In which of the following intervals, the function \(f(x)=\frac{x}{\log x}\) is decreasing?

The interval in which the function \(f(x)=2 x^3-3 x^2-36 x+7\) is strictly decreasing is :

The corner points of the bounded feasible region determined by a set of constraints in an LPP are P(0,5), Q(3,5), R(5, 0) and S(4, 1).
If the objective function is z = ax + 2by where a, b > 0 then the condition on a and b such that the maximum value of z occurs at Q and S is

If \(A\) is a square matrix, then \(\left(A^T-A\right)\) is-

If \(y=\frac{1}{x+1}\), then \(\frac{d^2 y}{d x^2}\) at x = 2 is:

If \(x \neq y \neq z\) then \(\left|\begin{array}{lll}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right|\) is equal to

If the relation \(R: A \rightarrow B\), where \(A=\{2,3,4\}\) and \(B=\{3,4,5\}\) is defined by \(R=\{(x, y): x < y, x \in A, y \in B\}\), then

Match List I with List - II.

List-I (Transformer)	List-II
(A) Flux leakage	(I) Laminated core
(B) Energy loss due to resistance of winding	(II) By winding the primary and secondary one over the other
(C) Eddy current loss	(III) Using thick wires
(D) Hysteresis	(IV) By using soft iron core

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Identify the chiral molecule from the following,

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Amines are considered as derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. In nature they occur among proteins, vitamins, alkaloids and hormones. These can be primary, secondary or tertiary depending on the number of hydrogen groups replaced. They can be prepared from nitro compounds, alkyl halides, nitriles, amides etc. Due to unshared pair of electrons they behave as Lewis bases. Influence of the number of hydrogen atoms at nitrogen atom is displayed in physical properties such as solubility, boiling point and chemical reactions including basicity. Basic character of amines is expressed in terms of their \(K_b\) and \(p K_b\) values. Three classes of amines can be distinguished with p-toluene sulphonyl chloride which reacts with primary and secondary ddu amines. Amino group when attached to benzene ring behaves as an activating and ortho para directing group.
Which reagent is used for the conversion of acetamide into ethylamine?

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Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles,
paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Hydrolytic products of maltose are?

Choose the correct match. '+' for beneficial interaction '-' for detrimental and 'O' for neutral effect.

LIst - I		LIst - II
Species A	Species B	Name of Interaction
(A) +	+	(I) Competition
(B) +	-	(II) Mutualism
(C) -	-	(III) Amensalism
(D) -	0	(IV) Predation

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DNA Fingerprinting
Polymorphism in DNA sequence is the basis of genetic mapping of the human genome as well as of DNA fingerprinting. DNA fingerprinting involves identification of differences in some specific regions in the DNA sequence called repetitive DNA. It works on the principle of polymorphisms in DNA sequences. The repetitive DNA are separated from bulk genomic DNA. The bulk DNA forms a major peak and the other small peaks are referred to as satellite DNA. These repetitive/satellite DNA sequences show a high degree of polymorphisms and form the basis of DNA fingerprinting.
Which one of the following techniques is involved in DNA fingerprinting?