Math Chapter Wise question with answer

Q01 What value of k makes the vectors (1, –1, 3), (1,2,-2), (k,0,1) linearly dependent? English · OPSC PGT 2017 Q02 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 Q03 The value of ∑ n k n k k=0 3 C is English · Bihar (TRE 2.0)-2023 Q04 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 Q05 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 Q06 Define f(x) = 1 x for x > 0. Then f is uniformly continuous English · Bihar (TRE 1.0) -2023