A tub contains \(60\) litres of milk. From this tub, \(6\) litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?

For any vector \(\vec{a}\), the value of \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is equal to :

On which of the following components, the pattern and behavior of the data in any time series is based?
(A). Secular trend component
(B). Seasonal component
(C). Cyclical component
(D). Regular component
Choose the correct answer from the options given below :

The integral \(\int \log x d x\) is equal to to:

Due to which of the following, the irregular variations in a time series are caused:
(A) Floods
(B) Rise in prices before festivals
(C) A fire in a factory
(D) Epidemics
Choose the correct answer from the options given below:

If \(\sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y)\),then \(\frac{d y}{d x}\) =

The function \(f(x)=\tan x-x\):

If \(|\vec{a}|=3\) and \(|\vec{b}|=4\), then a value of \(\lambda\) for which \(\vec{a}+\lambda \vec{b}\) and \(\vec{a}-\lambda \vec{b}\) are perpendicular is :

In RNAi, the genes are silenced by the formation of:

Second most abundant element in alloy misch metal is :

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 -

The complex \([\text{Co(NH}_3)_4(\text{NO}_2)_2]\text{Cl}\) exhibits :
A. Coordination isomerism
B. Linkage isomerism
C. Solvate isomerism
D. Ionisation isomerism
E. Geometrical isomerism
Choose the correct answer from the options given below :

Identify the order of reaction if its rate constant is \(k = 2 \times 1 0 ^{- 2 } s ^{- 1 }\) :