ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

Another name of quadratic equation is

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

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

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

Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when

• q = 0, r = 0,p ≠ 0 A
• p = 0,qr≠ 0 B
• r = 0,pq≠ 0 C
• q = 0, pq≠ 0 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

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

• 11 A
• 6 B
• -11 C
• 13 D

• Linear equation A
• Quadratic equation B
• Cubic 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

Find a if 1 is a root of the equation x²+ ax + 2 = 0

• 3 A
• -3 B
• 2 C
• 0 D

The product of the four fourth roots of unity is

• 0 A
• 1 B
• -1 C
• None of these D

Roots of the equation x²- x = 2 are

• {2, -1} A
• {1, 0} B
• {2, 1} C
• {-2, 1} D

w²⁹= ______

• 0 A
• 1 B
• w C
• w² D

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

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

(x-1) is a factor of

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

A quadratic equation has two

• roots A
• degree B
• variables C
• constants 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

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

• 0 A
• 2 B
• 18 C
• 14 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

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 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 polynomial p(x) is divided by x-c, then the remainder is

• p(x) A
• x-c B
• c C
• P(c) 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 x³+ ax²- a²x - a³is divided by x + a, then the remainder is

• 0 A
• a³ B
• 2a³ C
• -2a³ 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

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

• 
  A
• 
  B
• 
  C
• 
  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

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

• 8 A
• -16 B
• -64 C
• 16 D

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

• 0 A
• 7 B
• -7 C
• 5 D

The synthetic division method is only used to divide a polynomial by

• quadratic equation A
• binomial B
• linear equation C
• monomial D

• 0 A
• 1 B
• 2 C
• 3 D