ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D

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

Another name of quadratic equation is

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

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

• 
  A
• 
  B
• 
  C
• 
  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

The product of cube roots of unity is

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

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

• -5 A
• 5 B
• 0 C
• 1 D

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

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

(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if

• a+b=c+d A
• a+c=b+d B
• a+d=b+c C
• All are correct D

The roots of the equation x2 +6x-7=0,are

• 1 A
• 2 B
• 1 and -7 C
• -7 D

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

• 3 A
• -3 B
• 2 C
• 0 D

w²⁹= ______

• 0 A
• 1 B
• w C
• w² D

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

• -6 A
• 2 B
• -2 C
• 6 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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 2 B
• 0 C
• 4 D

• 1 A
• -1 B
• 5 C
• 2 D

The vertex of the graph of the quadratic function f(x) = x2 -10, is

• (0 , -10) A
• (-10,0) B
• (10,0) C
• (0,10) D

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

• (5, 3, 1) A
• (4, 3, 2) B
• (5, 5, 1) C
• (6, 4, 1) 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

For the equation |x²| + |x| -6 =0, the roots are

• One and only one real number A
• Real with sum one B
• Real with sum zero C
• Real with product zero D

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

• (x + 2)2(x - 1) A
• (x + 2)(x - 1)2 B
• (x+2)(x2- x- 2) C
• (x + 2)2(x - 1)2 D

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

• 0 A
• 2 B
• 18 C
• 14 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

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

Two quadratic equation in which xy term is missing and the coefficients of x²and y²are equal, give a linear equation by ______

• Addition A
• Subtraction B
• Multiplication C
• Division D

w⁴= ______

• 0 A
• 1 B
• w C
• w² D