Identify the cells responsible for androgen synthesis and indicate their location in the provided diagram.

Testicular hormones, specifically androgens like testosterone, are synthesized and secreted by the Leydig cells (also known as interstitial cells) in the testes.

The diagram shows a cross-section of testicular tissue.

• Label 'a' points to the lumen of a seminiferous tubule.
• Label 'b' points to the cells located in the interstitial spaces between the seminiferous tubules. These are the Leydig cells.
• Label 'c' points to cells within the wall of a seminiferous tubule (e.g., Sertoli cells or spermatogonia).
• Label 'd' points to an entire seminiferous tubule.

Since Leydig cells (interstitial cells) are responsible for androgen synthesis and are indicated by label 'b', option (3) is correct.

The final answer is $\boxed{\text{3}}$

Statement A: "High level of hCG stimulates the thickening of endometrium."
Human Chorionic Gonadotropin (hCG) primarily functions to maintain the corpus luteum, which in turn produces progesterone. Progesterone is the hormone directly responsible for maintaining and further thickening the endometrium. While hCG indirectly supports the endometrium by ensuring progesterone production, it does not directly stimulate the initial thickening of the endometrium in the same way estrogen does. Its role is more about maintenance of the thickened state. Therefore, this statement is generally considered incorrect in terms of direct stimulation.

Statement B: "High level of FSH and LH stimulates the thickening of endometrium."
Follicle-Stimulating Hormone (FSH) stimulates the growth of ovarian follicles and the production of estrogen. Estrogen is the primary hormone that causes the proliferation (thickening) of the endometrium during the proliferative phase of the menstrual cycle. Luteinizing Hormone (LH) triggers ovulation and the formation of the corpus luteum, which produces progesterone. Progesterone further prepares and thickens the endometrium for implantation. Thus, FSH and LH are crucial for stimulating the ovarian hormone production (estrogen and progesterone) that directly leads to endometrial thickening. This statement is correct.

Based on the analysis, Statement A is incorrect, and Statement B is correct.
Option (1) states that Statement B is correct and statement A is wrong.

The final answer is $\boxed{\text{1}}$

• (A) Trophoblast: This is the outer layer of the blastocyst that helps in implantation and later forms the placenta. It attaches to the endometrium. So, (A) matches with (III) "Outer layer of blastocyst attached to the endometrium".
• (B) Cleavage: This refers to the rapid mitotic divisions of the zygote that increase the number of cells (blastomeres) without increasing the overall size of the embryo. So, (B) matches with (IV) "Mitotic division of zygote".
• (C) Inner cell mass: This is a cluster of cells inside the blastocyst that will develop into the embryo proper. So, (C) matches with (II) "Group of cells that will differentiate as embryo".
• (D) Implantation: This is the process by which the blastocyst embeds itself into the uterine wall (endometrium). So, (D) matches with (I) "Embedding of blastocyst in the endometrium".

The correct matches are: A-III, B-IV, C-II, D-I.
Comparing this with the given options:
(1) a - ii, b - i, c - iii, d - iv
(2) a - iii, b - iv, c - ii, d - i
(3) a - iii, b - i, c - ii, d - iv
(4) a - ii, b - iv, c - i, d - iii

Option (2) correctly reflects our matches.

The final answer is $\boxed{\text{2}}$