ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

• 
  A
• 
  B
• 
  C
• 
  D

A polynomial P(x)has a factor (x-a)if P(a) =

• a A
• x B
• 1 C
• 0 D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

If a polynomial P(x) is divided by x + a, then the remiander is

• P(a) A
• P(-a) B
• P(0) C
• None of these D

The roots of the equation will be irrational if b²- 4ac is

• Positive and perfect square A
• Positive but not a perfect square B
• Negative C
• Zero 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 minimum value of the quadratic function f(x) = 5 x 2-11,is

• -11 A
• 6 B
• -7 C
• 7 D

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

• 
  A
• 
  B
• 
  C
• 
  D

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

• 7 A
• -2 B
• 6 C
• 1 D

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

• 1 A
• 2 B
• 0 C
• -4 D

w^-12= ______

• 0 A
• 1 B
• w C
• w² D

• 
  A
• 
  B
• 
  C
• 
  D

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

• 8 A
• -16 B
• -64 C
• 16 D

w⁴= ______

• 0 A
• 1 B
• w C
• w² 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 maximum value of the quadratic function f(x) = -2x2+20x,is

• 4 A
• 3 B
• 50 C
• 7 D

The solution set of x²- 5x + 6 = 0 is

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

The roots of the equation ax²+ bx + x = 0 are real and distinct if

• b²- 4ac <0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 C
• None of these D

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

• (-3,10) A
• (-3,-10) B
• (3,10) C
• (3,-10) D

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

• 2 A
• 5 B
• 2,5 C
• 7 D

• 0 A
• 1 B
• 2 C
• 3 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

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

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

• Positive A
• Negative B
• Real 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

• 4 A
• 6 B
• 8 C
• 10 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 x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

• -7 A
• 7 B
• 0 C
• None of these D