Find the value of \(4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}\)
\( \frac{1}{8} \)
\( \frac{1}{4} \)
\( \frac{2}{9} \)
\( \frac{8}{3} \)
To solve this complex fraction, we will simplify it from the innermost part outwards. This involves performing addition and division operations step-by-step, working our way up the fraction until we reach the final subtraction.
Start with the innermost part of the fraction: \(2+\frac{1}{4}\).
\[ 2+\frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]Substitute this value back into the next level of the fraction: \[\frac{1}{2+\frac{1}{4}}\].
\[ \frac{1}{\frac{9}{4}} = \frac{4}{9} \]Now, consider the next part: \[3+\frac{1}{2+\frac{1}{4}}\].
\[ 3+\frac{4}{9} = \frac{27}{9} + \frac{4}{9} = \frac{31}{9} \]Next, evaluate \[\frac{1}{3+\frac{1}{2+\frac{1}{4}}}\].
\[ \frac{1}{\frac{31}{9}} = \frac{9}{31} \]Proceed to \[1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}\].
\[ 1+\frac{9}{31} = \frac{31}{31} + \frac{9}{31} = \frac{40}{31} \]Evaluate \[\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}\].
\[ \frac{5}{\frac{40}{31}} = 5 \times \frac{31}{40} = \frac{155}{40} = \frac{31}{8} \]Finally, perform the last subtraction: \[4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}\].
\[ 4 - \frac{31}{8} = \frac{32}{8} - \frac{31}{8} = \frac{1}{8} \]A) \( \frac{1}{8} \) is the correct result obtained after simplifying the complex fraction step-by-step.
This is a blood relation problem. We need to establish the relationships between the individuals mentioned in the problem statement to determine how Monica is related to Phoebe. We can use a family tree diagram or simply list the relationships to deduce the final connection.
Now, let's combine these facts:
B) Granddaughter — As established, Phoebe is the mother of Grace and Kathy. One of Grace's siblings is the parent of Chandler (and Monica). This makes Phoebe the grandmother of Chandler and Monica. Therefore, Monica is Phoebe's granddaughter.
The question asks for the establishment date of the United States Environmental Protection Agency (EPA). This is a factual recall question related to environmental history and governance. Knowing key dates for significant environmental organizations is important for competitive exams.
Correct Option: D) December 1970
The United States Environmental Protection Agency (EPA) was established on December 2, 1970, by an executive order from President Richard Nixon. This agency was created to consolidate various federal research, monitoring, standard-setting, and enforcement activities into one agency to ensure environmental protection.
The problem asks us to identify the number that does not fit the pattern in the given series. We need to analyze the relationship between consecutive terms to find the underlying rule and then check each term against this rule.
Let's examine the relationship between consecutive terms in the series: \(3, 7, 22, 89, 446, 2677, 18739\).
Consider the first two terms:
\[ 3 \times 2 + 1 = 7 \]Consider the second and third terms:
\[ 7 \times 3 + 1 = 22 \]Consider the third and fourth terms:
\[ 22 \times 4 + 1 = 88 + 1 = 89 \]From these steps, a pattern emerges: each term is obtained by multiplying the previous term by an increasing integer (starting from 2) and then adding 1. The general rule appears to be \(T_n = T_{n-1} \times n + 1\), where \(n\) is the multiplier for the \(n\)-th term (starting \(n=2\)). Let's verify this for the subsequent terms.
Using the pattern, the next term after 89 should be:
\[ 89 \times 5 + 1 = 445 + 1 = 446 \]This matches the given fifth term.
The next term after 446 should be:
\[ 446 \times 6 + 1 = 2676 + 1 = 2677 \]This matches the given sixth term.
The next term after 2677 should be:
\[ 2677 \times 7 + 1 = 18739 + 1 = 18740 \]However, the given seventh term is 18739. This means 18739 does not follow the established pattern.
B) 18739 — According to the pattern \(T_n = T_{n-1} \times n + 1\), the term after 2677 should be \(2677 \times 7 + 1 = 18740\). The given term is 18739, which is incorrect.
The question asks about the purpose of the Kumar Mangalam Birla Committee. This requires knowledge of significant committees and their mandates in the Indian economic and regulatory landscape. We need to identify the specific area this committee was tasked to investigate or provide recommendations on.
Correct Option: A) Corporate governance. The Kumar Mangalam Birla Committee was indeed set up by SEBI in 1999 to recommend measures to improve corporate governance standards in India. Its report was a landmark in the development of corporate governance norms in the country, leading to significant regulatory changes.
The question asks to identify the meaning of 'Jallikattu'. This requires knowledge of cultural practices and traditional sports in India, specifically Tamil Nadu.
Correct Option: D) A traditional bull-taming sport popular in Tamil Nadu
Jallikattu is indeed a traditional bull-taming sport that is very popular in the state of Tamil Nadu, India. It is typically celebrated as part of the Pongal harvest festival. Participants attempt to grab the hump of a bull and hold onto it for a certain distance or time. It is considered a cultural and religious event, though it has been a subject of controversy regarding animal welfare.
Study the given pattern carefully and select the letter that can replace the question mark (?) in it.
| N | R | V |
| Q | M | ? |
| P | T | X |
| O | K | G |
The problem presents a sequence of letters and asks us to find the missing letter. We need to identify the pattern or rule governing the sequence by analyzing the alphabetical positions of the given letters.
A) I is the correct option because following the identified pattern of \(-4\) for the second group, the letter after M (13) would be the 9th letter, which is I.
The question asks to identify the act in India that was based on the report of a committee headed by British Prime Minister Lord North. This requires knowledge of the historical context and origins of key British parliamentary acts related to India.
C) Regulating Act 1773
The Regulating Act of 1773 was indeed based on the report of a secret committee headed by the then British Prime Minister, Lord North. This act was a significant step towards parliamentary control over the East India Company's administration in India.
This is a coding-decoding problem where each letter is assigned a unique symbol. We need to identify the symbol for each letter in the target word 'NATIVE' by comparing the given coded words.
So, 'NATIVE' will be coded as '@ ! L % G *'.
Correct Option: C) @ ! L % G *
The question asks for the establishment year of the National Testing Agency (NTA). This is a factual question related to current affairs and institutional bodies in India. Recalling the correct year of its formation is key.
Correct Option: A) 2017 is the correct year when the National Testing Agency (NTA) was established.