This question pertains to the provisions of Indian citizenship law, specifically regarding the loss of citizenship. Indian law does not permit dual citizenship for its citizens. Therefore, if an Indian citizen acquires the citizenship of another country, there are clear legal consequences.
C) Their Indian citizenship ends automatically. This is in accordance with Section 9(1) of the Citizenship Act, 1955, which mandates the automatic termination of Indian citizenship upon the voluntary acquisition of foreign citizenship.
While covering a distance of 37 km, a man noticed that after cycling for 1 hour 5 minutes, the distance covered by him was \( \frac{4}{3} \) of the remaining distance. What was his speed (in km/hr, rounded off to one decimal place)?
The problem involves calculating the speed of a man cycling a certain distance. We are given the total distance, the time for which he cycled, and a relationship between the distance covered and the remaining distance after that time. We will use these pieces of information to find the distance covered in the given time and then calculate the speed.
Let the total distance be \(D = 37 \text{ km}\).
Let the distance covered after 1 hour 5 minutes be \(d_c\).
The remaining distance will be \(d_r = D - d_c\).
We are given that after cycling for 1 hour 5 minutes, the distance covered by him was \( \frac{4}{3} \) of the remaining distance. So, we can write the equation:
\[ d_c = \frac{4}{3} d_r \]Substitute \(d_r = D - d_c\) into the equation:
\[ d_c = \frac{4}{3} (D - d_c) \]Now, substitute the total distance \(D = 37 \text{ km}\):
\[ d_c = \frac{4}{3} (37 - d_c) \]Multiply both sides by 3 to eliminate the fraction:
\[ 3 d_c = 4 (37 - d_c) \]\[ 3 d_c = 148 - 4 d_c \]Add \(4 d_c\) to both sides:
\[ 3 d_c + 4 d_c = 148 \]\[ 7 d_c = 148 \]Solve for \(d_c\):
\[ d_c = \frac{148}{7} \text{ km} \]Now, convert the given time into hours. Time \(T = 1 \text{ hour } 5 \text{ minutes}\).
\[ 5 \text{ minutes} = \frac{5}{60} \text{ hours} = \frac{1}{12} \text{ hours} \]\[ T = 1 + \frac{1}{12} \text{ hours} = \frac{12+1}{12} \text{ hours} = \frac{13}{12} \text{ hours} \]The speed (\(S\)) is calculated as distance covered divided by time taken:
\[ S = \frac{d_c}{T} \]\[ S = \frac{\frac{148}{7}}{\frac{13}{12}} \]\[ S = \frac{148}{7} \times \frac{12}{13} \]\[ S = \frac{1776}{91} \]Calculate the numerical value and round it to one decimal place:
\[ S \approx 19.516 \text{ km/hr} \]\[ S \approx 19.5 \text{ km/hr} \]Correct Option: B) 19.5
The problem presents a proportion, which means two ratios are equal. We need to find the unknown value \(x\) by setting up the proportion and solving for \(x\).
The given proportion is \(3.5 : 17.4 :: 14 : x\). This can be written in fraction form as:
\[ \frac{3.5}{17.4} = \frac{14}{x} \]To solve for \(x\), we can cross-multiply:
\[ 3.5 \times x = 17.4 \times 14 \]Calculate the product on the right side:
\[ 17.4 \times 14 = 243.6 \]Now the equation becomes:
\[ 3.5x = 243.6 \]Divide both sides by \(3.5\) to find \(x\):
\[ x = \frac{243.6}{3.5} \]To simplify the division, we can multiply the numerator and denominator by 10 to remove the decimal points:
\[ x = \frac{2436}{35} \]Perform the division:
\[ x = 69.6 \]Correct Option: C) 69.6
The problem provides a list of marks for 12 students, including the lowest mark \(x\) and the highest mark \(y\). We are given the range and the average (mean) of these marks. We need to use these two pieces of information to form a system of equations and solve for \(x\) and \(y\).
Correct Option: C) (25, 95)
The problem asks us to identify a triad that follows the same pattern as the two given triads: EL-GN-IK and GN-IP-KM. We need to analyze the positional values of the letters in the English alphabet to find the underlying pattern.
C) IP-KR-MO
This triad perfectly matches the established pattern.
The question asks to identify the state that launched a specific initiative in 2025 to eliminate mother-to-child transmission of HIV, syphilis, and Hepatitis B by 2026. This requires knowledge of recent health initiatives by Indian states.
In 2025, West Bengal launched a comprehensive initiative with the ambitious goal of eradicating mother-to-child transmission of HIV, syphilis, and Hepatitis B by 2026. This program focuses on screening pregnant women, providing timely treatment, and ensuring follow-up care to prevent the transmission of these infections to newborns. Such initiatives are crucial for improving maternal and child health outcomes.
To simplify the given expression \( (2x +3)^{2} - (x + 1)^{2} \), we can use the algebraic identity \( (a+b)^2 = a^2 + 2ab + b^2 \) to expand each squared term. Alternatively, we can use the difference of squares identity \( a^2 - b^2 = (a-b)(a+b) \).
Method 1: Expanding each term
Method 2: Using the difference of squares identity
A) \( 3x^{2} + 10x + 8 \) is the correct simplified expression, as derived by both methods.
The question asks about the major impact of penicillin's discovery. To answer this, one needs to recall the historical context and the primary medical application of penicillin.
Based on the nature and use of penicillin, Option B aligns perfectly with its historical and medical significance.
B) First effective antibiotic against bacterial infections
Penicillin was indeed the first widely effective antibiotic. Its discovery revolutionized medicine by providing a powerful tool to combat bacterial diseases, saving millions of lives and significantly reducing mortality rates from infections that were previously untreatable.
The problem requires us to transform each given word based on specific rules: vowels change to the next letter, and consonants change to the previous letter. After transformation, we need to count how many of the new letter clusters contain no vowels.
Correct Option: D) Three