This question tests knowledge of significant mergers in the Indian banking sector. Specifically, it asks about the merger of Dena Bank and Vijaya Bank in 2019. Recalling the major banking consolidations that took place around that period is key to answering this question.
Correct Option: D) Bank of Baroda
To solve this problem, we first need to determine the speed of the train using the given distance and time. Once the speed is known, we can use it to calculate the time required to cover the new distance.
Given:
The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]Substitute the given values:
\[ \text{Speed} = \frac{35 \text{ km}}{60 \text{ min}} \]This means the train covers 35 km in 60 minutes.
We need to find the time (\(T_2\)) to cover a new distance (\(D_2\)) = 105 km. Since the speed of the train remains constant, we can set up a proportion or use the speed calculated.
Using proportionality:
If 35 km is covered in 60 min, then 1 km is covered in \(\frac{60}{35}\) min.
So, 105 km will be covered in:
\[ T_2 = \frac{60 \text{ min}}{35 \text{ km}} \times 105 \text{ km} \] \[ T_2 = \frac{60 \times 105}{35} \text{ min} \]Simplify the expression:
\[ T_2 = \frac{60 \times (3 \times 35)}{35} \text{ min} \] \[ T_2 = 60 \times 3 \text{ min} \] \[ T_2 = 180 \text{ min} \]The value of \(\left\{\left(2-\frac{1}{3}\right)+\left(\frac{2}{3}\times1\frac{1}{5}\right)\right\}+\frac{3}{5}\times2\frac{5}{7}\) is:
4 \( \frac{2}{27} \)
4 \( \frac{2}{21} \)
2 \( \frac{4}{21} \)
2 \( \frac{4}{27} \)
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS). First, we will simplify the terms inside the parentheses, then perform multiplication, and finally addition. Mixed fractions will be converted to improper fractions for easier calculation.
\[1\frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}\]
\[2\frac{5}{7} = \frac{2 \times 7 + 5}{7} = \frac{14 + 5}{7} = \frac{19}{7}\]
\[2 - \frac{1}{3} = \frac{2 \times 3 - 1}{3} = \frac{6 - 1}{3} = \frac{5}{3}\]
\[\frac{2}{3} \times 1\frac{1}{5} = \frac{2}{3} \times \frac{6}{5} = \frac{12}{15} = \frac{4}{5}\]
The expression becomes: \[\left\{\frac{5}{3} + \frac{4}{5}\right\} + \frac{3}{5} \times \frac{19}{7}\]
Find a common denominator for \(\frac{5}{3}\) and \(\frac{4}{5}\), which is 15:
\[\frac{5}{3} + \frac{4}{5} = \frac{5 \times 5}{3 \times 5} + \frac{4 \times 3}{5 \times 3} = \frac{25}{15} + \frac{12}{15} = \frac{25 + 12}{15} = \frac{37}{15}\]
\[\frac{3}{5} \times 2\frac{5}{7} = \frac{3}{5} \times \frac{19}{7} = \frac{3 \times 19}{5 \times 7} = \frac{57}{35}\]
The expression is now: \[\frac{37}{15} + \frac{57}{35}\]
Find the least common multiple (LCM) of 15 and 35. The prime factorization of 15 is \(3 \times 5\), and for 35 is \(5 \times 7\). So, LCM(15, 35) = \(3 \times 5 \times 7 = 105\).
\[\frac{37}{15} = \frac{37 \times 7}{15 \times 7} = \frac{259}{105}\]
\[\frac{57}{35} = \frac{57 \times 3}{35 \times 3} = \frac{171}{105}\]
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 \(\frac{86}{21}\) to a mixed number:
\(86 \div 21 = 4\) with a remainder of \(86 - (21 \times 4) = 86 - 84 = 2\).
So, \[\frac{86}{21} = 4\frac{2}{21}\]
Correct Option: B) \(4 \frac{2}{21}\)
The question asks to identify which part of the human body the Pons belongs to. This requires basic knowledge of human anatomy, specifically the major organs and their subdivisions.
