If A is an invertible symmetric matrix, then \(A^{-1}\) is

Which of the following statements are NOT correct about Standard Normal Distribution?
(A) The probability curve of the Standard Normal Distribution is a bell-shaped curve.
(B) The Standard Normal variate ( Z ) score describes the position of each data point in terms of its distance from the mean, when measured in standard deviation units.
(C) The Z -score is negative if the data point lies above the mean, and positive if it lies below the mean.
(D) There is a \(95.45 \%\) probability of randomly selecting a score between \(\mu-\sigma\) and \(\mu+\sigma\), when \(\sigma\) is standard deviation and \(\mu\) is mean.
Choose the correct answer from the options given below :

The greatest possible value of \(a\) such that the function\(f(x)=x^2+a x+1\) is always decreasing in the interval \([1,2]\), is:

\(\int_0^{1.5}[x] d x\), where [x] denotes the greatest integer function \(\leq x\), is equal to:

Let \(A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 3 & 2 \\ 2 & 4 & 1\end{array}\right]\) and \(M_{i j}, A_{i j}\) respectively denote the minor, co-factor of an element \(a_{i j}\) of matrix \(A\), then which of the following are true?
(A) \(M_{22}=-1\)
(B) \(A_{23}=0\)
(C) \(A_{32}=3\)
(D) \(M_{23}=1\)
(E) \(M_{32}=-3\)
Choose the correct answer from the options given below:

For \(x \in(0,1)\), the derivative of \(\sin ^{-1} x\) with respect to \(\cos ^{-1} \sqrt{1-x^2}\) is:

The interval in which \(f(x)=x^2 e^{-x}+7\) is increasing is :

Which of the following organism helps the plants in the absorption of phosphorus from soil?

If \(\left[\begin{array}{lll}1 & 2 & 3\end{array}\right] A=\left[\begin{array}{ll}4 & 5\end{array}\right]\), then the order of matrix \(A\) is:

Which of the following is NOT correct in the case of the output obtained from a full wave rectifier?

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-

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Statins, used as blood-cholesterol lowering agents are produced by -

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, \(3 d\) series ( \(S c\) to Zn), \(4 d\) series (Y to Cd), 5d series (La and Hf to Hg) and 6d series which has \(A c\) and elements from Rf to Cn. The two series of the inner transition metals; \(4 f\) (Ce to Lu) and \(5 f\) (Th to Lr) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of \(s\) and p-block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
In series Sc to Zn, the lowest enthalpy of atomization is shown by