NDA Mathematics Question (2026) — Solution

Step-by-step solution

The given limit is _ x 1 x^ (n^2-1) -1 x^ (n+1) -1 . As x 1, the expression takes the indeterminate form 0 0 . Applying L'Hospital's rule, we differentiate the numerator and the denominator with respect to x: _ x 1 (n^2-1)x^ n^2-2 (n+1)x^n Substituting x=1, we get: n^2-1 n+1 (n-1)(n+1) n+1 n-1 Answer: n-1