ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

• 8 A
• 6 B
• 4 C
• None of these D

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

• b²+ 4ac A
• b²- 4ac B
• 4ac - b² C
• a²- 4ac 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 a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is

• ay2 +2by+c=0 A
• ay2+2by+4c=0 B
• ay2+2by+c=0 C
• ay2+by+4c=0 D

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

w⁷³= ______

• 0 A
• 1 B
• w C
• w² 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

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 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

• 1 A
• 2 B
• 0 C
• 4 D

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

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

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² 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

• Linear equation A
• Quadratic equation B
• Cubic equation 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

• 
  A
• 
  B
• 
  C
• 
  D

• b = c A
• a = c B
• a = c C
• 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

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

The graph of a quadratic function is

• Circle A
• Ellipse B
• Parabola C
• Hexagon 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

w²⁹= ______

• 0 A
• 1 B
• w C
• w² D

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

• equal A
• Irrational B
• Rational C
• Imaginary 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

Roots of the equation x²+ 7x + 12 = 0 are

• {3, -4} A
• {-3, 4} B
• {3, 4} C
• {-3, -4} 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

If one root of the equation x²- 3x + a = 0 is 2 then a = ______

• 0 A
• 1 B
• 2 C
• 3 D