The quantity of charge required to obtain one mole of aluminum from \(\text{Al}_2\text{O}_3\) is :

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The crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules. The five d orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands (either anions or the negative ends of dipolar molecules like NH3 and H2O) in a complex, it becomes asymmetrical and the degeneracy of the d orbitals is lifted. It results in splitting of the d orbitals. The pattern of splitting depends upon the nature of the crystal field.
In tetrahedral coordination complexes, low-spin configurations are rare because:

What is the formula of following coordination compound: Potassium trioxalatoaluminate(III)

The vapour pressure of pure water at \(25^{\circ} C\) is 23.75 mmHg.
The vapour pressure of the solution obtained by dissolving 34.2 g of sucrose \(\left( C _{12} H _{22} O _{11}\right)\) in 100 g of water will be :

Identify the hormone from the following

Answer the question on the basis of passage given below :
For the transition elements
Sc \(\quad\) Ti \(\quad\) V \(\quad\) Cr \(\quad\) Mn\(\quad\) Fe \(\quad\) Co \(\quad\) Ni \(\quad\) Cu \(\quad\) Zn
Atomic numbers :
21 \(\quad\) 22 \(\quad\) 23 \(\quad\) 24 \(\quad\) 25 \(\quad\) 26 \(\quad\) 27 \(\quad\) 28 \(\quad\) 29 \(\quad\) 30 \(\quad\)
Which transition metal has the greatest number of oxidation state?

Match List-l with List-ll:

List-l (Items)	List-ll (Properties)
(A) Primary batteries	(I) Pollution free energy converter.
(B) Secondary batteries	(II) Takes place in the presence of air, moisture and H+
(C) Fuel cells	(III)Large number of charging/discharging and long-lasting
(D) Corrosion	(IV) Mercury cell is used in hearing aids

Choose the correct answer from the options given below:

In a series LCR circuit, the voltage across \(R\) is \(200 V, C=5 \mu F\), and \(R=2 k \Omega\). The resonant frequency \(\omega\) is \(1 0 0 ~ r a d / s\). At resonance, the voltage across \(L\) is:

Match List - I with List - II.

List - I	List - II
(A) Range of \(y=\operatorname{cosec}^{-1} x\)	(I) \(\quad R-(-1,1)\)
(B) Domain of \(\sec ^{-1} x\)	(II) \(\quad(0, \pi)\)
(C) Domain of \(\sin ^{-1} x\)	(III) \(\quad[-1,1]\)
(D) Range of \(y=\cot ^{-1} x\)	(IV) \(\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\}\)

Choose the correct answer from the options given below :

Which of the following are examples of irregular trends in a time series?
(A) Decrease in production due to a sudden strike.
(B) The rise in prices before festivals.
(C) Unusual rise in income of the printing press due to the announcement of an election.
(D) Fall in crop yield due to floods.
Choose the correct answer from the options given below :

In free space, all components of the complete electromagnetic spectrum have the same

The objective of a reflecting telescope is a :

Read the following passage carefully and answer the given questions.
Restriction endonuclease on finding its specific recognition sequence, bind to the DNA and cut each of the two strands of the double helix at specific points in their sugar -phosphate backbones. Each restriction endonuclease recognises a specific palindromic nucleotide sequences in the DNA. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. This can be achieved by treating the bacterial cells/plant or animal tissue with enzymes such as lysozyme (bacteria), cellulase (plant cells), chitinase (fungus). Now a days the most commonly used matrix is agarose which is a natural polymer extracted from sea weeds. The DNA fragments separate (resolve) according to their size through sieving effect provided by the agarose gel. The first restriction endonuclease-Hind II, whose functioning depended on a specific DNA nucleotide sequence was isolated and characterised five years later. It was found that Hind II always cut DNA molecules at a particular point by recognising a specific sequence of six base pairs. In addition to 'ori', the vector requires a selectable marker, which helps in identifying and eliminating non-transformants and selectively permitting the growth of the transformants. Transformation is a procedure through which a piece of DNA is introduced in a host bacterium. Normally, the genes encoding resistance to antibiotics such as ampicillin, chloramphenicol, tetracycline or kanamycin, etc., are considered useful selectable markers for E. coli.
A natural polymer extracted from sea weeds used in the field of biotechnology is: