ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

• 0 A
• 7 B
• -7 C
• 5 D

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

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

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

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

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

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

• 1 A
• 2 B
• 1 and -7 C
• -7 D

Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then

• α = β A
• αβ = 1 B
• α = β C
• α = 1 D

w^-12= ______

• 0 A
• 1 B
• w C
• w² D

The sum of the roots of the equation x2 -6x +2 = 0 is

• -6 A
• 2 B
• -2 C
• 6 D

Each complex cube root of unity is square of

• itself A
• 1 B
• -1 C
• the other 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

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

• (0, 2π) A
• (-π, -0) B
• (0,π) C
• None of these D

Root of the equation 3^x-1+ 3^1-x= is

• 2 A
• 1 B
• 0 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

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

• 0 A
• -1 B
• 1 C
• 2 D

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

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

Which of the following is factor of x11+a11, where n is an odd integer

• x-a A
• x+a B
• 2x-a C
• 2x+a 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

• Rational A
• Irrational B
• Non-real C
• Zero D

If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

• 0 A
• a³ B
• 2a³ C
• -2a³ 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

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

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

Roots of the equation x²- x = 2 are

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

• 
  A
• 
  B
• 
  C
• 
  D

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D

• Linear equation A
• Quadratic equation B
• Cubic equation C
• None of these D

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 D