ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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 a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

• p²+ c/a A
• p²+ a/c B
• p²+ c/a C
• p²- c/a D

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

• 4 A
• 3 B
• 50 C
• 7 D

• 1 A
• 2 B
• 0 C
• 4 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

• 
  A
• 
  B
• 
  C
• 
  D

• n if n is even A
• 0 for any natural number n B
• 1 if in odd C
• None of these D

Each complex cube root of unity is square of

• itself A
• 1 B
• -1 C
• the other 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

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

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

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

The graph of the quadratic equation is

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

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

• 2 A
• 1 B
• 0 C
• -1 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

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

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

w²⁹= ______

• 0 A
• 1 B
• w C
• w² D

If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

• x²+ Sx - P = 0 A
• x²- Sx + P = 0 B
• x²- Sx - P = 0 C
• X²+ Sx + P = 0 D

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

• 0 A
• 2 B
• 18 C
• 14 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

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  D

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

• 0 A
• -1 B
• 1 C
• 2 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 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

The minimum value of the quadratic function f(x) = x2 +6x -2, is

• 11 A
• 6 B
• -11 C
• 13 D

• 
  A
• 
  B
• 
  C
• 
  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

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

If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

• Negative A
• Positive B
• Zero C
• Nothing can be said D