ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

• 0 A
• 1 B
• 2 C
• None of these D

4^1+x+ 4^1-x= 10 is called

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

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

• a A
• x B
• 1 C
• 0 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

• 
  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

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

If a parabola opens down, then its vertex is at the

• Right of the parabola A
• Left of parabola B
• Lowest point on the parabola C
• Highest point on the parabola 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

If w is a cube root of unity then 1 + w + w²= ______

• 1 A
• 2 B
• 0 C
• -1 D

The roots of the equations will be equal if b²- 4ac is

• Positive A
• Negative B
• 1 C
• Zero D

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

• 7 A
• -2 B
• 6 C
• 1 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

• 
  A
• 
  B
• 
  C
• 
  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

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

• Rational A
• Irrational B
• Non-real C
• Zero 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

w²⁹= ______

• 0 A
• 1 B
• w C
• w² D

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

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

The minimum value of the quadratic function f(x) = x2 +6x -2, is

• 11 A
• 6 B
• -11 C
• 13 D

The roots of the equation 4x - 3.2x+2 + 32 = 0 would include

• 1 and 3 A
• 1 and 4 B
• 1 and 2 C
• 2 and 3 D

• 0 A
• -1-w² B
• 
  C
• 
  D

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

• 0 A
• -1 B
• 1 C
• 2 D

w⁴= ______

• 0 A
• 1 B
• w C
• w² D

Another name of quadratic equation is

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

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