ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

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

• Polynomial of degree 0 A
• Polynomial of degree 2 B
• Quadratic equation C
• None of these D

The discriminant of the quadratic equation ax²+ bx + c = 0 is

• b²+ 4ac A
• b²- 4ac B
• 4ac - b² C
• a²- 4ac 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

• 2 A
• 4 B
• 8 C
• 16 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

• 
  A
• 
  B
• 
  C
• 
  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 9x²- 12x + 4 = 0 are

• Real and equal A
• Real and distinct B
• Complex C
• None of these D

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

• 0 A
• -1 B
• 1 C
• 2 D

If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

• x²+ Sx - P = 0 A
• x²- Sx + P = 0 B
• x²- Sx - P = 0 C
• X²+ Sx + P = 0 D

if one root of the equation ix2 - 2(i + 1) x +(2 - i)= 0 is 2 - i then the other root is

• -i A
• 2 + i B
• i C
• 2 - i 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

If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

• 0 A
• a³ B
• 2a³ C
• -2a³ D

• 0 A
• 1 B
• 2 C
• 3 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 cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  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

• c/a A
• -c/a B
• b/a C
• -b/a D

If the roots of ax²- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is

• 
  A
• 
  B
• 
  C
• 
  D

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

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

The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

• 2 A
• 1 B
• -1 C
• -2 D

If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is

• ay2 +2by+c=0 A
• ay2+2by+4c=0 B
• ay2+2by+c=0 C
• ay2+by+4c=0 D

• 
  A
• 
  B
• 
  C
• 
  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 quadratic equation has two

• roots A
• degree B
• variables C
• constants 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 + px + 1 is a factor of ax³+ bx +c, then

• a²+ c²= -ab A
• a²- c²= -ab B
• a²- c²= ab C
• None of these 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