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

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 product of cube roots of unity is

• Zero A
• 1 B
• -1 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

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

• 4 A
• 6 B
• 8 C
• 10 D

• 
  A
• 
  B
• 
  C
• 
  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 f(x) = ax², and a>0, then the lowest point on the parabola is called.

• Vertex of parabola A
• Co-ordinates of parabola B
• Roots of the equation C
• Coefficient of the equation D

If a polynomial P(x) is divided by x - a, then the remainder is

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

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

• 11 A
• 6 B
• -11 C
• 13 D

If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then

• k=0 A
• k=1 B
• k=w C
• k=w2 D

• Polynomial of degree 0 A
• Polynomial of degree 1 B
• Polynomial of degree 2 C
• Polynomial of degree n D

• 0 A
• 1 B
• 2 C
• 3 D

If a > 0,b > 0, c > 0 then the roots of the equation ax2+ bx + c =0 are

• Real and negative A
• Non-real with negative real parts B
• Real and positive C
• Nothing can be said D

• c/a A
• -c/a B
• b/a C
• -b/a D

There are ______ basic techniques for solving a quadratic equation

• Two A
• Three B
• Four C
• None of these 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

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 D

Roots of the equation 9x²- 12x + 4 = 0 are

• Real and equal A
• Real and distinct B
• Complex 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

The roots of the equation x2 +6x-7=0,are

• 1 A
• 2 B
• 1 and -7 C
• -7 D

A quadratic equation has two

• roots A
• degree B
• variables C
• constants D

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

• 1 A
• 2 B
• 0 C
• -1 D

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

• 
  A
• 
  B
• 
  C
• 
  D

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is

• 0 A
• 2 B
• 1 C
• 5 D

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

• (5, 3, 1) A
• (4, 3, 2) B
• (5, 5, 1) C
• (6, 4, 1) 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

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

(x-1) is a factor of

• 2x³-3x²+9 A
• 2x³-5x-8 B
• 48x^2-46x-9 C
• x⁹-1 D