Math Chapter Wise question with answer

Q01 Which of the following sequenceis not convergent? English · LT 2018 Q02 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 Q03 Which of the following series converges? I. n n 1 3 cosn e ∞ = + ∑ ∑ II. n 1 1 cos n ∞ = ∑ English Q04 For an orthonormal subset β of H, which of the following are equivalent? 1. β is a basis 2. β is complete 3. Span β... English · OPSC PGT 2017 Q05 Which of the following maps are linear transformations? 1. T: R2 → →R defined by T(x, y) = 2x 3y 2. T: R2 → →R defi... English · OPSC PGT 2017 Q06 If { xn } n is a convergent sequence in R and {yn } n is a bounded sequence in R, then we can conclude that English · Bihar (TRE 1.0) -2023