Which of the following fractions is the smallest?
\( \frac{7}{8} \)
\( \frac{7}{10} \)
\( \frac{5}{7} \)
\( \frac{3}{4} \)
To find the smallest fraction among the given options, we can convert each fraction into a decimal or find a common denominator to compare them. Converting to decimals is often the most straightforward method for comparison.
Comparing these values, \( 0.7 \) is the smallest decimal.
B) \( \frac{7}{10} \)
As calculated, \( \frac{7}{10} = 0.7 \), which is the smallest value among all the options.
The rectangle represents a set of calculations that are common across all the given equations. Identify the calculations involved and solve the fourth equation on the same basis:
7 â–¬ 4 = \( \frac{27}{4} \)
6 â–¬ 1 = 5
4 â–¬ 3 = \( \frac{11}{3} \)
a â–¬ b = ?
\(\frac{ab}{a+b}\)
\(\frac{ab+1}{a}\)
\(\frac{a-b}{ab}\)
\(\frac{ab-1}{b}\)
The problem presents a set of equations with a common, hidden calculation represented by the symbol 'â–¬'. We need to identify this calculation by analyzing the given examples and then apply it to solve the fourth equation.
D) \(\frac{ab-1}{b}\) is the correct expression that represents the common calculation.
When were the words 'Socialist, Secular and Democratic Republic' added in the Indian Constitution?
In the 44th amendment in 1978
In the 42nd amendment in 1976
In the 42nd amendment in 1985
In the 35th amendment in 1974
The question asks about the specific amendment and year when the words 'Socialist, Secular and Democratic Republic' were added to the Indian Constitution. This is a factual question related to constitutional amendments.
Correct Option: B) In the 42 nd amendment in 1976
The words 'Socialist' and 'Secular' were added to the Preamble of the Indian Constitution by the 42nd Constitutional Amendment Act, 1976. The word 'Democratic Republic' was already part of the original Preamble, but the question implies the addition of the entire phrase 'Socialist, Secular and Democratic Republic' where 'Socialist' and 'Secular' were the new additions, modifying the existing 'Democratic Republic'.
This question asks about the range of frequencies of sound waves that humans can typically hear. This range is a fundamental concept in physics, specifically in the study of sound and acoustics.
D) have the frequency range between 20 Hz to 20000 Hz
This option correctly states the full range of frequencies that the average human ear can detect. Frequencies below 20 Hz are known as infrasound, and frequencies above 20,000 Hz are known as ultrasound. Humans cannot typically hear either infrasound or ultrasound.
The question asks to identify the largest country in Europe by land area. This requires knowledge of the geographical sizes of European countries.
Here are the approximate land areas for the countries mentioned:
Comparing these figures, Russia's European part alone is significantly larger than any other country listed, and indeed, larger than any other country entirely within Europe.
D) Russia is the largest country in Europe by land area. Its European territory covers approximately \(3,972,400 \text{ km}^2\), which is by far the largest among all European nations.
The question asks for the inspiration behind the temperature-regulated green homes built at IIT Kanpur in 2012. This requires knowledge of the specific project and its underlying design philosophy.
Correct Option: D) Cocoon structure — The IIT Kanpur project for temperature-regulated green homes, initiated in 2012, was specifically inspired by and named after the concept of a "cocoon structure." This design principle aims to create a highly insulated and thermally stable building envelope, much like a natural cocoon protects its inhabitant from external temperature fluctuations. The project focused on achieving thermal comfort with minimal energy use by adopting this biomimetic approach.
Find the value of 4 × {\(\frac{2.4}{0.9}\) × \(\frac{0.27}{0.08}\ ×\frac{0.50}{0.05}\)}.
The problem requires us to simplify an expression involving multiplication of decimals. The key is to convert the decimals into fractions to simplify the calculations, or to carefully handle the decimal points during multiplication and division.
First, let's simplify each fraction inside the curly braces separately.
First term: \(\frac{2.4}{0.9}\)
To remove the decimals, multiply the numerator and denominator by 10:
\[ \frac{2.4 \times 10}{0.9 \times 10} = \frac{24}{9} \]Second term: \(\frac{0.27}{0.08}\)
To remove the decimals, multiply the numerator and denominator by 100:
\[ \frac{0.27 \times 100}{0.08 \times 100} = \frac{27}{8} \]Third term: \(\frac{0.50}{0.05}\)
To remove the decimals, multiply the numerator and denominator by 100:
\[ \frac{0.50 \times 100}{0.05 \times 100} = \frac{50}{5} \]Now, substitute these simplified fractions back into the expression:
\[ 4 \times \left( \frac{24}{9} \times \frac{27}{8} \times \frac{50}{5} \right) \]Simplify the fractions where possible:
The expression becomes:
\[ 4 \times \left( \frac{8}{3} \times \frac{27}{8} \times 10 \right) \]Now, perform the multiplication inside the parentheses. Notice that 8 in the numerator of the first term and 8 in the denominator of the second term cancel out. Also, 3 in the denominator of the first term and 27 in the numerator of the second term can be simplified (\(27 \div 3 = 9\)).
\[ 4 \times \left( \frac{\cancel{8}}{3} \times \frac{27}{\cancel{8}} \times 10 \right) \]\[ 4 \times \left( \frac{1}{3} \times 27 \times 10 \right) \]\[ 4 \times \left( \frac{27}{3} \times 10 \right) \]\[ 4 \times \left( 9 \times 10 \right) \]Finally, perform the remaining multiplication:
\[ 4 \times 90 = 360 \]Correct Option: C) 360
The question asks to identify the Indian states that share a border with Bangladesh. This requires knowledge of India's political geography, specifically the borders of its northeastern states.
D) West Bengal, Assam, Meghalaya, Tripura, Mizoram
This option correctly lists all five Indian states that share a border with Bangladesh. These states form a significant part of India's eastern frontier.
The question asks for the headquarters of the Geological Survey of India (GSI). This is a factual question requiring knowledge of the locations of prominent government organizations in India.
A) Kolkata is the correct answer. The headquarters of the Geological Survey of India is located in Kolkata, West Bengal.
The question asks for the definition of peripheral devices. We need to identify the option that best describes these devices in the context of computer systems.
Correct Option: C) These are internal or external device that connect directly to a computer but do not contribute to the computer's primary functions
This option accurately defines peripheral devices. Peripherals can be internal (e.g., an internal modem or sound card) or external (e.g., keyboard, mouse, printer, scanner). They connect to the computer and enhance its functionality, but the computer can still perform its primary operations (like booting up and running basic software) without them. For example, a computer can function without a printer, but a printer cannot function without a computer.