Mathematics  Hello friends here is the question paper 📜 which given on our PUT's  To get this in full quality just click here For second page click here  In second page you will get very very very important question and have 70% change to come in exam made by experienced teacher SECTION-A (2Marks each) Q1. Find the symmetry of the curve x^3y^2=x^2-a^2x Q2. if x =rcos@ ,y=rsin@ find del(x,y)/del(r,@) Q3. Find the stationary points of the function x^3y^2(6-x-y) Q4. Is the following matrix orthogonal ? Q5. Evaluate β(2,3/2) Q6. Find the outward normal vector of 2x^3+2xy+y^2=3 at point (1,2,3) Q7. Find the acceleration of the particle moving along curve x=Sint,y=cos2t,z=e^t at (t=2) SECTION-B(3marks each) Q8. Y=xlog(x-1/x+1) show that,  Y =(-1) (n-2)! [(x-n/(x-1)^n)-(x+n/(x+1)^n)]  Q9. Show that rectangular solid of maximum volume that can be inscribed in a given sphere is a cube Q10. Prove that  Γ(m) Γ(m)+1/2=√π/2^(2m-1) Γ(2m) Q11. Find the Eigen Values and Eigen Vectors of A =   Q1

 Vector and its Initialization Vector is a Dynamic Array that changes its size on run time, and provides flexibility to use it without initializing the size, but needs to declare the data type like int, string, etc   basic initialization of vector class format vector<data type> vector name ; Ex: vector <int> v1; here in the above example, the vector is initialized with data type int and the name of the vector is v1  let us take another example to initialize the vector  Ex: vector<data type>vector name (initial size, every indexing address value); vector <bool>v2(3,0); here the vector gets initialized from 3 instead of initialized from 0 and here the vector is bool type and all 3 means if  arr1 is an array then  vector <bool>v2(3,0); bool arr[3]={0,0,0} both have the same value but only v2 can be mutable and have a size of 4 in this situation because vectors always have the size in terms of 2**n where n is an integer likewise if the vector v2 gets filled to

This is the solution of palindrome program in C++ / Cpp  What is palindrome : Ans: Palindrome is a type of number or string which will be same when we operate a negative 1 loop on it  For Ex; NAYAN is Same as Its mirror image NAYAN so it is A Palindrome String , SHIVAM is Not same as its mirror image of negative loop image which is MAVIHS , SO It is Not A Palindrome , Here 121 is a palindrome but 211 is not and 1553443551 is a palindrome number. CODE: PALINDROME OF STRING IN C++ #include <iostream>  #include <cstring>    using namespace std;    int main(){     string i;     bool k;     cout<<"Enter the string : ";     cin>>i;     for(int o=0;o<i.length();o++) i[o]=toupper(i[o]);     int n=i.length();     for(int l=0;l<n;l++){         if(i[l]==i[n-1-l]){             k=1;         }         else {             cout<<"Not a palindrome"<<n;             return 0;         }     };     if (k){         cout<<&quo

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