List - I (Set Laws) List - II (Form) A. Idempotent law I. $A\cup B=B\cup A$ B. Commutative law II. $A\cap (B\cap C)=(A\cap B)\cap C$ C. Associative law III. $A\cup A=A$ D. De-Morgan law IV. $(A\cap B)'=A'\cup B'$
Choose the correct answer from the options given below :
Matching Set Laws
This question requires matching fundamental Set Laws from List-I with their corresponding mathematical forms in List-II.
Idempotent Law Match
The Idempotent law states that applying an operation to a set with itself results in the same set. For the union operation, this is represented as $A\cup A=A$. This matches form III in List-II.
Commutative Law Match
The Commutative law states that the order of sets does not affect the outcome of the operation. For the union operation, this is $A\cup B=B\cup A$. This matches form I in List-II.
Associative Law Match
The Associative law states that the grouping of sets does not change the outcome when performing the same operation multiple times. For intersection, this is represented as $A\cap (B\cap C)=(A\cap B)\cap C$. This matches form II in List-II.
De-Morgan Law Match
De-Morgan's laws provide rules for negating set operations. One of the laws states that the complement of the intersection of two sets is the union of their complements: $(A\cap B)'=A'\cup B'$. This matches form IV in List-II.
Correct Matching
Based on the analysis:
- A. Idempotent law matches with III. ($A\cup A=A$)
- B. Commutative law matches with I. ($A\cup B=B\cup A$)
- C. Associative law matches with II. ($A\cap (B\cap C)=(A\cap B)\cap C$)
- D. De-Morgan law matches with IV. ($(A\cap B)'=A'\cup B'$)
Therefore, the correct option is A-III, B-I, C-II, D-IV.
Important Questions from Miscellaneous
- Which of the following relationships is/are not true?
(A). Most probable velocity = $\sqrt{\frac{2RT}{M}}$
(B). PV = $\frac{3}{2}kT$
(C). Compressibility factor Z = $\frac{pV}{nRT}$
(D). Average kinetic energy of gas = $\frac{1}{2}kT$
Choose the correct answer from the options given below - Match List-I with List-II
List-I List-II Electronic Configuration First Ionisation energy (kJ mol$^{-1}$) (A). ns$^2$ (I). 2100 (B). ns$^2$np$^1$ (II). 1400 (C). ns$^2$np$^3$ (III). 800 (D). ns$^2$np$^6$ (IV). 900
Choose the correct answer from the options given below: - The shielding constant of a 2p electron (calculated using Slater's rules) is
- Match List-I with List-II
List-I List-II Spectroscopy Property (A). Raman (I). Polarizability (B). FTIR (II). Dipole Moment (C). UV-Visible (III). Absorbance (D). NMR (IV). Spin
Choose the correct answer from the options given below: - The structure of protein comprises of:
(A). Primary structure of protein is associated with amino acids
(B). Secondary structure of protein is associated to peptides
(C). Tertiary structure of protein is associated with polypeptide chains
(D). Quaternary structure of protein is associated with polypeptide chains
Choose the correct answer from the options given below:
