Math Chapter Wise question with answer

Q01 According to Beach's criterion, a normed vector space X is complete if and only if every: English · OPSC PGT 2017 Q02 Let E and F are Banach spaces. T∈B(E,F) becomes an open map When it is: English · OPSC PGT 2017 Q03 Let () [ ] ∈ ∞ 2 2 nx gn x =,x 0, 1+ n x Which of the following is true as n → → → ∞ ∞ ∞? English · Bihar (TRE 1.0) -2023 Q04 Let n be a fixed natural number. Thus, the series () ≥ ∑ m m n –1 m is– English · DSSSB PGT 2021 Q05 Let (H, <..>) be an inner product space, then for a, b∈H, the relation 2 2 2 2 x y x y 2 x 2 y is known as: English · OPSC PGT 2017 Q06 Let H be a separable Hilbert space. All orthonormal bases of H are: English · OPSC PGT 2017