Test:300 QNo:1

Comprehension Type (Question 1-3)

Given the following limits answer the questions that follow:

L₁ = lim ( {x} + {2x} + {3x} .............. + {nx} )
nâ†’âˆž n(n+1)

L₂ = lim ( [x] + [2x] + [3x] .............. + [nx] )
nâ†’âˆž n(n+1)

M₁ = lim ( {x} + {2x} + {3x} .............. + {nx} )
nâ†’âˆž n²

M₂ = lim ( [x] + [2x] + [3x] .............. + [nx] )
nâ†’âˆž n²

P₁ = lim ( {x} + {2x} + {3x} .............. + {nx} )
xâ†’âˆž n²

P₂ = lim ( [x] + [2x] + [3x] .............. + [nx] )
xâ†’âˆž n²

Question
Which of these is pairs are odd?

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω