If we take each row of the triangle and write the numbers as a single number (for example, 1,3,11,3,1 becomes 131131), these numbers form powers of

Consider Pascal's triangle when answering the questions below.Select options belowThe middle term value on the line that begins with 1,81,8 is Select Option.If we take each row of the triangle and write the numbers as a single number (for example, 1,3,11,3,1 becomes 131131), these numbers form powers of Select Option.Skip For Now

Check whether the given number is a triangular number.Input Format:Accept an integer as inputOutput Format:Print the output as "Triangular Number"  or  "Not a Triangular Number"Constraints:1 <= N <= 10^9Sample Input 1:10Sample Output 1:Triangular NumberSample Input 2:16Sample Output 2:Not a Triangular Number

Write a program to print Pascal's Triangle.Input: 6Output: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 Input format :The input consists of a number.Output format :The output displays the required pattern.Sample test cases :Input 1 :6Output 1 : 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 Input 2 :2Output 2 : 1 1 1

Write a C program to implement Pascal's Triangle generation and manipulation functionalities using functions and structures. Your program should provide the following capabilities: ·      Generate Pascal's Triangle: Implement a function to generate Pascal's Triangle up to a specified number of rows.·      Display Pascal's Triangle: Implement a function to display the generated Pascal's Triangle in a readable format.·      Calculate Column Sum: Implement a function to calculate the sum of all values in a specified column of Pascal's Triangle.Pascal triangle is constructed using the following rules:·      The first and last elements of each row are always 1.·      Each element in the interior of the triangle is the sum of the two elements directly above it in the previous row.Instructions:·      Define a structure named "Triangle" to represent Pascal's Triangle.·      Implement functions to perform the operations mentioned above. Use appropriate function prototypes and definitions.·      Use dynamic memory allocation to allocate memory for the triangle array based on the number of rows.·      Ensure error handling for invalid input values and memory allocation failures.·      Document your code with comments to explain the purpose of each function and significant code blocks. Note: Pascal's Triangle can grow rapidly in size, so consider efficiency and memory usage while implementing the generation and manipulation functions.

c). Write a recursive function to find the nth “Triangular” number and write therecurrence relation for the function. [20%](Hint: A triangular number is the sum of itself and all other smaller numbers. Forexample, the triangular number of 4 is, 4+3+2+1 = 10.)