If \(A\) is a square matrix such that \(A^2=A\), then the value of \((I-A)^2-(I+A)^3\) is :

Solution of the differential equation \(y \log _e y d x-x d y=0\) is (Where \(c\) is an arbitrary constant)

Which of the following is correct about the Sinking Fund?

If \(A\) and \(B\) are symmetric matrices of same order, then \(A B-B A\) is a

Consider the LPP, Min Z = x + 3y subject to the conditions:
\(2 x+y \geq 2\)
\(x+2 y \geq 4\),
\(x \geq 0, y \geq 0\).
Which of the following statement is correct about the feasible region of the above LPP.

If \(y=\sin ^{-1} x+\sin ^{-1} \sqrt{1-x^2}, x \in(-1,0)\), then \(\frac{d y}{d x}\) is equal to

If \(A=\left[\begin{array}{ll}5 & 6 \\ 3 & 2\end{array}\right]\), then which of the following is correct?
(A) \(|A|\) is positive
(B) \(|a d j A|=-8\)
(C) Cofactor of 3 is 6
(D) \(|2 A|=-32\)
Choose the correct answer from the options given below :

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.
Which one of the followings is not a symbiotic microbe?

An eye specialist prescribes spectacles having a combination of a converging lens of focal length 25 cm and a diverging lens of focal length of 20 cm. The power of the combination of two lenses (in dioptre) is

If \(A=\left[\begin{array}{cc}1 & 2 \\ 4 & -3\end{array}\right]\) and \(f(x)=2 x^2-4 x+5\), then \(f(A)\) is equal to

If a matrix has 12 elements, then the possible orders it can have, are
(A) \(1 \times 12\)
(B) \(4 \times 3\)
(C) \(6 \times 3\)
(D) \(6 \times 2\)
Choose the correct answer from the options given below :

X-rays of wavelength \( = 1\text{\AA} \) have frequency

Reaction of Ethene with Bromine in CCl\(_4\) will result in