Match List-I with List-II (Given that \(c\) is an arbitrary constant)

List-I	List-II
(A) \(\int \frac{d x}{\sqrt{a^2-x^2}}\)	(I) \(\log _e\left|x+\sqrt{x^2-a^2}\right|+c\)
(B) \(\int \sqrt{a^2-x^2} d x\)	(II) \(\sin ^{-1} \frac{x}{a}+c\)
(C) \(\int \sqrt{x^2-a^2} d x\)	(III) \(\frac{x}{2} \sqrt{a^2-x^2}+\frac{a^2}{2} \sin ^{-1} \frac{x}{a}+c\)
(D) \(\int \frac{d x}{\sqrt{x^2-a^2}}\)	(IV) \(\frac{x}{2} \sqrt{x^2-a^2}-\frac{a^2}{2} \log _e\left|x+\sqrt{x^2-a^2}\right|+c\)

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Applied Mathematics
Which of the following are NOT correct about "Sinking Fund"?
(A) It does not have any specific purpose.
(B) It can be used in any emergency.
(C) Any amount, any time can be deposited in it.
(D) It is set up for a particular upcoming expense.
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If \(P(A)=\frac{3}{5}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P(\bar{A} \mid \bar{B})\) is

For the system \(\left[\begin{array}{cc}2 & -3 \\ -4 & 6\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}5 \\ -10\end{array}\right]\), which of the following statements are correct?
(A) The system has no solution.
(B) The system is consistent.
(C) It has infinitely many solutions.
(D) It has a unique solution.
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Let \(f:[-2,2] \rightarrow[-2,2]\) be a function defined by \(f(x)=x|x|\), then \(f\) is:

The following system of equations \(2 x-y+3 z=5,3 x+2 y-z=7,4 x+5 y-\lambda z=\mu\) is consistent. Then

The probability that a student is not a swimmer is \(\frac{1}{5}\). Then, the probability that out of 5 students, 4 are swimmers is

Salicylaldehyde can be prepared by treating phenol with

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.

Male grasshopper is an example of

Arrange the following compounds in increasing order of their basicity
(A) Aniline
(B) p-Nitroaniline
(C) p-Toluidine
(D) p-Methoxyaniline
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Which is not a type of sexually transmitted infections?

Out of the following half cells, which two half cell combination gives the largest \(E_{\text{cell}}\text{}\) value?
(I) \(A^{3-} \rightarrow A^{2-} + e^-\text{}\) \(E^{\circ} = +1.5\text{V}\)
(II) \(B^{+} + e^- \rightarrow B\) \(E^{\circ} = -0.5\text{V}\)
(III) \(C^{2+} + e^- \rightarrow C^{+}\) \(E^{\circ} = +0.5\text{V}\)
(IV) \(D \rightarrow D^{2+} + 2e^-\text{}\) \(E^{\circ} = -1.5\text{V}\)
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