Step-by-step Solution:

Let's analyze each statement to determine its validity: (A) A equation \( ax^2 + bx + c = 0 \) has real and distinct roots if \( b^2 - 4ac \geq 0 \) and \( a \neq 0 \). For a quadratic equation to have real and distinct roots, the discriminant must be positive, i.e., \( b^2 - 4ac > 0 \). The statement says \( b^2 - 4ac \geq 0 \), which includes the case of equal roots (when \( b^2 - 4ac = 0 \)). Therefore, \[the statement is *false*.\] (B) The unit digit in \( 49^{18} \) is 1. To find the unit digit of \( 49^{18} \), observe the pattern of the unit digit of powers of 9: - \( 9^1 = 9 \) (unit digit 9) - \( 9^2 = 81 \) (unit digit 1) - \( 9^3 = 729 \) (unit digit 9) - \( 9^4 = 6561 \) (unit digit 1) The unit digit alternates between 9 and 1 for odd and even exponents, respectively. Since 18 is even, the unit digit of \( 49^{18} \) is 1. Therefore, \[the statement is *true*.\] (C) If two lines make complementary angles with the axis of x then the product of their slopes is 1. If two lines make complementary angles \( \theta \) and \( 90^\circ - \theta \) with the x-axis, their slopes are \( m_1 = \tan \theta \) and \( m_2 = \tan (90^\circ - \theta) = \cot \theta \). The product of the slopes is: \[ m_1 \cdot m_2 = \tan \theta \cdot \cot \theta = 1 \] Therefore, \[the statement is *true*.\] (D) The line \( bx - ay = 0 \) meet the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \). To check if the line intersects the hyperbola, substitute \( y = \frac{b}{a}x \) into the hyperbola equation: \[ \frac{x^2}{a^2} - \frac{\left(\frac{b}{a}x\right)^2}{b^2} = 1 \] \[ \frac{x^2}{a^2} - \frac{b^2 x^2}{a^2 b^2} = 1 \] \[ \frac{x^2}{a^2} - \frac{x^2}{a^2} = 1 \] \[ 0 = 1 \] This is a contradiction, meaning the line does not intersect the hyperbola. Therefore, the statement is false. Correct Statements: - (B) and (C) are true. Final Answer: \[ \boxed{B} \]