Statement Analysis

The question asks to identify the correct statements among the given five options related to ancient Indian texts and concepts.

• A. Vedas were composed in one period of time.
  This statement is incorrect. The composition of the Vedas spanned a long period, evolving over centuries, not a single period.
• B. Aśvamedha sacrifice is first mentioned in the Ṛgveda.
  This statement is correct. The Ṛgveda contains early references to the Aśvamedha (horse sacrifice).
• C. Hindu marriage is of eight kinds.
  This statement is correct. Ancient Hindu texts, like the Manusmṛti, describe eight forms of marriage (e.g., Brahma, Daiva, Ārṣa, Prājāpatya, Āsura, Gāndharva, Rākṣasa, Paiśāca).
• D. Kapila was the propounder of Yoga philosophy.
  This statement is incorrect. Kapila is traditionally considered the sage who systematized Sāṃkhya philosophy. Patañjali is credited with propounding the Yoga Sutras.
• E. Caste is fixed on the basis of the observance of religious code.
  This statement is considered correct in the context of traditional Vedic and post-Vedic ideals, where adherence to one's *dharma* (religious and social duty) was intrinsically linked to the *varna* system, although birth became the predominant factor over time.

Selecting Correct Statements

Based on the analysis, statements B, C, and E are correct.

• Statement B is correct.
• Statement C is correct.
• Statement E is correct.

Conclusion

The correct statements are B, C, and E. Therefore, the most appropriate option is the one listing B, C, and E only.