If A and B are symmetric matrices of the same order, then

If A = \(\left[\begin{array}{ccc}0 & 1 & -3 \\ -1 & 0 & 5 \\ 3 & -5 & 0\end{array}\right]\), then the value of \(\left|A^{2025}\right|\) is

The largest open interval in which the function \(f(x)=4 x^3-5 x^2-8 x+12\) increases, is:

The sum of the order and degree of the differential equation representing the family of curves \(y=m x+m^4\), where \(m\) is arbitrary constant, is

The value of the integral \(I=\int_{-3}^3\left(x^3-x\right) d x\) is :

\(\int_0^{\frac{\pi}{2}} \sqrt{1-\sin 2 x} d x\) is equal to :

A person has an initial investment of \(25000\) in an investment plan. After \(2\), years it has grown \(30000\), then the rate of return on his investment is:

Which of the following option is correct for ammensalism?

Read the following passage carefully and answer the given questions.
Biofertilisers
Biofertilisers are organisms that enrich the nutrient quality of the soil and their main sources are bacteria, fungi and cyanobacteria. You have studied about the nodules on the roots of leguminous plants formed by the symbiotic association of Rhizobium. These bacteria can fix atmospheric nitrogen into organic forms. Other bacteria can also fix atmospheric nitrogen while free-living in the soil (examples Azospirillum and Azotobacter). Fungi are also known to form symbiotic associations with plants (mycorrhiza). Many members of the genus Glomus form mycorrhiza. Plants having such associations show other benefits also, such as resistance to root-borne pathogens, tolerance to salinity and drought, and an overall increase in plant growth and development. Cyanobacteria are autotrophic microbes widely distributed in aquatic and terrestrial environments many of which can fix atmospheric nitrogen, e.g. Anabaena, Nostoc, Oscillatoria, etc. In paddy fields, cyanobacteria serve as an important biofertiliser. Blue green algae also add organic matter in to the soil and increase its fertility. Currently, in our country, a number of biofertilisers are available commercially in the market and farmers use these regularly in their fields to replenish soil nutrients and to reduce dependence on chemical fertilisers.
In organic farming, there is -

Read the following passage carefully and answer the given questions.
Productivity in the Ecosystem
The flow of energy through a terrestrial ecosystem starts with the harnessing of sunlight by autotrophs. The radiant energy is converted by photosynthesis to organic compounds is known as productivity. The productivity is expressed in units of energy per unit of area per unit time. The amount of organic matter present at any given time is biomass. The productivity of any ecosystem is affected by many parameters like weather conditions, nutrient availability etc. The productivity of any ecosystem does vary seasonally and yearly.
The amount of organic matter accumulated in an ecosystem at a given time is known as-

If time taken for a first order reaction to get \(90\%\) complete is \(24\ min\), its \(t_{99.9\%}\) will be:

The common name of the following compound is

\(A\) runs \(3\) times as fast as \(B\) . If A gives \(B\) a start of \(30\) meters, how far must the goal on the race course be so that \(A\) and \(B\) reach it at the same time?