Q67.The statement (p ∧q) ⇒(p ∧r) is equivalent to (1) q ⇒(p ∧r) (2) p ⇒(p ∧r) (3) (p ∧r) ⇒(p ∧q) (4) (p ∧q) ⇒r JEE Main 2022 (29 Jul Shift 1) JEE Main Previous Year Paper
What This Question Tests
This question is a direct test of fundamental logical equivalences using propositional logic, which can be solved using truth tables or known logical identities.
Concepts Tested
Formulas Used
p ⇒ q ≡ ~p ∨ q
Distributive law: p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
📚 NCERT Sections This Tests
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
14.1 — In An N-Type Silicon, Which Of The Following Statement Is True:
Physics Class 12 · Chapter 14
14.1 In an n-type silicon, which of the following statement is true: (a) Electrons are majority carriers and trivalent atoms are the dopants. (b) Electrons are minority carriers and pentavalent atoms are the dopants. (c) Holes are minority carriers and pentavalent atoms are the dopants. (d) Holes are majority carriers and trivalent atoms are the dopants.
11.3 — Zeroth Law Of Thermodynamics (A)
Physics Class 12 · Chapter 11
11.3 ZEROTH LAW OF THERMODYNAMICS (a) Imagine two systems A and B, separated by an adiabatic wall, while each is in contact with a third system C, via a conducting wall [Fig. 11.2(a)]. The states of the systems (i.e., their macroscopic variables) will change until both A and B come to thermal equilibrium with C. After this is achieved, suppose that the adiabatic wall between A and B is replaced by a conducting wall and C is insulated from A and B by an adiabatic wall [Fig.11.2(b)]. It is found that the states of A and B change no (b) further i.e. they are found to be in thermal Fig. 11.2 (a) Systems A and B are separated by an equilibrium with each other. This observation adiabatic wall, while each is in contact forms the basis of the Zeroth Law of with a third system C via a conducting Thermodynamics, which states that ‘two wall. (b) The adiabatic wall between A systems in thermal equilibrium with a third and B is replaced by a conducting wall, system separately are in thermal equilibrium while C is insulated from A and B by an adiabatic wall.with each other’. R.H. Fowler formulated this * Both the variables need not change. It depends on the constraints. For instance, if the gases are in containers of fixed volume, only the pressures of the gases would change to achieve thermal equilibrium. Reprint 2025-26 THERMODYNAMICS 229
📋 Question Details
- Chapter
- Mathematical Reasoning
- Topic
- Logical Equivalence
- Year
- 2022
- Shift
- 29 Jul Shift 1
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 14: Mathematical Reasoning
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