A
• 1 B
• -1 C
• -2 D

Roots of the equation x²+ 5x - 1 = 0 are

• Rational A
• Irrational B
• Complex C
• None of these 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

There are ______ basic techniques for solving a quadratic equation

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

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 D

w⁷³= ______

• 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

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

• -6 A
• 2 B
• -2 C
• 6 D

• 15 A
• 9 B
• 7 C
• 8 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

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