ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

The roots of ax2 + bx + c = 0 are always unequal if

• b2 - 4ac = 0 A
• b2- 4ac ≠ 0 B
• b2- 4ac > 0 C
• b2- 4ac ≥ 0 D

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 D

w¹¹= ______

• 0 A
• 1 B
• w C
• w² D

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

• p²- q²+ 2pr = 0 A
• (p + r)²= q²- r² B
• p²+ q²- 2pr = 0 C
• (p - r)²= q²+ r² D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• (a - c)²= b²- c² A
• (a - c)²= b²+ c² B
• (a + c)²= b²- c² C
• (a + c)²= b²+ c² D

• 0 A
• 1 B
• 2 C
• 3 D

In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are

• 6, 10 A
• -6, -10 B
• 8, 8 C
• -8, -8 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 0 A
• 2 B
• 18 C
• 14 D

The product of the four fourth roots of unity is

• 0 A
• 1 B
• -1 C
• None of these D

• 0 A
• 1 B
• 2 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

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

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

• 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

If x-2 and x-1 both are factors of x³-3x³+2x-4p, then P must equal to

• 1 A
• 2 B
• 0 C
• -2 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

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

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

• 2, 8 A
• 1, 3 B
• 1, 8 C
• 2, 3 D

the largest degree of the terms in the polynomials is called

• terms of the polynomial A
• degree of a polynomial B
• co-efficient C
• monomial D

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

• (0, 2π) A
• (-π, -0) B
• (0,π) C
• None of these D

The maximum value of the quadratic function f(x) = 2x2-4x+7,is

• 3 A
• 5 B
• -3 C
• -5 D

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

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

The standard parabolic form of the equation f(x) = x² +4 x +1 is

• x(x+4)+1 A
• (x+2)²-3 B
• (x+4)³ + 9 C
• x(x-2)²+1 D

The condition for ax2 + bx c to be expressed as the product of linear polynomials is

• b4 - 4ac =0 A
• b4- 4ac ≥0 B
• b4- 4ac <0 C
• b4= 4ac D

The solution of the quadratic equation x2 -7x + 10=0, is

• 2 A
• 5 B
• 2,5 C
• 7 D

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

• 
  A
• 
  B
• 
  C
• 
  D