ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

• 1 A
• 0 B
• 4 C
• None of these 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

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

• 0 A
• 1 B
• 2 C
• 3 D

Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

• c = 0 A
• c = 0,b≠ 0 B
• b = 0,c = 0 C
• b = 0,c≠ 0 D

Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

• 
  A
• 
  B
• 
  C
• 
  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+ b = 0 are real and distinct then

• ab > 0 A
• a = 0 B
• ab < 0 C
• a > 0, b > 0 D

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

The solution set of x²- 5x + 6 = 0 is

• {1, 3} A
• {2, 3} B
• {1, 2} C
• None of these D

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

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

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

• 1 A
• 2 B
• 0 C
• -4 D

Another name of quadratic equation is

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

If the roots of 3x2+kx + 12 = 0 are equal then k = ______

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following is a factor of x³- 3x²+ 2x - 6

• x + 2 A
• x + 3 B
• x - 3 C
• x - 4 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

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

The roots of (b-c)x2+(c-a) x+a-b=0 are equal if

• 2b = a+c A
• 2a = b+c B
• 2c = a+b C
• a + b + c =0 D

If a polynomial p(x) is divided by x-c, then the remainder is

• p(x) A
• x-c B
• c C
• P(c) D

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

• 0 A
• 2 B
• 18 C
• 14 D

• 
  A
• 
  B
• 
  C
• 
  D

w^-1= ______

• 0 A
• 1 B
• w C
• w² 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 x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

• 8 A
• 6 B
• 4 C
• None of these D

• -1 A
• 0 B
• 2 C
• 1 D

• 1 A
• 2 B
• 0 C
• 4 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

w⁴= ______

• 0 A
• 1 B
• w C
• w² D