ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

If the roots of ax2 + b =0 are real and distinct then

• ab > 0 A
• a = 0 B
• ab < 0 C
• a > 0,b > 0 D

• 0 A
• -1-w² B
• 
  C
• 
  D

The expression x2 - x + 1 has

• One proper linear factor A
• No proper linear factor B
• Two proper linear factors C
• None of these D

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

• 0 A
• 1 B
• 2 C
• 3 D

• -1 A
• 0 B
• 2 C
• 1 D

Roots of the equation 2x²- 7x + 3 = 0 are

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

The condition for ax2 + bx c to be expressed as the product of linear polynomials is

• b4 - 4ac =0 A
• b4- 4ac ≥0 B
• b4- 4ac <0 C
• b4= 4ac D

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 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

There are ______ basic techniques for solving a quadratic equation

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

The roots of the equation ax²+ bx + x = 0 are real and distinct if

• b²- 4ac <0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 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

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

A quadratic equation in x is an equation that can be witten in the form

• ax² + b = 0 A
• ax³ +b²+c=0 B
• ax² +bx+c=0 C
• ax³ +bx³+cx=0 D

• 
  A
• 
  B
• 
  C
• 
  D

Roots of the equation x²- x = 2 are

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

w⁷³= ______

• 0 A
• 1 B
• w C
• w² 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+ 4x³- 2x +5 is divided by x - 1, then the reminder is

• 8 A
• 6 B
• 4 C
• None of these D

If ax²+ bx + x = 0 is satisfied by every value of x, then

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

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

• 0 A
• 7 B
• -7 C
• 5 D

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

• x+1 A
• 2x+1 B
• 3x+1 C
• 2x-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

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

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

• -11 A
• 6 B
• -7 C
• 7 D

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

• 11 A
• 6 B
• -11 C
• 13 D

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

• 0 A
• 2 B
• 18 C
• 14 D

The roots of the equation 4x - 3.2x+2 + 32 = 0 would include

• 1 and 3 A
• 1 and 4 B
• 1 and 2 C
• 2 and 3 D

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

• (5, 3, 1) A
• (4, 3, 2) B
• (5, 5, 1) C
• (6, 4, 1) D

• 4 A
• 6 B
• 8 C
• 10 D