ECAT Pre Engineering MCQ Test With Answer for Chapter 6 Mathematics

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

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

Which of the following is a factor of x³- 3x²+ 2x - 6

• x + 2 A
• x + 3 B
• x - 3 C
• x - 4 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

The roots of px2 - (p-q)x-q=0 are

• equal A
• Irrational B
• Rational C
• Imaginary 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

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 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

• c/a A
• -c/a B
• b/a C
• -b/a D

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

If the roots of ax²- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is

• 
  A
• 
  B
• 
  C
• 
  D

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

• 1 A
• 2 B
• 0 C
• -4 D

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

• 2 A
• 1 B
• 0 C
• -1 D

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

• {-1} A
• {-3/5} B
• Empty set C
• {-1/3} D

Roots of the equation x²+ 7x + 12 = 0 are

• {3, -4} A
• {-3, 4} B
• {3, 4} C
• {-3, -4} D

The product of cube roots of unity is

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

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

• (-3,10) A
• (-3,-10) B
• (3,10) C
• (3,-10) D

• Polynomial of degree 0 A
• Polynomial of degree 1 B
• Polynomial of degree 2 C
• Polynomial of degree n D

w⁴= ______

• 0 A
• 1 B
• w C
• w² 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

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

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

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

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

• 1 A
• 2 B
• 1 and -7 C
• -7 D

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

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

There are ______ basic techniques for solving a quadratic equation

• Two A
• Three B
• Four 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

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

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

• -11 A
• 6 B
• -7 C
• 7 D