To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
First, calculate the value inside the parentheses \((3 - 7)\).
\[ 3 - 7 = -4 \]The expression becomes:
\[ 20 \div [\{2 \times (-4)\} - 15 + 25] \]Next, perform the multiplication \(2 \times (-4)\).
\[ 2 \times (-4) = -8 \]The expression now is:
\[ 20 \div [-8 - 15 + 25] \]First, perform the subtraction \(-8 - 15\).
\[ -8 - 15 = -23 \]Then, perform the addition \(-23 + 25\).
\[ -23 + 25 = 2 \]The expression simplifies to:
\[ 20 \div 2 \] \[ 20 \div 2 = 10 \]Correct Option: C) 10
The question asks to identify the name of the mobile app launched by the Road Transport and Highways Minister, Nitin Gadkari, for highway users to access information. This is a factual recall question related to current affairs and government initiatives.
Correct Option: D) Sukhad Yatra
The "Sukhad Yatra" mobile app was launched by the National Highways Authority of India (NHAI) to provide information to highway users regarding road conditions, toll plazas, and other facilities, thereby enhancing their travel experience. This aligns with the description in the question.
This is a blood relation problem. We need to break down the statement "daughter-in-law of his mother’s only son" into smaller parts to identify the relationship between Raju and the girl.
Correct Option: C) Father-in-law
The problem asks for the work done in moving a mass up a slope. This work is done against gravity. We are given the gravitational potential difference per unit mass, which is equivalent to the change in gravitational potential energy per unit mass. We can use this to find the effective gravitational acceleration or directly calculate the change in potential energy for the given height.
A) 11.1 J is the calculated work done.
To find the percentage of Nathan's 3-year salary that goes towards EMI, we need to calculate his total salary over 3 years and the total EMI paid over 3 years. Then, we can express the total EMI as a percentage of the total salary.
Calculate Nathan's annual income:
Nathan's monthly income is Rs. 50,000.
\[ \text{Annual Income} = \text{Monthly Income} \times 12 \text{ months} \]\[ \text{Annual Income} = 50,000 \times 12 = \text{Rs. } 6,00,000 \]Calculate Nathan's total salary over 3 years:
\[ \text{Total Salary (3 years)} = \text{Annual Income} \times 3 \text{ years} \]\[ \text{Total Salary (3 years)} = 6,00,000 \times 3 = \text{Rs. } 18,00,000 \]Calculate the total EMI paid over 3 years:
Nathan pays an annual EMI amount of Rs. 30,000.
\[ \text{Total EMI (3 years)} = \text{Annual EMI} \times 3 \text{ years} \]\[ \text{Total EMI (3 years)} = 30,000 \times 3 = \text{Rs. } 90,000 \]Calculate the percentage of his 3-year salary that goes towards EMI:
\[ \text{Percentage} = \left( \frac{\text{Total EMI (3 years)}}{\text{Total Salary (3 years)}} \right) \times 100 \% \]\[ \text{Percentage} = \left( \frac{90,000}{18,00,000} \right) \times 100 \% \]\[ \text{Percentage} = \left( \frac{9}{180} \right) \times 100 \% \]\[ \text{Percentage} = \left( \frac{1}{20} \right) \times 100 \% \]\[ \text{Percentage} = 5 \% \]Therefore, 5% of Nathan's 3-year salary goes towards the EMI.
C) 5 is the correct answer.
According to the US Chamber of Commerce, India ranked ________ out of 50 countries in the Intellectual Property Index (as of 2018).
The question asks for India's rank in the Intellectual Property Index (as of 2018) according to the US Chamber of Commerce. This is a factual recall question related to international reports and rankings.
Correct Option: D) 44th
India ranked 44th out of 50 countries in the 2018 Intellectual Property Index published by the US Chamber of Commerce's Global Innovation Policy Center (GIPC). This marked an improvement from its 2017 ranking of 43rd out of 45 countries, primarily due to legislative reforms and efforts to strengthen IP enforcement.
This problem involves work and time. We need to find the individual time taken by Yukta to paint the whole wall. We are given the combined time for Mrinal and Yukta to paint half a wall, and a relationship between their individual times to paint half a wall. We will use the concept that work rate is the reciprocal of the time taken to complete a job.
Let the time taken by Yukta to paint half of the wall be \(Y\) days.
According to the problem, Mrinal would need thrice as much time as Yukta to paint half of the wall. So, the time taken by Mrinal to paint half of the wall is \(3Y\) days.
The work rate is the reciprocal of the time taken. For painting half of the wall:
Mrinal and Yukta together can paint half of a wall in 6 days. Their combined rate for painting half a wall is \(\frac{1}{6}\) (half wall per day).
The sum of their individual rates equals their combined rate:
\[ \frac{1}{Y} + \frac{1}{3Y} = \frac{1}{6} \]Solve the equation for \(Y\):
\[ \frac{3}{3Y} + \frac{1}{3Y} = \frac{1}{6} \] \[ \frac{4}{3Y} = \frac{1}{6} \] \[ 3Y = 4 \times 6 \] \[ 3Y = 24 \] \[ Y = \frac{24}{3} \] \[ Y = 8 \text{ days} \]So, Yukta takes 8 days to paint half of the wall.
The question asks for the number of days Yukta alone can paint the whole wall. If Yukta takes 8 days to paint half the wall, she will take twice that time to paint the whole wall.
\[ \text{Time for whole wall} = 2 \times Y = 2 \times 8 = 16 \text{ days} \]D) 16 days. This is the time Yukta takes to paint the whole wall.
This is a direction-based reasoning question. In a standard chess seating arrangement, two players sit opposite each other. If one player is facing a certain direction, the opponent will be facing the exact opposite direction.
Correct Option: C) West
The question asks for the \((n+l)\) value for a 4p orbital. To solve this, we need to identify the principal quantum number (\(n\)) and the azimuthal quantum number (\(l\)) for a 4p orbital and then sum them up.
Therefore, the \((n+l)\) value for the 4p orbital is 5.
A) 5 is the correct answer because for a 4p orbital, \(n=4\) and \(l=1\), so \(n+l = 4+1 = 5\).
To find the next term in the series, we need to identify the pattern or rule governing the sequence of numbers. We will analyze the differences between consecutive terms to determine if there's an arithmetic progression or a more complex pattern.
The differences between consecutive terms are 9, 10, and 11. This shows a clear pattern where the difference increases by 1 each time.
Following this pattern, the next difference should be \(11 + 1 = 12\).
To find the next term, add the predicted difference (12) to the last given term (75).
\[ 75 + 12 = 87 \]A) 87 is the correct option because the pattern of differences between consecutive terms is an increasing sequence (9, 10, 11, ...), leading to the next term being \(75 + 12 = 87\).