The question asks about the atmospheric conditions on early Earth when life first emerged. This refers to the primitive atmosphere, which was significantly different from today's atmosphere. We need to identify which gas, among the given options, was absent in its free state during that period.
Correct Option: A) Oxygen was not present in its free state in the early Earth's atmosphere when life arose. It was a reducing atmosphere, and free oxygen accumulated much later due to biological activity.
The question asks about the behavior of sound waves as they travel through different mediums. The speed of sound depends on the properties of the medium it travels through.
Correct Option: A) different speed in different mediums
This question tests knowledge of common chemical reactions, specifically the reaction between a metal (zinc) and an acid (hydrochloric acid). The general rule for such reactions is that a metal above hydrogen in the reactivity series will displace hydrogen from an acid.
A) Hydrogen is the gas evolved when zinc reacts with hydrochloric acid, as zinc displaces hydrogen from the acid.
The question asks to identify the famous personality on whose biography the 2016 movie "The Man Who Knew Infinity" is based. This requires knowledge of prominent Indian personalities and their biographical films.
Correct Option: A) The movie “The Man Who Knew Infinity” (2016) is a biographical drama film about the Indian mathematician Srinivasa Ramanujan. It chronicles his life, his self-taught mathematical genius, and his extraordinary collaboration with Professor G.H. Hardy at Cambridge University during World War I.
This question asks us to evaluate the strength of two arguments in relation to a given statement. A strong argument is one that is directly relevant to the statement and provides a logical, factual, or generally accepted reason to support or refute it. Weak arguments are subjective, irrelevant, or based on personal preferences rather than objective facts.
Correct Option: A) Only argument I is strong.
The question asks to identify the person who does not belong to the group among the given options. This requires knowledge of the sport each individual is associated with.
Correct Option: C) Saina Nehwal is a badminton player, while the others are chess players.
To find the minimum energy required to launch a satellite, we need to calculate the change in the total mechanical energy of the satellite from its initial position on the Earth's surface to its final position in a circular orbit. The total mechanical energy is the sum of its kinetic energy and potential energy.
Correct Option: D) \( \frac{5}{6} \) mgR
The question asks for the primary reason Mendel chose pea plants for his genetic experiments. To answer this, we need to recall the characteristics of pea plants that made them ideal for studying inheritance patterns.
D) They had many pairs of distinct, contrasting traits — This is the most crucial reason. Mendel's ability to identify and track specific traits like tall vs. dwarf, round vs. wrinkled seeds, or yellow vs. green seeds was fundamental to his discovery of the laws of inheritance. Without such clear, contrasting traits, it would have been very difficult to discern the patterns of dominant and recessive alleles.
To find the value of the given expression, we need to calculate the square root of each decimal number in the numerator and the denominator separately, and then divide the results. We will convert the decimals to fractions to simplify the square root calculation.
The given expression is \( \frac{\sqrt{0.64}}{\sqrt{0.16}} \).
First, convert the decimal numbers into fractions:
\[ 0.64 = \frac{64}{100} \]\[ 0.16 = \frac{16}{100} \]Now, substitute these fractions back into the original expression:
\[ \frac{\sqrt{\frac{64}{100}}}{\sqrt{\frac{16}{100}}} \]Apply the square root property \[\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\]:
\[ \sqrt{\frac{64}{100}} = \frac{\sqrt{64}}{\sqrt{100}} = \frac{8}{10} \]\[ \sqrt{\frac{16}{100}} = \frac{\sqrt{16}}{\sqrt{100}} = \frac{4}{10} \]Now, divide the square root of the numerator by the square root of the denominator:
\[ \frac{\frac{8}{10}}{\frac{4}{10}} \]To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
\[ \frac{8}{10} \times \frac{10}{4} \]\[ \frac{8 \times 10}{10 \times 4} \]\[ \frac{80}{40} \]\[ 2 \]A) The calculated value of the expression is 2.
The question asks for the minimum age limit to be eligible for appointment as the Prime Minister of India. This requires knowledge of the constitutional provisions regarding the eligibility criteria for Members of Parliament, as the Prime Minister must be a member of either the Lok Sabha or the Rajya Sabha.
B) 25 years is the minimum age required to be a member of the Lok Sabha, and thus the minimum age to be eligible for appointment as Prime Minister.