For redirect to 301

– Temporary redirect to an individual page by using the below piece of code.

rewrite ^/test1 /test2 redirect;

– Permanent redirect to a specific page by using the below piece of code.

rewrite ^/test1 /test2 permanent;

For redirect to 410 without the query string, you can use the below code lines.

Url = http://example.com/test1.php
location /test1.php {
    return 410;
}

For redirect to 410 with query string, you can use the below code lines.

Url = http://example.com/test1.php?page=1
location = /test1.php {
  if ($args ~* (page=1)(.*)){
    return 410;
  }
}

If the query string URL having special characters like + then use the below code.

Url = http://example.com/test1.php?page=1+cat=1
location = /test1.php {
  if ($args ~* (page=1(.+)cat=1)(.*)){
    return 410;
  }
}