The question asks to identify the host city of the 2012 Summer Olympics. This requires knowledge of major international sporting events and their venues.
Correct Option: A) London
The 2012 Summer Olympics, officially known as the Games of the XXX Olympiad, were held in London, United Kingdom, from 27 July to 12 August 2012. This marked the third time London had hosted the Olympic Games, making it the first city to officially host the modern Games three times.
Evaluate:
\(\left\{\left(2-\frac{1}{3}\right)+\left(\frac{2}{3}\times1\frac{1}{5}\right)\right\}+\frac{3}{5}\times2\frac{5}{7}\)
2 \( \frac{4}{27} \)
4 \( \frac{2}{27} \)
2 \( \frac{4}{21} \)
4 \( \frac{2}{21} \)
To evaluate the given expression, we will follow the order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division/Multiplication (from left to right), Addition/Subtraction (from left to right). We will first simplify the terms inside the curly braces and then perform the remaining operations.
The expression is:
\[ \left\{\left(2-\frac{1}{3}\right)+\left(\frac{2}{3}\times1\frac{1}{5}\right)\right\}+\frac{3}{5}\times2\frac{5}{7} \]Convert mixed fractions:
\[ 1\frac{1}{5} = \frac{1\times5+1}{5} = \frac{6}{5} \]and
\[ 2\frac{5}{7} = \frac{2\times7+5}{7} = \frac{14+5}{7} = \frac{19}{7} \]Substitute these back into the expression:
\[ \left\{\left(2-\frac{1}{3}\right)+\left(\frac{2}{3}\times\frac{6}{5}\right)\right\}+\frac{3}{5}\times\frac{19}{7} \]First, evaluate \(2 - \frac{1}{3}\):
\[ 2 - \frac{1}{3} = \frac{2\times3 - 1}{3} = \frac{6-1}{3} = \frac{5}{3} \]Next, evaluate \[\frac{2}{3} \times \frac{6}{5}\]:
\[ \frac{2}{3} \times \frac{6}{5} = \frac{2\times6}{3\times5} = \frac{12}{15} = \frac{4}{5} \]The expression inside the curly braces becomes:
\[ \left\{\frac{5}{3} + \frac{4}{5}\right\} \]Find a common denominator for \( \frac{5}{3} \) and \( \frac{4}{5} \), which is \(3 \times 5 = 15\):
\[ \frac{5}{3} + \frac{4}{5} = \frac{5\times5}{3\times5} + \frac{4\times3}{5\times3} = \frac{25}{15} + \frac{12}{15} = \frac{25+12}{15} = \frac{37}{15} \]Now, evaluate \[\frac{3}{5} \times \frac{19}{7}\]:
\[ \frac{3}{5} \times \frac{19}{7} = \frac{3\times19}{5\times7} = \frac{57}{35} \]The full expression is now:
\[ \frac{37}{15} + \frac{57}{35} \]Find a common denominator for \(15\) and \(35\). The least common multiple (LCM) of \(15\) and \(35\) is \(105\).
\[ 15 = 3 \times 5 \]\[ 35 = 5 \times 7 \]
\[ \text{LCM}(15, 35) = 3 \times 5 \times 7 = 105 \]
Convert the fractions:
\[ \frac{37}{15} = \frac{37 \times 7}{15 \times 7} = \frac{259}{105} \]\[ \frac{57}{35} = \frac{57 \times 3}{35 \times 3} = \frac{171}{105} \]
Add them:
\[ \frac{259}{105} + \frac{171}{105} = \frac{259+171}{105} = \frac{430}{105} \]Both \(430\) and \(105\) are divisible by \(5\):
\[ \frac{430 \div 5}{105 \div 5} = \frac{86}{21} \]Convert the improper fraction \( \frac{86}{21} \) to a mixed number:
\[ 86 \div 21 = 4 \text{ with a remainder of } 2 \]So, \[\frac{86}{21} = 4\frac{2}{21}\].
D) \(4\frac{2}{21}\) is the correct evaluation of the expression.
The question asks to identify the place associated with Gautam Buddha from the given options. This requires knowledge of the historical and geographical context of Buddha's life.
Gautam Buddha, the founder of Buddhism, was born in Lumbini. This place is located in present-day Nepal and is a significant pilgrimage site for Buddhists.
D) Lumbini — Lumbini is widely recognized as the birthplace of Siddhartha Gautama, who later became Gautam Buddha. It is one of the most sacred places for Buddhists worldwide.
The question asks to identify the European country that does not have the Alps mountain range within its geographical boundaries. This requires knowledge of the geography of Europe and the distribution of the Alps.
Correct Option: C) Belgium
Evaluate:
18[4 − 3{6 − (8 × \( \frac{1}{2} \))}]
To evaluate the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS (Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). We will start by solving the innermost brackets and work our way outwards.
First, evaluate the expression inside the innermost parentheses:
\[ (8 \times \frac{1}{2}) \]\[ = \frac{8}{2} \]\[ = 4 \]Substitute this value back into the expression:
\[ 18[4 - 3\{6 - 4\}] \]Next, evaluate the expression inside the curly braces:
\[ \{6 - 4\} \]\[ = 2 \]Substitute this value back into the expression:
\[ 18[4 - 3 \times 2] \]Now, perform the multiplication inside the square brackets:
\[ 3 \times 2 \]\[ = 6 \]Substitute this value back into the expression:
\[ 18[4 - 6] \]Evaluate the expression inside the square brackets:
\[ 4 - 6 \]\[ = -2 \]Finally, perform the multiplication:
\[ 18 \times (-2) \]\[ = -36 \]Correct Option: B) -36
This question asks us to identify implicit assumptions in a given statement. An implicit assumption is something that is taken for granted or presupposed by the speaker when making the statement. We need to analyze the statement and each assumption to see if the statement necessarily relies on that assumption being true.
As analyzed above, the statement only suggests that moral education should be compulsory at the primary level. It does not preclude the possibility or necessity of moral education for older children or at other stages of life. Therefore, neither of the given assumptions is implicit in the statement.
The question asks for the location of the headquarters of the Forest Survey of India (FSI). This is a factual question requiring knowledge of the administrative structure of India's environmental and forest organizations.
Correct Option: B) Dehradun
The question asks to identify the Indian state that does not share a border with Bhutan. This requires knowledge of the geographical boundaries of Bhutan with respect to Indian states.
Correct Option: D) Odisha does not share its boundary with Bhutan. It is located on the eastern coast of India, far from Bhutan's borders.
To find the youngest person, we need to establish the relative ages of A, B, C, and D based on the given statements. We will use inequalities to represent the age relationships and then combine them to determine the order from oldest to youngest.
Statement 1: A is older than B.
This can be written as: \(A > B\)
Statement 2: D is younger than B.
This can be written as: \(D < B\)
Statement 3: C is older than D but younger than B.
This implies two relationships:
Combining these, we get: \(D < C < B\)
Combine all relationships:
From step 1, we have \(A > B\).
From step 3, we have \(D < C < B\).
Putting these together, we get the complete order from oldest to youngest:
\(A > B > C > D\)
Identify the youngest:
From the combined order \(A > B > C > D\), D is the youngest.
Correct Option: B) D
The question asks to identify which of the given options was NOT a part of the revolutionary movement for Indian Independence. This requires knowledge of various revolutionary organizations and their roles during the freedom struggle.
B) Young Party
The term "Young Party" is not recognized as a specific revolutionary organization or movement that played a significant role in the Indian Independence struggle. While there were youth wings or younger members within various parties, a distinct entity named "Young Party" with revolutionary aims is not historically documented in this context.