AP EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

AP EAMCET Mathematics - Quadratic Expressions

1. 51. Which of the following is the general form of a quadratic expression?
   • a) \( ax^2 + bx + c \) - Answer
   • b) \( ax^2 + bx = 0 \)
   • c) \( ax^2 = 0 \)
   • d) \( a + bx + c = 0 \)
2. 52. The roots of the quadratic equation \( ax^2 + bx + c = 0 \) can be determined using which of the following formulas?
   • a) Factorization method
   • b) Completing the square
   • c) The quadratic formula
   • d) All of the above - Answer
3. 53. If the discriminant of a quadratic equation \( ax^2 + bx + c = 0 \) is positive, the equation has:
   • a) One real root
   • b) Two distinct real roots - Answer
   • c) No real roots
   • d) Infinite real roots
4. 54. What is the maximum or minimum value of the quadratic expression \( f(x) = ax^2 + bx + c \) when \( a > 0 \)?
   • a) Maximum value
   • b) Minimum value - Answer
   • c) Zero
   • d) Not defined
5. 55. The vertex of the quadratic graph \( y = ax^2 + bx + c \) lies at:
   • a) \( \left( -\frac{b}{2a}, f\left( -\frac{b}{2a} \right) \right) \) - Answer
   • b) \( \left( \frac{b}{2a}, f\left( \frac{b}{2a} \right) \right) \)
   • c) \( \left( 0, c \right) \)
   • d) \( \left( 0, -c \right) \)
6. 56. The sign of a quadratic expression \( ax^2 + bx + c \) depends on:
   • a) The value of \( a \) alone
   • b) The value of \( b \) alone
   • c) The value of \( c \) alone
   • d) The values of \( a \), \( b \), and \( c \) - Answer
7. 57. Which of the following is the correct condition for a quadratic equation to have real and equal roots?
   • a) \( b^2 - 4ac > 0 \)
   • b) \( b^2 - 4ac = 0 \) - Answer
   • c) \( b^2 - 4ac < 0 \)
   • d) \( a = 0 \)
8. 58. Which of the following methods can be used to solve quadratic inequalities?
   • a) Graphing method
   • b) Sign analysis method
   • c) Both a and b - Answer
   • d) None of the above
9. 59. If \( x^2 - 4x + 3 \) is a quadratic expression, what is its value when \( x = 1 \)?
   • a) 0 - Answer
   • b) 1
   • c) 2
   • d) 3
10. 60. The quadratic inequality \( x^2 - 5x + 6 < 0 \) has solutions in the range:
    • a) \( 1 < x < 6 \) - Answer
    • b) \( 1 \leq x \leq 6 \)
    • c) \( x < 1 \) or \( x > 6 \)
    • d) \( x < 0 \) or \( x > 6 \)

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