The isotope \({ }^{42} K\) has a half life of about 12 hours. What fraction of the initial concentration remains after 48 hours?

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Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
Sucrose on hydrolysis gives

Identify the incorrect statement about the \(H _2- O _2\) fuel cell from the following:

Arrange the metal ions of the following compounds in increasing order of oxidation number :
(A) \(\text{TiCl}_3\)
(B) \(\text{CrF}_6\)
(C) \(\text{ZnO}\)
(D) \(\text{Mn}_2\text{O}_7\)
Choose the correct answer from the options given below :

Which of the following is correct about the nature of ligand?

Haloalkanes can be represented by the formula

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A homogeneous mixture of two or more than two components has uniform composition and properties. The binary solutions have two components, which may be solid, liquid or gas. The resultant solution has a larger amount of solvent and a smaller amount of solute. The amount of solute in a given amount of solvent decides the concentration of the resulting solution. The concentration can be expressed in various ways, like molarity, molality, normality and mole fraction.
Glucose dissolved in water and ethanol dissolved in water are examples of:

The probability that A hits a target is \(\frac{1}{5}\) and the probability that B hits it is \(\frac{2}{3}\) The probability that the target will be hit if both A and B shoot at it independently is:

A short solenoid of radius a and \( n_{1} \) number of turns per unit length and length L is kept coaxially inside a very long solenoid of radius b and \( n_{2} \) number of turns per unit length. What is the mutual inductance of the system.

Darwin's finches and Australian marsupials are an example of:

C and Z in the species-area relationship log S = log C + Z log A represents:

If z = 5x + 8y is the objective function of a LPP and (0,0), (3, 1), (2, 4), (0, 3), (5,0) are corner points of the bounded feasible region, then the maximum value of the objective function is

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 -