ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 6

• 1 A
• -1 B
• 5 C
• 2 D

Each complex cube root of unity is square of

• itself A
• 1 B
• -1 C
• the other D

The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in

• 
  A
• 
  B
• 
  C
• 
  D

In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is

• Straight line A
• Circle B
• Hyperbola C
• Symmetric w.r.t.0 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

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

• x+1 A
• 2x+1 B
• 3x+1 C
• 2x-1 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

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

• a + b + c = 0 A
• a + b + c > 0 B
• a + b + c < 0 C
• None of these D

The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0

• 4 A
• 64 B
• 8 C
• All values of k D

Two quadratic equation in which xy term is missing and the coefficients of x²and y²are equal, give a linear equation by ______

• Addition A
• Subtraction B
• Multiplication C
• Division D

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  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

The two parts into which 57 should be divided so that their product is 782 are

• 43,14 A
• 34,23 B
• 33,24 C
• 44,13 D

2x³+ 3x + 9 is a ______

• Polynomial of degree 3 A
• Quadratic equation B
• Cubic equation C
• Polynomial of degree 2 D

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

• Rational A
• Irrational B
• Complex C
• None of these 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 the equation |x²| + |x| -6 =0, the roots are

• One and only one real number A
• Real with sum one B
• Real with sum zero C
• Real with product zero 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 x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

• 8 A
• 6 B
• 4 C
• None of these D

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

• 0 A
• 1 B
• 2 C
• 3 D

The graph of a quadratic function is

• Circle A
• Ellipse B
• Parabola C
• Hexagon D

If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

• -5 A
• 5 B
• 0 C
• 1 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

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

• Opens up A
• Opens down B
• close up C
• symmetric w.r.t.x.axis D

In quadratic equation y=ax³ +bx+c, if b and c are both zero then the graph is

• Symmetric w.r.t.y-axis A
• Symmetric w.r.t.x-axis B
• Straight Line C
• Circle 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

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

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

If b²- 4ac is positive then the roots of the equation are

• Real A
• Imaginary B
• Positive C
• Negative D