ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

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

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

• 15 A
• 9 B
• 7 C
• 8 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 product of cube roots of unity is

• Zero A
• 1 B
• -1 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

• -1 A
• 0 B
• 2 C
• 1 D

Which of the following is factor of x11+a11, where n is an odd integer

• x-a A
• x+a B
• 2x-a C
• 2x+a D

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

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

w⁴= ______

• 0 A
• 1 B
• w C
• w² 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

w^-12= ______

• 0 A
• 1 B
• w C
• w² 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

The standard form of the quadratic function f(x) = -x² +4x+2, is

• (x-2)²+6 A
• -(x-2)² + 6 B
• (x-3)²+5 C
• (x+4)²-7 D

The minimum value of the quadratic function f(x) = 5 x 2-11,is

• -11 A
• 6 B
• -7 C
• 7 D

5x³+ 3x - is a ______

• Polynomial of degree 3 A
• Polynomial of degree 2 B
• Polynomial of degree 1 C
• Polynomial of degree 0 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 expression x2 - x + 1 has

• One proper linear factor A
• No proper linear factor B
• Two proper linear factors C
• None of these D

Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then

• α = β A
• αβ = 1 B
• α = β C
• α = 1 D

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 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 solution of equation x2 + 2 = 0 in the set of real number is

• Infinite set A
• Singleton set B
• Null set C
• None of these 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

• n if n is even A
• 0 for any natural number n B
• 1 if in odd C
• None of these 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

• 
  A
• 
  B
• 
  C
• 
  D

w⁷³= ______

• 0 A
• 1 B
• w C
• w² 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

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

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D