Who asked, "What is a woman without a husband?"

Question 1: Which statement is illogical?

Step 1: Option (A) Padma's father is a woman – a father is defined as male, so this is impossible.

Step 2: Options (B), (C), (D) are possible statements.

Thus, the answer is A.

$\boxed{A}$

Question 2: Who became the ruler?

Step 1: In the Yayati-Devayani story from Puranas, Sukracharya was the guru, Devayani his daughter, Yayati the initial king cursed to old age.

Step 2: Puru, son of Yayati and Sharmishtha, sacrificed his youth; Yayati ruled then crowned Puru as ruler.

Thus, the answer is D.

$\boxed{D}$

Question 3: In which year was the first [event]?

Note: Exact event unclear from transcription, but based on prominent Indian events, December 1992 marks Babri Masjid demolition (major historical first in context).

Thus, the answer is A.

$\boxed{A}$

Question 4: Due to what will the quality of life erode?

Step 1: Overpopulation leads to resource strain, pollution, and reduced living standards.

Step 2: Deforestation contributes but secondary; damage/earthquakes are specific, not primary ongoing cause.

Thus, the answer is A.

$\boxed{A}$

Question 5: If births are slightly higher than deaths, population growth rate is

Step 1: Slight excess of births over deaths means low positive growth rate.

Step 2: Not very high or medium high; "very low" fits "slightly higher."

Thus, the answer is C.

$\boxed{C}$

Question 6: Related to Echo overcoming shyness/crept from whom?

Step 1: In Greek mythology, nymph Echo was cursed by Hera (jealous wife of Zeus) to repeat only last words, causing shyness; she hid and echoed.

Step 2: Hera is the one involved.

Thus, the answer is A.

$\boxed{A}$