C) brain — The Pons is a major structure in the brainstem, which is part of the hindbrain. It serves as a relay station between different parts of the brain and plays a critical role in various involuntary functions.
The question asks to identify the institution that introduced the Udyam Abhilasha Program. This requires knowledge of various financial institutions in India and their specific initiatives, particularly those related to entrepreneurship and small businesses.
D) SIDBI — The Small Industries Development Bank of India (SIDBI) launched the 'Udyam Abhilasha' program in 2018. This national-level entrepreneurship awareness campaign aimed to provide entrepreneurship training to aspiring youth in rural areas, encouraging them to set up their own businesses.
A cylinder has 14 cm height and 660 cm² curved surface area. The volume of the cylinder is: (Take π = \( \frac{22}{7} \))
To find the volume of the cylinder, we first need to determine its radius. We are given the height and the curved surface area. Using the formula for the curved surface area, we can calculate the radius. Once the radius is known, we can use the formula for the volume of a cylinder to find the answer.
The formula for the curved surface area of a cylinder is:
\[ \text{CSA} = 2 \pi r h \]Substitute the given values into the CSA formula:
\[ 660 = 2 \times \frac{22}{7} \times r \times 14 \]\[ 660 = 2 \times 22 \times r \times \frac{14}{7} \]\[ 660 = 2 \times 22 \times r \times 2 \]\[ 660 = 88 r \]\[ r = \frac{660}{88} \]Divide both numerator and denominator by 4:\[ r = \frac{165}{22} \]Divide both numerator and denominator by 11:\[ r = \frac{15}{2} \]\[ r = 7.5 \text{ cm} \]The formula for the volume of a cylinder is:
\[ V = \pi r^2 h \]Substitute the calculated radius and given height into the volume formula:
\[ V = \frac{22}{7} \times \left(\frac{15}{2}\right)^2 \times 14 \]\[ V = \frac{22}{7} \times \frac{225}{4} \times 14 \]\[ V = 22 \times \frac{225}{4} \times \frac{14}{7} \]\[ V = 22 \times \frac{225}{4} \times 2 \]\[ V = 22 \times \frac{225}{2} \]\[ V = 11 \times 225 \]\[ V = 2475 \text{ cm}^3 \]Correct Option: A) 2475 cm3
Raj is 60% more efficient than Sundar and Sundar can finish a certain task in 16 days. How many days will Raj alone take to complete the same task?
This problem involves the concept of work and time, specifically efficiency. We are given the efficiency of Raj relative to Sundar and the time Sundar takes to complete a task. We need to find the time Raj takes. The key idea is that efficiency is inversely proportional to the time taken to complete a task.
If Sundar's efficiency is \(E_S\), then Raj's efficiency \(E_R\) is \(60\%\) more than \(E_S\).
\[ E_R = E_S + 0.60 \times E_S = 1.60 \times E_S \]So, Raj's efficiency is 1.6 times Sundar's efficiency.
Efficiency is inversely proportional to the time taken to complete a task. This means if someone is more efficient, they take less time.
\[ \text{Efficiency} \propto \frac{1}{\text{Time}} \]Therefore, the ratio of efficiencies is inversely proportional to the ratio of times taken:
\[ \frac{E_R}{E_S} = \frac{T_S}{T_R} \]Where \(T_S\) is the time taken by Sundar and \(T_R\) is the time taken by Raj.
We know \(E_R = 1.6 E_S\) and \(T_S = 16\) days.
\[ \frac{1.6 E_S}{E_S} = \frac{16}{T_R} \] \[ 1.6 = \frac{16}{T_R} \]Now, solve for \(T_R\):
\[ T_R = \frac{16}{1.6} \] \[ T_R = \frac{160}{16} \] \[ T_R = 10 \text{ days} \]Correct Option: B) 10
To find Ravi's salary, we first need to calculate 20% of Mohan's salary and then add this amount to Mohan's original salary. This will give us Ravi's salary, which is 20% more than Mohan's.
