JNU SIS 2021 Question 5: Goodness of fit and model selection

Consider the following two regression models: Model 1: $y_i = \alpha_0 + \alpha_1 x_{1i} + u_i$ Model 2: $y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + u_i$ Which of the following statements are true?
A. Model 2 must have an $R^2$ at least as high as that of model 1
B. Model 2 must have an adjusted $R^2$ at least as high as that of model 1
C. Models 1 and 2 would have identical values of $R^2$ if the estimated coefficient on $\beta_2$ is zero
D. Models 1 and 2 would have identical values of adjusted $R^2$ if the estimated coefficient on $\beta_2$ is zero Choose the correct answer from the options given below: