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 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 Q03 The infinite series p p p p 1 1 1 1...... 1 2 3 4 + + + + ∞ + + + + ∞ + + + + ∞ + + + + ∞ is convergent, if English · LT 2018 Q04 The value of ∑ n k n k k=0 3 C is English · Bihar (TRE 2.0)-2023 Q05 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 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