Which of the following statements are correct ?
(A) Determinant is a square matrix
(B) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{21}+a_{13} c_{31}\left(a_{i j}=\right.\) element, \(c_{i j}=\) cofactor \()\)
(C) Determinant is a number associated with a matrix
(D) Determinant is a number associated with a square matrix
(E) Determinant of a matrix of order \(3 \times 3\) is \(a_{11} c_{11}+a_{12} c_{12}+a_{13} c_{13}\), where \(a_{i j}\) is the element, while \(c_{i j}\) is its corresponding cofactor
Choose the correct answer from the options given below :

The value of \(\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\tan x}+\sqrt{\cot x}} d x\) is:

If \(\left[\begin{array}{cc}4 x & 5 x-7 \\ 4 x & 2 x+y\end{array}\right]=\left[\begin{array}{cc}x+6 & y \\ 7 y-13 & 7\end{array}\right]\) then the value of \(2 x+y\) is:

If the matrix \(\begin{bmatrix} 3 & a+b & 4 \\ 2 & 0 & -1 \\ a-b & c & 5 \end{bmatrix}\) is symmetric, then the value of a, b and c is given by:

A person has invested Rs. 20,000 in 2020 for 5 years.
If the CAGR for his investment is 11.84%, the end balance of his investment is [Given \((1.1184)^5=1.7498\) ]

The unit's digit of \(12^{12}\) is equal to :

Which of the following is the correct equation to find the area of the shaded region, with reference to the figure given below ?

Read the following paragraph and answer the given questions:
DRUGS AND ALCOHOL ABUSE
The drugs, commonly abused are opioids, cannabinoids, and coca alkaloids. Opioids are the drugs, which bind to specific opioid receptors present in our central nervous system and gastrointestinal tract. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. Cannabinoids are a group of chemicals, which interact with cannabinoid receptors present principally in the brain. Natural cannabinoids are obtained from the inflorescences of the plant Cannabis sativa. The flower tops, leaves and the resin of cannabis plant are used in various combinations to produce marijuana, hashish, charas and ganja. Generally taken by inhalation and oral ingestion, these are known for their effects on cardiovascular system of the body. It interferes with the transport of the neuro-transmitter dopamine. Cocaine, commonly called coke or crack is usually snorted. It has a potent stimulating action on central nervous system, producing a sense of euphoria and increased energy. Excessive dosage of cocaine causes hallucinations. Other well-known plants with hallucinogenic properties are Atropa belladona and Datura. These days cannabinoids are also being abused by some sportspersons. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery. Several plants, fruits and seeds having hallucinogenic properties have been used for hundreds of years in folk-medicine, religious ceremonies and rituals all over the globe.
__________ are used as medicines to help patients cope with mental illnesses like depression and insomnia.

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complez to yield three orbitals of lower energy, \(t_{2 g}\) set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_{\circ}\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_0\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_{\circ}\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
Choose the correct statement from the following:

For what distance is ray optics a good approximation when the aperture is 3 mm wide and the wavelength is 500 nm?

According to Alexander Zaitsev the most preferred product for dehydrohalogenation of 2-Bromopentane will be :

An earthed conductor is placed near another positively charged conductor. The net charge acquired by the earthed conductor will be :

DNA recombinant technology involves the use of restriction endonucleases. After having cloned the gene of interest and having optimised the conditions to induce the expression of the target protein, one has to consider producing it on a large scale. The cells harbouring cloned genes of interest may be grown on a small scale in the laboratory. In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. 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. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.
pBR322, which is used in recombinant DNA technology, is a -