With reference to the scientific progress of ancient India, which of the statements given below are correct?
$1$. Different kinds of specialized surgical instruments were in common use by AD $1$st century.
$2$. Transplant of internal organs in the human body had begun by the beginning of AD $3$rd century.
$3$. The concept of sine of an angle was known in AD $5$th century.
$4$. The concept of cyclic quadrilaterals was known in AD $7$th century.
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With reference to the history of ancient India, which of the following was/were common to both Buddhism and Jainism?
1. Avoidance of extremities of penance and enjoyment.
2. Indifference to the authority of the Vedas.
3. Denial of the efficacy of rituals.
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Which of the following statements is/apply to Jaina Doctrine?

$1$. The surest way of annihilating Karma is to practice penance.

$2$. Every object, even the smallest particle, has a soul.

$3$. Karma is the bane of the soul and must be ended.

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With reference to Indian history, which of the following is/are the essential element/elements of the Feudal System?
1. A very strong centralised political authority and a very weak provincial or local political authority.
2. Emergence of administrative structure based on control and possession of land.
3. Creation of lord-vassal relationship between the feudal lord and his overlord.

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In the context of the history of India, consider the following pairs

Term                                                             Description
1. Eripatti                                                    Land, revenue from which was set apart for the maintenance of the village tank
2. Taniyurs                                                  Village donated to a single Brahmin or a group of Brahmins
3.Ghatikas                                                  Colleges generally attached to the temples
Which of the pairs given above is/are correctly matched?