ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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 product of cube roots of unity is

• Zero A
• 1 B
• -1 C
• None of these 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 discriminant of the quadratic equation ax²+ bx + c = 0 is

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

• 2 A
• 4 B
• 8 C
• 16 D

The vertex of the graph of the quadratic function f(x) = x2 -10, is

• (0 , -10) A
• (-10,0) B
• (10,0) C
• (0,10) 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

For any integer k, wⁿ= ______ when n = 3k

• 1 A
• 2 B
• 0 C
• -4 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

4^1+x+ 4^1-x= 10 is called

• Reciprocal equation A
• Exponential equation B
• Radical equation C
• None of these 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

There are ______ basic techniques for solving a quadratic equation

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

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 minimum value of the quadratic function f(x) = 5 x 2-11,is

• -11 A
• 6 B
• -7 C
• 7 D

• 1 A
• -1 B
• 5 C
• 2 D

w¹¹= ______

• 0 A
• 1 B
• w C
• w² D

• 4 A
• 6 B
• 8 C
• 10 D

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

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

The roots of (x - a)(x - b) = ab x2 are always

• Real A
• Depends upon a B
• Depends upon b C
• Depends upon a and b 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

• 
  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

• (-1, 2) A
• (-1, 1) B
• (1, 2) C
• {-1} D

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

• 0 A
• -1 B
• 1 C
• 2 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

• 0 A
• 1 B
• 2 C
• None of these D

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

• 3 A
• 5 B
• -3 C
• -5 D

• c/a A
• -c/a B
• b/a C
• -b/a D