The question asks to identify the specific Article of the Indian Constitution that grants High Courts the power to issue writs, thereby exercising their original jurisdiction. We need to recall the constitutional provisions related to the powers of High Courts and the Supreme Court regarding writ jurisdiction.
Correct Option: A) Article 226
Article 226 of the Indian Constitution empowers the High Courts to issue writs, including habeas corpus, mandamus, prohibition, quo warranto, and certiorari. This power is part of their original jurisdiction and can be exercised for the enforcement of Fundamental Rights as well as for any other purpose (e.g., enforcement of ordinary legal rights). This makes the High Courts' writ jurisdiction broader than that of the Supreme Court under Article 32.
Consider the following statements about Exercise LA PEROUSE, in which India participated in January 2025.
1. The Indian Navy participated in the 4th edition of the exercise with INS Mumbai, a guided missile destroyer.
2. The exercise was held in Indian territorial waters near the Andaman and Nicobar Islands.
3. India's participation aligns with its SAGAR vision to promote maritime cooperation in the Indo-Pacific.
4. It is a bilateral naval exercise conducted exclusively between India and Indonesia.
Which of the above statements are correct?
Only 1 and 3
Only 1, 3 and 4
Only 1, 2 and 4
Only 2 and 3
The question asks to identify the correct statements regarding Exercise LA PEROUSE, focusing on India's participation. We need to evaluate each statement based on factual knowledge about this naval exercise.
A) Only 1 and 3
Based on the evaluation:
Therefore, only statements 1 and 3 are correct.
The question asks for the specific title of a poetry collection by Michael Madhusudan Dutt, published in 1849, which focuses on the story of Prithviraj Chauhan. This requires knowledge of the literary works of Michael Madhusudan Dutt, a prominent figure in Bengali literature.
Correct Option: C) The Captive Lady
The Captive Lady is a significant early work by Michael Madhusudan Dutt, published in 1849. It is an English narrative poem that recounts the tale of Prithviraj Chauhan, a legendary Hindu king of the Chahamana dynasty, and his love for Samyukta. This work marked Dutt's initial foray into English poetry before he turned his focus to Bengali literature, where he made his most profound impact.
The question asks to identify the dance form that specifically depicts the love stories of Radha and Krishna. This requires knowledge of various Indian folk and classical dance forms and their associated themes.
Correct Option: A) Raslila is a traditional folk theatre and dance form that vividly portrays the divine love stories and playful interactions between Lord Krishna and Radha, along with the Gopis.
The problem involves finding the HCF (Highest Common Factor) of three numbers given their ratio and their LCM (Least Common Multiple). We can represent the numbers using a common factor, which will be their HCF. Then, we can use the relationship between the numbers, their HCF, and their LCM to solve for the HCF.
Let the three numbers be \(N_1, N_2, N_3\). Since they are in the ratio 5 : 1 : 7, and their HCF is a common factor, let their HCF be \(x\).
Then the numbers can be written as:
\[ N_1 = 5x \] \[ N_2 = 1x = x \] \[ N_3 = 7x \]The LCM of \(5x, x, 7x\) is found by taking the product of the highest powers of all prime factors involved. The prime factors here are 5, 1 (which is ignored in LCM calculations as it's not a prime factor), 7, and \(x\).
So, the LCM of \(5x, x, 7x\) is \(5 \times 7 \times x\).
\[ \text{LCM}(5x, x, 7x) = 35x \]We are given that the LCM of the three numbers is 7595.
Therefore, we can set up the equation:
\[ 35x = 7595 \]Now, solve for \(x\):
\[ x = \frac{7595}{35} \]Perform the division:
\[ x = 217 \]As established in step 1, \(x\) is the HCF of the three numbers \(5x, x, 7x\).
So, the HCF is 217.
C) 217 — The HCF of the three numbers is 217, as calculated by setting up the numbers in terms of their HCF and using the given LCM.
Simplify: 10 × (24 − 12) + (\( \frac{165}{33} \))
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
A) 125 is the correct simplification of the given expression.
This question tests general awareness regarding recent certifications and recognitions of Public Sector Undertakings (PSUs) in India. Candidates need to recall which company received the 'Great Place to Work' certification in December 2024.
Correct Option: A) Steel Authority of India Limited (SAIL)
To find the scheme that fetches the maximum selling price, we need to determine which scheme results in the minimum overall discount. The selling price is calculated as the Marked Price minus the total discount. A lower total discount means a higher selling price. We will calculate the effective discount for each scheme and compare them.
Let the Marked Price (MP) of the article be \(P\).
The effective discount for two successive discounts of \(d_1\)% and \(d_2\)% can be calculated using the formula:
\[ \text{Effective Discount} = \left( d_1 + d_2 - \frac{d_1 \times d_2}{100} \right)\% \]Alternatively, we can calculate the final selling price directly. If an item is discounted by \(d\)%, its price becomes \((100-d)\)% of the original. For successive discounts, we multiply the remaining percentages.
\[ \text{Selling Price} = P \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \]We want to maximize the Selling Price, which means we want to maximize the factor \[\left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)\].
Here, \(d_1 = 27\%\) and \(d_2 = 27\%\).
\[ \text{Effective Discount}_I = \left( 27 + 27 - \frac{27 \times 27}{100} \right)\% \] \[ = \left( 54 - \frac{729}{100} \right)\% = (54 - 7.29)\% = 46.71\% \]Alternatively, Selling Price \(= P \times (1 - 0.27) \times (1 - 0.27) = P \times 0.73 \times 0.73 = 0.5329 P\)
Here, \(d_1 = 7\%\) and \(d_2 = 6\%\).
\[ \text{Effective Discount}_{II} = \left( 7 + 6 - \frac{7 \times 6}{100} \right)\% \] \[ = \left( 13 - \frac{42}{100} \right)\% = (13 - 0.42)\% = 12.58\% \]Alternatively, Selling Price \(= P \times (1 - 0.07) \times (1 - 0.06) = P \times 0.93 \times 0.94 = 0.8742 P\)
Here, \(d_1 = 45\%\) and \(d_2 = 29\%\).
\[ \text{Effective Discount}_{III} = \left( 45 + 29 - \frac{45 \times 29}{100} \right)\% \] \[ = \left( 74 - \frac{1305}{100} \right)\% = (74 - 13.05)\% = 60.95\% \]Alternatively, Selling Price \(= P \times (1 - 0.45) \times (1 - 0.29) = P \times 0.55 \times 0.71 = 0.3905 P\)
Here, \(d_1 = 20\%\) and \(d_2 = 38\%\).
\[ \text{Effective Discount}_{IV} = \left( 20 + 38 - \frac{20 \times 38}{100} \right)\% \] \[ = \left( 58 - \frac{760}{100} \right)\% = (58 - 7.6)\% = 50.4\% \]Alternatively, Selling Price \(= P \times (1 - 0.20) \times (1 - 0.38) = P \times 0.80 \times 0.62 = 0.496 P\)
Now, let's compare the effective discounts or the selling prices:
The scheme with the minimum effective discount will fetch the maximum selling price. Comparing the effective discounts, 12.58% (Scheme II) is the smallest. Therefore, Scheme II will result in the maximum selling price.
D) II — Scheme II offers the lowest effective discount of 12.58%, which means it will result in the highest selling price (0.8742 P).