Identify Mohan's salary:
Mohan's salary \( = \text{₹}1,600 \)
Calculate 20% of Mohan's salary:
Percentage increase \( = 20\% \)
Amount of increase \( = 20\% \text{ of } \text{₹}1,600 \)
\[ = \frac{20}{100} \times 1,600 \]\[ = 20 \times 16 \]\[ = \text{₹}320 \]Calculate Ravi's salary:
Ravi's salary \( = \text{Mohan's salary} + \text{Amount of increase} \)
\[ = \text{₹}1,600 + \text{₹}320 \]\[ = \text{₹}1,920 \]Alternatively, we can directly calculate Ravi's salary as \(100\% + 20\% = 120\%\) of Mohan's salary:
\[ \text{Ravi's salary} = 120\% \text{ of } \text{₹}1,600 \]\[ = \frac{120}{100} \times 1,600 \]\[ = 12 \times 160 \]\[ = \text{₹}1,920 \]B) ₹1,920 is the correct answer, as calculated above.
Which rank was given by EIU Global Democracy Index to India for the year 2019?
The question asks for India's rank in the EIU Global Democracy Index for the year 2019. This requires knowledge of specific reports and their findings related to global indices.
Correct Option: A) 51st — India was ranked 51st in the EIU Global Democracy Index for the year 2019, marking a significant drop from its previous position.
The value of (3 \( \frac{1}{7} \) + 4 \( \frac{3}{7} \)) + \( \frac{7}{6} \) is:
\( \frac{432}{42} \)
\( \frac{367}{42} \)
\( \frac{267}{42} \)
\( \frac{342}{42} \)
To solve this problem, we need to add mixed fractions and a proper fraction. The key steps involve converting mixed fractions to improper fractions, finding a common denominator for all fractions, adding the numerators, and simplifying the result if possible.
The given expression is \[\left(3 \frac{1}{7} + 4 \frac{3}{7}\right) + \frac{7}{6}\].
First, convert \(3 \frac{1}{7}\) to an improper fraction:
\[ 3 \frac{1}{7} = \frac{(3 \times 7) + 1}{7} = \frac{21 + 1}{7} = \frac{22}{7} \]Next, convert \(4 \frac{3}{7}\) to an improper fraction:
\[ 4 \frac{3}{7} = \frac{(4 \times 7) + 3}{7} = \frac{28 + 3}{7} = \frac{31}{7} \]Now, substitute these back into the expression:
\[ \left(\frac{22}{7} + \frac{31}{7}\right) + \frac{7}{6} \]Since the fractions inside the parenthesis have the same denominator, add their numerators:
\[ \frac{22}{7} + \frac{31}{7} = \frac{22 + 31}{7} = \frac{53}{7} \]The expression becomes:
\[ \frac{53}{7} + \frac{7}{6} \]The denominators are 7 and 6. The least common multiple (LCM) of 7 and 6 is \(7 \times 6 = 42\).
For \( \frac{53}{7} \): Multiply the numerator and denominator by 6.
\[ \frac{53}{7} = \frac{53 \times 6}{7 \times 6} = \frac{318}{42} \]For \( \frac{7}{6} \): Multiply the numerator and denominator by 7.
\[ \frac{7}{6} = \frac{7 \times 7}{6 \times 7} = \frac{49}{42} \]Now, add the fractions with the common denominator:
\[ \frac{318}{42} + \frac{49}{42} = \frac{318 + 49}{42} = \frac{367}{42} \]The fraction \( \frac{367}{42} \) cannot be simplified further because 367 is a prime number and not divisible by 2, 3, 7, or any factor of 42.
B) \( \frac{367}{42} \) is the correct answer, as derived from the step-by-step calculation.