The question asks for the approximate altitude of the International Space Station (ISS) above Earth's surface. This is a factual question related to space science and general knowledge, often tested in competitive exams.
Correct Option: C) 400 km
The International Space Station (ISS) orbits at an average altitude of approximately 400 km above the Earth's surface. This is a well-known fact about the ISS and its orbital parameters.
To find the smaller of the two numbers, we first represent the numbers using the given ratio and a common multiplier. Then, we use their product to form an equation and solve for the multiplier. Finally, we substitute the multiplier back into the expressions for the numbers to find their actual values and identify the smaller one.
Correct Option: C) 24 is the smaller of the two numbers.
Select the Venn diagram that best represents the relationship between man, smokers and cricketers.
To determine the correct Venn diagram, we need to understand the relationship between the categories: man, smokers, and cricketers. Some men can be smokers, some can be cricketers, and some can be both.
Correct Option: A) The diagram with concentric circles correctly represents the relationship where all cricketers are smokers and all smokers are men.
To find the initial number, we need to set up an algebraic equation based on the operations performed by Atul and Pratul. Let the initial number be \(x\). We will translate their actions into mathematical expressions and then equate them to solve for \(x\).
Correct Option: A) 8 — As derived from the algebraic equation, the initial number is 8.
The question asks to identify the type of data storage device a hard disk is. We need to understand the different categories of computer storage and classify the hard disk accordingly.
C) Secondary storage — A hard disk drive (HDD) is a non-volatile storage device that stores digitally encoded data on rapidly rotating platters with magnetic surfaces. It is used for permanent storage of data and programs, making it a classic example of secondary storage.
The question asks to identify the state associated with the dance form 'Kathakali' based on the analogy provided. The analogy establishes a relationship between a dance form and its originating state. We need to apply the same relationship to the second pair.
C) Kerala is the correct answer because Kathakali is a classical dance form that originated in and is primarily associated with the state of Kerala.
If \(\frac{121}{0.121}=\frac{12.1}{x}\), then the value of x will be:
The problem requires us to solve for the unknown variable \(x\) in a given equation involving fractions and decimals. We will simplify the fractions by converting decimals to powers of 10 and then cross-multiply to find the value of \(x\).
The given equation is:
\[ \frac{121}{0.121} = \frac{12.1}{x} \]The decimal \(0.121\) can be written as \(\frac{121}{1000}\). So, the left side becomes:
\[ \frac{121}{0.121} = \frac{121}{\frac{121}{1000}} \]When dividing by a fraction, we multiply by its reciprocal:
\[ \frac{121}{\frac{121}{1000}} = 121 \times \frac{1000}{121} = 1000 \]Now the equation becomes:
\[ 1000 = \frac{12.1}{x} \]To find \(x\), we can rearrange the equation:
\[ x = \frac{12.1}{1000} \]Dividing \(12.1\) by \(1000\) means moving the decimal point three places to the left:
\[ x = 0.0121 \]A) The calculated value of \(x\) is \(0.0121\), which matches option A.
The question asks about the primary connection of a modem. A modem's fundamental function is to modulate and demodulate signals, primarily for transmitting digital data over analog lines. Understanding this function helps identify its core connection.
Correct Option: C) A modem is connected to a phone line. This connection allows the modem to convert digital data from a computer into analog signals for transmission over the telephone network and to convert incoming analog signals back into digital data for the computer.
Simplify the following. \(\frac{289\times289\times289+111\times111\times111}{289\times289-289\times111+111\times111}\)
This problem involves simplifying an algebraic expression that resembles the sum of cubes formula. By recognizing the pattern and applying the formula \(a^3 + b^3 = (a+b)(a^2 - ab + b^2)\), the expression can be significantly simplified.
Identify the structure of the given expression:
\[\frac{289\times289\times289+111\times111\times111}{289\times289-289\times111+111\times111}\]Let \(a = 289\) and \(b = 111\). Substitute these values into the expression:
\[\frac{a\times a\times a + b\times b\times b}{a\times a - a\times b + b\times b} = \frac{a^3 + b^3}{a^2 - ab + b^2}\]Recall the algebraic identity for the sum of cubes:
\[a^3 + b^3 = (a+b)(a^2 - ab + b^2)\]Substitute this identity into the expression:
\[\frac{(a+b)(a^2 - ab + b^2)}{a^2 - ab + b^2}\]Since \(a^2 - ab + b^2\) is present in both the numerator and the denominator, and it is not zero (as \(a\) and \(b\) are positive numbers), we can cancel out this term:
\[a+b\]Now, substitute the original values of \(a\) and \(b\) back into the simplified expression:
\[a+b = 289 + 111\]Perform the addition:
\[289 + 111 = 400\]A) The simplified value of the expression is 400.
The question asks to identify the technology company that launched helicopter services in New York in October 2019. This is a factual question related to current affairs and business expansions of major tech companies.
Correct Option: D) Uber