Samar can cover \( \frac{3}{5} \)th of the distance covered by Swapnali in \( \frac{5}{7} \)th of the time taken by the latter. If Swapnali takes 42 minutes to complete the journey, how many minutes would it take Samar to cover the same distance?
This problem involves calculating the time taken by Samar to cover a certain distance, given information about Samar's and Swapnali's relative speeds and distances covered. We will use the fundamental relationship between distance, speed, and time: \(\text{Distance} = \text{Speed} \times \text{Time}\).
Let the total distance be \(D\) and the total time taken by Swapnali be \(T_S\).
We are given that Swapnali takes 42 minutes to complete the journey. So, \(T_S = 42\) minutes.
Let Swapnali's speed be \(V_S\). Then, for the total journey:
\[ D = V_S \times T_S \]\[ D = V_S \times 42 \quad \text{(Equation 1)} \]Now, let's consider Samar. Samar covers \(\frac{3}{5}\)th of the distance covered by Swapnali in \(\frac{5}{7}\)th of the time taken by Swapnali.
Distance covered by Samar (let's call it \(D_M\)) is:
\[ D_M = \frac{3}{5} \times D \]Time taken by Samar for this distance (let's call it \(T_M\)) is:
\[ T_M = \frac{5}{7} \times T_S \]\[ T_M = \frac{5}{7} \times 42 \]\[ T_M = 5 \times 6 \]\[ T_M = 30 \text{ minutes} \]Let Samar's speed be \(V_M\). For the distance \(D_M\) and time \(T_M\):
\[ D_M = V_M \times T_M \]\[ \frac{3}{5} D = V_M \times 30 \quad \text{(Equation 2)} \]We need to find the time Samar would take to cover the same distance \(D\). Let this time be \(T_{\text{Samar total}}\).
\[ D = V_M \times T_{\text{Samar total}} \quad \text{(Equation 3)} \]From Equation 2, we can express \(V_M\) in terms of \(D\):
\[ V_M = \frac{3D}{5 \times 30} \]\[ V_M = \frac{3D}{150} \]\[ V_M = \frac{D}{50} \]Now substitute this expression for \(V_M\) into Equation 3:
\[ D = \left(\frac{D}{50}\right) \times T_{\text{Samar total}} \]Divide both sides by \(D\) (assuming \(D \neq 0\)):
\[ 1 = \frac{1}{50} \times T_{\text{Samar total}} \]\[ T_{\text{Samar total}} = 50 \text{ minutes} \]D) 50 minutes. Samar would take 50 minutes to cover the same distance.
This question asks us to evaluate the strength of arguments related to encouraging electricity saving. We need to determine which argument provides a logical and strong reason to support or refute the statement: "Should people be encouraged to save electricity, since one unit of electricity saved is equal to two units produced?"
A) Only argument I is strong
Argument I directly supports the premise that saving electricity is beneficial and easier, which is a strong reason to encourage it, especially given the statement's efficiency ratio (1 unit saved = 2 units produced).
Who was honoured with the Indian Film Personality of 2017 Award at the 48th International Film Festival of India (IFFI)?
Shammi Kapoor
Akshay Kumar
Prabhas
Amitabh Bachchan
The question asks to identify the recipient of the Indian Film Personality of 2017 Award at the 48th International Film Festival of India (IFFI). This is a factual question requiring knowledge of specific awards and events in the Indian film industry.
Correct Option: D) Amitabh Bachchan was honoured with the Indian Film Personality of 2017 Award at the 48th International Film Festival of India (IFFI) for his immense contribution to Indian cinema.
The problem asks us to calculate the future population of a city given its current population and a constant annual growth rate. This is a compound growth problem, similar to compound interest calculations. We can use the formula for compound growth to find the population after a certain number of years.
The population after \(n\) years (\(P_n\)) can be calculated using the formula:
\[ P_n = P_0 \left(1 + \frac{r}{100}\right)^n \]In this case, since the rate is already given as a percentage, we can use \(r\) directly as a decimal (0.04).
\[ P_2 = 1,200,000 \times (1 + 0.04)^2 \]B) 1297920 is the correct population after 2 years, calculated using the compound growth formula.
The question asks to identify the country of origin of the famous football player Maradona. This requires general knowledge about prominent sports figures.
Correct Option: B) Diego Maradona was an iconic football player from Argentina.
30 – [29 – {28 – (25 – \(\overline{21 – 22}\))}] =?
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS). This means we evaluate expressions inside the innermost brackets first, starting with the vinculum (bar), then parentheses, curly braces, and finally square brackets.
The expression is \( \overline{21 - 22} \).
\[ 21 - 22 = -1 \]The expression becomes \( 25 - (-1) \).
\[ 25 - (-1) = 25 + 1 = 26 \]The expression is \( 28 - \{26\} \).
\[ 28 - 26 = 2 \]The expression is \( 29 - [2] \).
\[ 29 - 2 = 27 \]The final expression is \( 30 - 27 \).
\[ 30 - 27 = 3 \]Thus, the value of the entire expression is 3.
D) 3 is the correct answer, as derived from the step-by-step calculation.
The question asks about the scientist who introduced the system of scientific naming or nomenclature. This refers to the binomial nomenclature system, a fundamental concept in biology for classifying organisms.
Correct Option: A) Linnaeus
Carl Linnaeus (1707-1778), a Swedish botanist, zoologist, and physician, is widely regarded as the "father of modern taxonomy." He developed and formalized the modern system of naming organisms called binomial nomenclature. In this system, each species is given a unique two-part name: the first part is the genus name, and the second part is the specific epithet (species name). His seminal work, Systema Naturae, laid the foundation for modern biological classification.
The 14th Hockey World Cup will be held in which city of India in 2018?
The question asks for the host city of the 14th Hockey World Cup in 2018. This is a factual question related to major sporting events and their venues, which is common in general knowledge sections of competitive exams.
Correct Option: B) Bhubaneswar was the host city for the 14th Men's Hockey World Cup in 2018.
The question asks about the resistance offered by an insulator. To answer this, we need to understand the fundamental property of an insulator, which is its ability to resist the flow of electric current. This property is directly related to its electrical resistance.
Therefore, an insulator is characterized by its very high electrical resistance.
D) high — An insulator is defined by its property of opposing the flow of electric current. This opposition is quantified as electrical resistance. For current to be negligible or zero, the resistance must be very high.
At 6 % simple interest per annum a certain sum yields a total amount of Rs 3,228 at the end of 5\( \frac{3}{4} \) years. What was the sum invested?
This problem involves calculating the principal amount (sum invested) given the total amount, simple interest rate, and time period. We will use the formula for simple interest and the formula for the total amount.
The sum invested (Principal) was Rs 2,400.
Correct Option: D) Rs 2,400