ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

• 0 A
• 1 B
• 2 C
• 3 D

The product of cube roots of unity is

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 1 A
• 2 B
• 1 and -7 C
• -7 D

The roots of the equation ax²+ bx + c = 0 are real and equal if

• b²- 4ac < 0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 C
• None of these 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

• n if n is even A
• 0 for any natural number n B
• 1 if in odd 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 solution of the quadratic equation x2 -7x + 10=0, is

• 2 A
• 5 B
• 2,5 C
• 7 D

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

Roots of the equation x²- 7x + 10 = 0 are

• {2, 5} A
• {-2, 5} B
• {2,5} C
• {-2,-5} D

The roots of ax2 + bx + c = 0 are always unequal if

• b2 - 4ac = 0 A
• b2- 4ac ≠ 0 B
• b2- 4ac > 0 C
• b2- 4ac ≥ 0 D

w²⁹= ______

• 0 A
• 1 B
• w C
• w² D

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

• 1 A
• 2 B
• 0 C
• -1 D

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 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 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

• 4 A
• 6 B
• 8 C
• 10 D

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

• -5 A
• 5 B
• 0 C
• 1 D

Roots of the equation x²+ 5x - 1 = 0 are

• Rational A
• Irrational B
• Complex C
• None of these 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

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

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

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

• a > 0 A
• a < 0 B
• a≠ 0 C
• a≠ 0,b ≠ 0 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

(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if

• a+b=c+d A
• a+c=b+d B
• a+d=b+c C
• All are correct D

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

• (x + 2)2(x - 1) A
• (x + 2)(x - 1)2 B
• (x+2)(x2- x- 2) C
• (x + 2)2(x - 1)2 D

• 15 A
• 9 B
• 7 C
• 8 D

If a parabola opens down, then its vertex is at the

• Right of the parabola A
• Left of parabola B
• Lowest point on the parabola C
• Highest point on the parabola D