The question asks to identify the Indian Institute of Technology (IIT) where ISRO established a Regional Academic Centre for Space (RAC-S) in December 2020. This requires knowledge of recent collaborations and initiatives by ISRO.
Correct Option: D) Varanasi
The question asks for the specific date when the United Nations adopted the 'Charter of Economic Rights and Duties of States'. This is a factual recall question related to international relations and economic history.
A) December 1974 is the correct answer. The United Nations General Assembly adopted the 'Charter of Economic Rights and Duties of States' on December 12, 1974, through Resolution 3281 (XXIX).
This problem involves analyzing logical statements and drawing conclusions. We can use Venn diagrams or logical deductions to determine which conclusions follow from the given statements. We will represent each category as a circle and show their relationships based on the statements.
A) Only conclusion III follows.
The question asks about the behavior of marginal utility as consumption of a good increases, according to the Law of Diminishing Marginal Utility. This fundamental economic principle describes how the satisfaction derived from consuming additional units of a good changes.
Correct Option: B) diminish. This option accurately reflects the core principle of the Law of Diminishing Marginal Utility, which states that as consumption of a good increases, the marginal utility derived from each additional unit tends to decrease.
The question asks to identify the individual appointed as the President of the Asian Cricket Council (ACC) in 2021. This is a factual question related to sports administration and requires knowledge of key appointments in cricket governance.
Correct Option: D) Jay Shah was appointed as the President of the Asian Cricket Council (ACC) in January 2021. He is also the current Secretary of the Board of Control for Cricket in India (BCCI).
The problem is a coding-decoding question. We need to identify the pattern or mapping between letters and numbers from the given coded words and then apply that pattern to decode the target word.
Let's list the letter-to-number mappings we can deduce:
Combining these, PANTHER will be coded as 7681203.
Correct Option: D) 7681203
This is a logical deduction problem. We need to assign a unique colour to each box based on the given clues. We will create a table or list the possibilities and eliminate them as new information is provided.
List the boxes and colours:
From the given statements, let's fill in the definite assignments and eliminate possibilities:
Now, let's consider the remaining boxes and colours:
"S and U are neither painted with white nor grey colour."
"Q is not painted with white or blue colour."
Let's update the assignments:
Now, consider the remaining boxes and colours:
From step 4, we know \(\text{S} \in \{\text{Blue, Green}\}\) and \(\text{U} \in \{\text{Blue, Green}\}\).
Finally, we have:
Remaining Boxes: S, U
Since S and U must be painted with Blue or Green, and these are the only two colours left, S can be either Blue or Green. The question asks for the colour of box S.
D) Blue or Green. Based on our deductions, S must be painted with either Blue or Green, as these are the only two remaining colours for S and U, and no further information distinguishes between S and U for these specific colours.
Find the value of \(\frac{(0.01)^2+(0.22)^2+(0.333)^2+(0.4444)^2+(0.55555)^2}{(0.001)^2+(0.022)^2+(0.0333)^2+(0.04444)^2+(0.055555)^2}\)
The problem asks us to evaluate a complex fraction. The key to solving this efficiently is to observe the relationship between the terms in the numerator and the denominator. Each term in the numerator is a multiple of 10 times the corresponding term in the denominator. By factoring out a common term, the expression can be simplified significantly.
Let's write down the given expression:
\[ \frac{(0.01)^2+(0.22)^2+(0.333)^2+(0.4444)^2+(0.55555)^2}{(0.001)^2+(0.022)^2+(0.0333)^2+(0.04444)^2+(0.055555)^2} \]Observe the relationship between the terms in the numerator and the denominator:
Substitute these relationships into the numerator:
\[ (10 \times 0.001)^2 + (10 \times 0.022)^2 + (10 \times 0.0333)^2 + (10 \times 0.04444)^2 + (10 \times 0.055555)^2 \]Factor out \(10^2\) from each term in the numerator:
\[ 10^2 \times (0.001)^2 + 10^2 \times (0.022)^2 + 10^2 \times (0.0333)^2 + 10^2 \times (0.04444)^2 + 10^2 \times (0.055555)^2 \]\[ = 100 \times [(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2] \]Now, substitute this back into the original expression:
\[ \frac{100 \times [(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2]}{[(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2]} \]The common sum of squares in the numerator and denominator cancels out:
\[ \frac{100 \times \cancel{[(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2]}}{\cancel{[(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2]}} = 100 \]Correct Option: B) 100
The question asks to identify the British Governor-General or Viceroy who is credited with the establishment and early development of railways in India. This requires knowledge of key historical figures and their contributions during British rule.
Correct Option: C) Lord Dalhousie is widely recognized as the 'Father of Indian Railways' because the first railway line in India was laid during his tenure as Governor-General (1848-1856). He also introduced the 'Railway Minute of 1853', which outlined a comprehensive plan for the development of railways in India.
The question asks for the motto of the Supreme Court of India. This requires knowledge of the specific mottos associated with prominent Indian institutions.
Correct Option: D) Yato Dharmastato Jayaḥ