ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

w²⁹= ______

• 0 A
• 1 B
• w C
• w² 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

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 a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

• p²+ c/a A
• p²+ a/c B
• p²+ c/a C
• p²- c/a D

• 
  A
• 
  B
• 
  C
• 
  D

If b²- 4ac = 0 then the roots of the equation are

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

Another name of quadratic equation is

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

Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

• c = 0 A
• c = 0,b≠ 0 B
• b = 0,c = 0 C
• b = 0,c≠ 0 D

w^-1= ______

• 0 A
• 1 B
• w C
• w² D

The maximum value of the quadratic function f(x) = 2x2-4x+7,is

• 3 A
• 5 B
• -3 C
• -5 D

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

• p²- q²+ 2pr = 0 A
• (p + r)²= q²- r² B
• p²+ q²- 2pr = 0 C
• (p - r)²= q²+ r² 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 product of cube roots of unity is

• Zero A
• 1 B
• -1 C
• None of these D

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

The roots of ax2+bx+c=0 are

• Rational ⇔ b2 -4 ac ≥ 0 A
• Irrational ⇔ b2-4 ac > 0 B
• Real ⇔ b2-4 ac ≠ 0 C
• Rational⇔ b2-4 ac = 0 D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

w^-12= ______

• 0 A
• 1 B
• w C
• w² D

w⁴= ______

• 0 A
• 1 B
• w C
• w² 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

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

• 1 A
• 0 B
• 4 C
• None of these 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

If a polynomial P(x) is divided by x + a, then the remiander is

• P(a) A
• P(-a) B
• P(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

• 15 A
• 9 B
• 7 C
• 8 D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

• 4 A
• 6 B
• 8 C
• 10 D

• 0 A
• 1 B
• 2 C
• None of these D