Mathematical Python — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

Type of the Paper : DSE Programme : B.Sc. (Hons.) Mathematics 3. All commands to be written in Python code. (a). How do you find the minimum and maximum values in a NumPy array? (b). Consider the list, listl=[1,2,4,5,7,8,3]. Add an integer 8" at the third index of the list!. (c). How do you find the indices of maximum and minimum values in a NumPy array? (d). Write a SymPy code to find the sum of 13 + 23 + 3+...+ * till n = 5. (e). Consider an array, array l 3). , extract an array (0 3) from array 1. (f). What will be the output of the following code: (g). Use pretty printing to print the following expression (h). Write a SymPy code to solve the following equation for a x245x+4=1 (a). Using turtle graphics, write a python code that draw 60 hexagons turning right 10 degrees after each hexagon complete. (b), Write a python code to plot the functions y, = tanx, ½ = tan 2x in a single plot. The code must include the following requirements: (1). Legends, grid and a title of the plot. (ii). Different colour for each function. (c). Create a 5 x 5 matrix using NumPy, and (1). (ii). Calculate the sum of all elements. Find the mean of each row. (1Ii). Identify the maximum value in each column. (4). Write a python code for simple die rolling game, where we keep rolling the die until we have rolled a total of 50. Total marks: 5 x 3 = 15 (a). Write a NumPy code to find the characteristic polynomial, eigenvalues and eigenvectors for a given matrix A, (b). Use lambda function to evaluate the following function at x = 0. (c). Use SymPy to write and evaluate the following expression: (d). Write a Symly code to find the derivatives of all orders using loop for the following funtion Alempt any 3 parts. Total marks: 5% 3 = 15 (a). A store sells five types of fruits: apples, bananas, oranges, grapes, and mangoes. Sales figure fo a week are as follows: 50, 30. 45, 20 and 60, respectively. Write a python code to plot a basic bar plot showing the sales of cach fruit. Label each bar with the fruit name and provide axis labels. (b). What output will the following code produce: import numpy as np arr= np.array([E 1, 1,3).(-3, 6, 61)) print(np.concatenate([arrl, arr2], axis=I)) (c). Write a SymPy code to find the left hand limit and right hand limit of the following function at the point x = 0. (d). Write a SymPy code to solve the following second order differential equation with the d'y with the given initial conditions, (0) = 1,'(0) = 0. (a). Write a SymPy code to factorize the expression x? — y? and to expand (b). Write a python code for the following: (ii). Define a recursive sequence where: . it nis even with initial term ay = 1 12 x ap- .If n is odd (c). Write a NumPy code to solve the following system of linear quations using the inverse of coefficient matrix (d). Write a SymPy code to find the critical points of the following function and print the points of local maxima and minima. Total marks: 5 × 3 = 15 (a). Write a python code using SymPy for the following: