The question asks about the individual who proposed the 'Objectives Resolution' in 1946, a crucial step before the framing of the Indian Constitution. This is a direct factual question related to the history of the Indian Constituent Assembly.
Correct Option: B) Jawaharlal Nehru proposed the 'Objectives Resolution' in the Constituent Assembly on December 13, 1946. This resolution laid down the fundamentals and philosophy of the constitutional structure and was later adopted as the Preamble to the Constitution of India.
To arrange words as per their order in an English dictionary, we compare them letter by letter from left to right. The word that comes earlier alphabetically at the first differing letter will be placed earlier in the dictionary.
Based on this order, "Exercise" is the second word.
C) Exempt. Wait, let me re-evaluate. The question asks for the second word. My final order is: 1. Excuse, 2. Exercise, 3. Exempt, 4. Exit. So, "Exercise" is the second word. The provided correct answer is C) Exempt. Let me re-check the comparison between "Exercise" and "Exempt".
Comparing "Exercise" and "Exempt":
The first two letters 'Ex' are common. The third letter 'e' is common. Now compare the fourth letter:
Alphabetically, 'm' comes before 'r'. Therefore, "Exempt" comes before "Exercise".
Let's re-establish the correct order:
So the correct alphabetical order is:
Therefore, the second word in alphabetical order is "Exempt".
The problem asks us to decode a pattern from a given word-to-number mapping and then apply the same pattern to a new word. We need to find the positional value of each letter in the alphabet, sum them up, and then perform an operation to get the coded number.
Therefore, TAPLG will be written as 3136 in that language.
Correct Option: B) 3136
The question asks to identify the author of a specific quote emphasizing the link between societal well-being and the condition of its poorest members. This requires knowledge of prominent economists and their philosophical stances.
B) Adam Smith — The quote, "No society can surely be flourishing and happy, of which the far greater part of the members are poor and miserable," is directly attributable to Adam Smith from his work "The Wealth of Nations" (1776). This demonstrates that even the proponent of capitalism recognized the moral imperative of addressing poverty for a truly prosperous society.
The question asks about the number of states that initially signed the United Nations Charter, leading to the establishment of the United Nations. This is a factual question related to the history of international organizations.
Correct Option: C) 51
To find the surface area of a cuboid, we use the formula that accounts for the area of all six faces. A cuboid has three pairs of identical rectangular faces. We will identify the length, breadth, and height from the given dimensions and then apply the formula for the total surface area.
The total surface area of the cuboid is \(868 \text{ m}^2\).
Correct Option: D) 868 m²
A and B working together can finish a task in 18 days. B and C working together can finish it in 24 days. A and C working together can finish it in 36 days. In how many days will A, B and C finish the same task, working separately?
A = 48, B = 144 and C = 28 \( \frac{4}{5} \)
A = 28 \( \frac{4}{5} \), B = 144 and C = 48
A = 48, B = 28 \( \frac{4}{5} \) and C = 144
A = 28 \( \frac{4}{5} \), B = 48 and C = 144
This problem involves work and time. We can solve it by calculating the individual work rates of A, B, and C. The work rate is the reciprocal of the time taken to complete the task. We'll set up a system of equations based on the combined work rates and then solve for individual rates.
Let the time taken by A, B, and C to finish the task individually be \(A\), \(B\), and \(C\) days, respectively. Their one-day work rates will be \(1/A\), \(1/B\), and \(1/C\).
From the given information, we can form the following equations:
Add all three equations:
\[ \left(\frac{1}{A} + \frac{1}{B}\right) + \left(\frac{1}{B} + \frac{1}{C}\right) + \left(\frac{1}{A} + \frac{1}{C}\right) = \frac{1}{18} + \frac{1}{24} + \frac{1}{36} \]\[ \frac{2}{A} + \frac{2}{B} + \frac{2}{C} = \frac{4+3+2}{72} \]\[ 2\left(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\right) = \frac{9}{72} \]\[ 2\left(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\right) = \frac{1}{8} \]\[ \frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{16} \quad \text{(Equation 4)} \]This means A, B, and C working together can finish the task in 16 days.Now, subtract Equation 2 from Equation 4 to find A's work rate:
\[ \left(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\right) - \left(\frac{1}{B} + \frac{1}{C}\right) = \frac{1}{16} - \frac{1}{24} \]\[ \frac{1}{A} = \frac{3-2}{48} \]\[ \frac{1}{A} = \frac{1}{48} \]So, A takes 48 days to finish the task alone.Subtract Equation 3 from Equation 4 to find B's work rate:
\[ \left(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\right) - \left(\frac{1}{A} + \frac{1}{C}\right) = \frac{1}{16} - \frac{1}{36} \]\[ \frac{1}{B} = \frac{9-4}{144} \]\[ \frac{1}{B} = \frac{5}{144} \]So, B takes \(144/5 = 28 \frac{4}{5}\) days to finish the task alone.Subtract Equation 1 from Equation 4 to find C's work rate:
\[ \left(\frac{1}{A} + \frac{1}{B} + \frac{1}{C}\right) - \left(\frac{1}{A} + \frac{1}{B}\right) = \frac{1}{16} - \frac{1}{18} \]\[ \frac{1}{C} = \frac{9-8}{144} \]\[ \frac{1}{C} = \frac{1}{144} \]So, C takes 144 days to finish the task alone.Therefore, A = 48 days, B = \(28 \frac{4}{5}\) days, and C = 144 days.
C) A = 48, B = \(28 \frac{4}{5}\) and C = 144. This matches our calculated values for A, B, and C.
The question asks for the population density of India according to the 2011 Census. This is a factual recall question based on official census data.
As per the 2011 Census, the total population of India was approximately 1.21 billion, and its total land area is approximately 3.287 million square kilometers. Population density is calculated as:
\[ \text{Population Density} = \frac{\text{Total Population}}{\text{Total Land Area}} \]For India in 2011, this was:
\[ \text{Population Density} = \frac{1,210,854,977 \text{ persons}}{3,287,263 \text{ km}^2} \approx 382 \text{ persons/km}^2 \]Therefore, the population density was 382 persons per square kilometer.
D) 382 persons per sq km — This is the correct population density of India as per the 2011 Census data.
The question asks to identify the true statement regarding Fundamental Rights and Directive Principles of State Policy (DPSP) in the Indian Constitution. We need to evaluate each option based on the established characteristics and differences between these two parts of the Constitution.
B) Fundamental Rights are justiciable, whereas Directive Principles of State are non-justiciable. This statement is correct. Fundamental Rights are legally enforceable by the courts, meaning an individual can approach the Supreme Court or High Courts for their enforcement. In contrast, Directive Principles are not enforceable by any court, though they are fundamental in the governance of the country and it shall be the duty of the State to apply these principles in making laws.
What is the value of x in the following equation?
\( 8.5 - \left\{ 5\frac{1}{2} - \left( 7\frac{1}{2} + 2.8 \div x \right) \right\} \times 4.25 \div (0.2)^{2} = 306 \)
To solve this equation for \(x\), we need to simplify the expression by following the order of operations (BODMAS/PEMDAS). We will convert mixed fractions to decimals, simplify terms within parentheses and braces, and then isolate \(x\).
First, convert all mixed fractions and decimals to a consistent format. It's often easiest to work with decimals.
\[ 5\frac{1}{2} = 5.5 \]\[ 7\frac{1}{2} = 7.5 \]Substitute these values into the equation:
\[ 8.5 - \left\{ 5.5 - \left( 7.5 + 2.8 \div x \right) \right\} \times 4.25 \div (0.2)^{2} = 306 \]Calculate \((0.2)^2\):
\[ (0.2)^2 = 0.04 \]Substitute this back into the equation:
\[ 8.5 - \left\{ 5.5 - \left( 7.5 + 2.8 \div x \right) \right\} \times 4.25 \div 0.04 = 306 \]Perform the division \(4.25 \div 0.04\):
\[ 4.25 \div 0.04 = 106.25 \]The equation now becomes:
\[ 8.5 - \left\{ 5.5 - \left( 7.5 + 2.8 \div x \right) \right\} \times 106.25 = 306 \]Move the constant term \(8.5\) to the right side:
\[ - \left\{ 5.5 - \left( 7.5 + 2.8 \div x \right) \right\} \times 106.25 = 306 - 8.5 \]\[ - \left\{ 5.5 - \left( 7.5 + 2.8 \div x \right) \right\} \times 106.25 = 297.5 \]Divide both sides by \(-106.25\):
\[ 5.5 - \left( 7.5 + 2.8 \div x \right) = \frac{297.5}{-106.25} \]\[ 5.5 - \left( 7.5 + 2.8 \div x \right) = -2.8 \]Isolate the term with \(x\):
\[ - \left( 7.5 + 2.8 \div x \right) = -2.8 - 5.5 \]\[ - \left( 7.5 + 2.8 \div x \right) = -8.3 \]Multiply both sides by \(-1\):
\[ 7.5 + 2.8 \div x = 8.3 \]Subtract \(7.5\) from both sides:
\[ 2.8 \div x = 8.3 - 7.5 \]\[ 2.8 \div x = 0.8 \]Solve for \(x\):
\[ x = \frac{2.8}{0.8} \]\[ x = \frac{28}{8} \]\[ x = \frac{7}{2} \]\[ x = 3.5 \]B) The value of \(x\) is \(3.5\).