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However, with 2022 JEE-Main being postponed from April/May to 20–29 June/21–30 July, JEE-Advanced 2022 was also postponed and subsequently held on 28 August 2022. On 5 November 2024, it was announced by IIT Kanpur , and Joint Admission Board(JAB) that the attempts of JEE-Advanced are now increased from 2 to 3. [ 72 ]
A general form triangle has six main characteristics (see picture): three linear (side lengths a, b, c) and three angular (α, β, γ). The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three. A triangle can be uniquely determined in this sense when given any of the following: [1] [2]
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. . Accordingly, the necessary condition of extremum (functional derivative equal zero) appears in a weak formulation (variational form) integrated with an arbitrary function
The first-derivative test examines a function's monotonic properties (where the function is increasing or decreasing), focusing on a particular point in its domain.If the function "switches" from increasing to decreasing at the point, then the function will achieve a highest value at that point.
An important parameter of partial orders is order dimension: the dimension of a partial order is the least number of linear orders whose intersection is .For interval orders, dimension can be arbitrarily large.
For many substances, the formation reaction may be considered as the sum of a number of simpler reactions, either real or fictitious. The enthalpy of reaction can then be analyzed by applying Hess' law, which states that the sum of the enthalpy changes for a number of individual reaction steps equals the enthalpy change of the overall reaction.
The main factor affecting rates is charge: highly charged metal aquo cations exchange their water more slowly than singly charged cations. Thus, the exchange rates for [Na(H 2 O) 6 ] + and [Al(H 2 O) 6 ] 3+ differ by a factor of 10 9 .