Values of dissociation constant, K_a are given as follows.

Acid	Ka
HCN	6.2 × 10−10
HF	7.2 × 10−4
HNO2	4.0 × 10−4

Correct order of increasing base strength of the base CN⁻, F − and \(\rm NO_2^ -\) will be : 

CONCEPT:

Relationship Between Acid Strength and Conjugate Base Strength

• The strength of a base is inversely related to the strength of its conjugate acid.
• A weaker acid has a stronger conjugate base, and a stronger acid has a weaker conjugate base.
• The dissociation constant (Ka) of an acid can be used to determine the relative strength of its conjugate base.

EXPLANATION:

• Given the dissociation constants (Ka) for the acids:
  • HCN: Ka = 6.2 × 10^-10
  • HF: Ka = 7.2 × 10^-4
  • HNO₂: Ka = 4.0 × 10^-4
• The strength of the conjugate bases (CN^-, F^-, and NO₂^-) is inversely related to the Ka values of their corresponding acids.
  • HCN has the smallest Ka value (6.2 × 10^-10), so CN^- is the strongest base.
  • HNO₂ has a Ka value of 4.0 × 10^-4, so NO₂^- is weaker than CN^- but stronger than F^-.
  • HF has the largest Ka value (7.2 × 10^-4), so F^- is the weakest base.
• Therefore, the correct order of increasing base strength of CN^-, F^-, and NO₂^- is:
  • F^- < NO₂^- < CN^-

Therefore, the correct answer is option 3: F^- < NO₂^- < CN^-.