To determine which set of numbers forms co-prime numbers, we need to find the Greatest Common Divisor (GCD) for each pair. Two numbers are co-prime (or relatively prime) if their GCD is 1. This means they share no common prime factors.
Based on the analysis, only the pair (12, 7) has a GCD of 1.
Correct Option: A) (12, 7) is the set of co-prime numbers because their Greatest Common Divisor (GCD) is 1.
To find the new ratio of salaries, we first need to determine the initial salaries of P and Q based on the given ratio. Then, we calculate the increased salaries by applying the respective percentage increases. Finally, we find the ratio of these new salaries and simplify it.
Assume initial salaries:
Given that the monthly salaries of P and Q are in the ratio 4 : 3, let their initial salaries be \(4x\) and \(3x\) respectively, where \(x\) is a common multiplier.
Calculate the increase for P:
P gets an increase of 10% of the existing salary.
Calculate the new salary of P:
New salary of P \( = \text{Initial salary of P} + \text{Increase for P} = 4x + 0.4x = 4.4x \)
Calculate the increase for Q:
Q gets an increase of 5% of the existing salary.
Calculate the new salary of Q:
New salary of Q \( = \text{Initial salary of Q} + \text{Increase for Q} = 3x + 0.15x = 3.15x \)
Find the new ratio of salaries:
The new ratio of salaries of P and Q will be the ratio of their new salaries.
Simplify the ratio:
Cancel out \(x\) and multiply the numerator and denominator by 100 to remove decimals.
So, the new ratio is \( 88 : 63 \).
Correct Option: A) 88 : 63
The Home Rule Leagues set up in 1915-16 worked as auxiliary units of the _________.
Muslim League
Indian National Congress
Extremists
British Raj
The question asks about the relationship between the Home Rule Leagues and other political organizations in India during 1915-16. To answer this, we need to understand the objectives and operational context of the Home Rule Movement.
Correct Option: B) The Home Rule Leagues worked as auxiliary units of the Indian National Congress. They aimed to revitalize the nationalist movement and push for self-government, aligning with and supporting the broader objectives of the Congress, which was the main political body fighting for India's independence.
The question asks to identify the fundamental technology enabling future financial transactions, especially given the rise of mobile banking. We need to consider what core technology underpins mobile banking and allows for seamless, remote transactions.
D) Wireless — Mobile banking's existence and future expansion are entirely dependent on wireless communication technologies (e.g., cellular networks, Wi-Fi) that allow devices to connect to banking systems remotely without physical cables.
The question asks to identify the Assamese wildlife biologist who received the Royal Bank of Scotland (RBS) Earth Heroes Award in 2016. This requires knowledge of prominent environmentalists and their awards, specifically from the Assam region of India.
Correct Option: D) Purnima Devi Barman
Purnima Devi Barman is an Indian wildlife biologist from Assam. She is known for her conservation work with the Greater Adjutant Stork (locally known as 'Hargila') and leading the "Hargila Army" – an all-female conservation group. She received the Royal Bank of Scotland (RBS) Earth Heroes Award in 2016 for her significant contributions to wildlife conservation.
The question asks to identify which of the four Vedas is associated with treatments for diseases. This requires knowledge of the primary focus and content of each Veda.
D) Atharva. The Atharva Veda is distinct from the other three Vedas (Rig, Sama, Yajur) because it focuses on practical aspects of life, including healing, magic, and protection from evil. It contains numerous hymns and incantations related to medicine, diseases, and their remedies, making it the Veda most associated with treatments for diseases.
This is a word analogy question based on letter rearrangement. We need to identify the pattern of letter transformation from the first pair (HORSE : SERHO) and apply the same pattern to the second word (CURSE) to find the missing term.
Correct Option: D) SERCU
K and L can do a work in 15 and 20 days respectively. They work together for 5 days and leave. Calculate the unfinished portion of the work.
\( \frac{7}{12} \)
\( \frac{5}{12} \)
\( \frac{1}{13} \)
\( \frac{1}{4} \)
To find the unfinished portion of the work, we first need to calculate the individual work rates of K and L. Then, we find their combined work rate. We multiply their combined work rate by the number of days they worked together to find the completed portion. Finally, we subtract the completed portion from the total work (which is 1) to get the unfinished portion.
When K and L work together, their combined one day's work is the sum of their individual work rates:
\[ \text{Combined work rate} = \frac{1}{15} + \frac{1}{20} \]To add these fractions, find a common denominator, which is 60:
\[ \text{Combined work rate} = \frac{4}{60} + \frac{3}{60} = \frac{4+3}{60} = \frac{7}{60} \]So, K and L together complete \( \frac{7}{60} \) of the work in one day.
They work together for 5 days. The total work done in 5 days is:
\[ \text{Work done in 5 days} = 5 \times \frac{7}{60} = \frac{35}{60} \]This fraction can be simplified by dividing both numerator and denominator by 5:
\[ \text{Work done in 5 days} = \frac{35 \div 5}{60 \div 5} = \frac{7}{12} \]So, \( \frac{7}{12} \) of the work is completed.
The total work is considered as 1. The unfinished portion is the total work minus the work completed:
\[ \text{Unfinished portion} = 1 - \frac{7}{12} \] \[ \text{Unfinished portion} = \frac{12}{12} - \frac{7}{12} = \frac{12-7}{12} = \frac{5}{12} \]Correct Option: B) \( \frac{5}{12} \)
The question presents an analogy where a rank is associated with a specific branch of the armed forces. We need to identify the equivalent highest rank in the Indian Air Force that corresponds to an 'Admiral' in the Navy.
B) Air Chief Marshal — An Air Chief Marshal is the highest operational rank in the Indian Air Force, equivalent to an Admiral in the Indian Navy and a General in the Indian Army. The Chief of the Air Staff holds the rank of Air Chief Marshal.
The question asks for an overall assessment of the present level of the stock market index. This implies knowing the current value or at least its relation to significant historical values. We need to determine which statements, individually or in combination, provide enough information to make such an assessment.
B) Both statements I and III are sufficient
Statement I indicates that the current index is below the 3-year lowest point. Statement III provides the exact value of that 3-year lowest point (27,125). Together, they allow us to conclude that the current stock market index is below 27,125, which is a clear overall assessment of its present level.