Let the mean and standard deviation of marks of class \(A\) of 100 students be respectively 40 and \(\alpha(>0)\), an…

Let the mean and standard deviation of marks of class \(A\) of 100 students be respectively 40 and \(\alpha(>0)\), and the mean and standard deviation of marks of class \(B\) of \(n\) students be respectively 55 and \(30-\alpha\). If the mean and variance of the marks of the combined class of \(100+n\) students are respectively 50 and 350 , then the sum of variances of classes \(A\) and \(B\) is:

[JEE Main 2023, 31 Jan (Shift 2)]