MCQs – Solutions of Equations in One Variable
\[ \text{Question 1:} \]
\[ \text{Which of the following methods is not used to solve nonlinear equations in one variable?} \]
\[ \text{(a) Bisection Method, \quad (b) Newton-Raphson Method, \quad (c) Gaussian Elimination, \quad (d) Secant Method} \]
\[ \text{Answer: C} \]
\[ \text{Question 2:} \]
\[ \text{The convergence rate of the Newton-Raphson method is:} \]
\[ \text{(a) Linear, \quad (b) Quadratic, \quad (c) Cubic, \quad (d) Logarithmic} \]
\[ \text{Answer: B} \]
\[ \text{Question 3:} \]
\[ \text{Which of the following methods requires two initial guesses?} \]
\[ \text{(a) Newton-Raphson Method, \quad (b) Secant Method, \quad (c) Fixed-Point Iteration, \quad (d) Bisection Method} \]
\[ \text{Answer: B} \]
\[ \text{Question 4:} \]
\[ \text{Which numerical method guarantees convergence for solving a single-variable equation if the function is continuous?} \]
\[ \text{(a) Newton-Raphson Method, \quad (b) Secant Method, \quad (c) Bisection Method, \quad (d) Fixed-Point Iteration} \]
\[ \text{Answer: C} \]
\[ \text{Question 5:} \]
\[ \text{If the derivative of a function is zero at a certain point, Newton-Raphson method may:} \]
\[ \text{(a) Converge faster, \quad (b) Fail to converge, \quad (c) Have cubic convergence, \quad (d) Become more stable} \]
\[ \text{Answer: B} \]
\[ \text{Question 6:} \]
\[ \text{The Fixed-Point Iteration method is also known as:} \]
\[ \text{(a) Successive Approximations, \quad (b) Chord Method, \quad (c) Tangent Method, \quad (d) False Position Method} \]
\[ \text{Answer: A} \]
\[ \text{Question 7:} \]
\[ \text{Which method uses both function values and derivative values to approximate roots?} \]
\[ \text{(a) Bisection Method, \quad (b) Newton-Raphson Method, \quad (c) Secant Method, \quad (d) Regula Falsi Method} \]
\[ \text{Answer: B} \]
\[ \text{Question 8:} \]
\[ \text{Which method can be considered as an improvement over the Secant Method?} \]
\[ \text{(a) Fixed-Point Iteration, \quad (b) Bisection Method, \quad (c) Newton-Raphson Method, \quad (d) Regula Falsi Method} \]
\[ \text{Answer: C} \]
\[ \text{Question 9:} \]
\[ \text{In Regula Falsi method, the error reduces approximately at a rate of:} \]
\[ \text{(a) Linear, \quad (b) Quadratic, \quad (c) Superlinear, \quad (d) Exponential} \]
\[ \text{Answer: A} \]
\[ \text{Question 10:} \]
\[ \text{Which of the following methods is best suited for solving a highly oscillatory function?} \]
\[ \text{(a) Newton-Raphson Method, \quad (b) Bisection Method, \quad (c) Secant Method, \quad (d) Regula Falsi Method} \]
\[ \text{Answer: B} \]