The acceleration due to gravity (\(g\)) is determined by the mass and radius of the celestial body (like Earth) and the distance from its center. We need to identify which factor among the given options does not influence this value.
Correct Option: D) Mass of the object. The acceleration due to gravity is independent of the mass of the object experiencing the gravitational force.
Where was the 48th International Film Festival of India held in 2017?
The question asks for the location of the 48th International Film Festival of India (IFFI) in 2017. This is a factual question requiring knowledge of major cultural events in India.
Correct Option: D) Goa is the correct answer. The International Film Festival of India (IFFI) has been permanently held in Goa since 2004, making it the venue for the 48th edition in 2017 as well.
On which day is Major Dhyan Chand’s birthday celebrated as National Sports Day in India?
The question asks to identify the specific date on which Major Dhyan Chand's birthday is celebrated as National Sports Day in India. This requires knowledge of important national days and their associated personalities.
Correct Option: B) August 29 th
The problem provides information about four numbers arranged in ascending order and the averages of the smallest three and largest three numbers. We need to find the range of the data, which is the difference between the largest and smallest numbers.
Correct Option: B) 12
To solve this alphanumeric series, we need to analyze the pattern for both the numerical and alphabetical parts separately. We will look for a consistent mathematical operation or sequence in the numbers and a consistent shift in the letters of the alphabet.
Correct Option: A) 26U is the correct answer because the numerical part follows a pattern of adding consecutive odd numbers (3, 5, 7, 9...) and the alphabetical part follows a pattern of adding consecutive natural numbers to the letter's position (1, 2, 3, 4...).
Read the following question and decide which of the statements is/are sufficient to answer the question.
Find the value of ‘n’.
1. n2 – 20n + 100 = 0
2. n2 + x2 + y2 + 2 = 2n + 5
Only statement 2 is sufficient
Only statement 1 is sufficient
Neither statement 1 nor 2 is sufficient
Either statement 1 or 2 is sufficient
To determine if a statement is sufficient to find the value of 'n', we need to check if the statement leads to a unique value for 'n'. We will analyze each statement separately.
The given equation is \(n^2 - 20n + 100 = 0\).
This is a quadratic equation. We can solve it by factoring or using the quadratic formula. Notice that this equation is a perfect square trinomial:
\[ n^2 - 2 \cdot n \cdot 10 + 10^2 = 0 \]This simplifies to:
\[ (n - 10)^2 = 0 \]Taking the square root of both sides:
\[ n - 10 = 0 \]Solving for \(n\):
\[ n = 10 \]Since statement 1 yields a unique value for \(n\), it is sufficient to answer the question.
The given equation is \(n^2 + x^2 + y^2 + 2 = 2n + 5\).
Rearrange the terms to group variables:
\[ n^2 - 2n + x^2 + y^2 + 2 - 5 = 0 \] \[ n^2 - 2n + x^2 + y^2 - 3 = 0 \]This equation contains three variables: \(n\), \(x\), and \(y\). We have only one equation and three unknowns. We cannot find a unique value for \(n\) because \(x\) and \(y\) are unknown and can take various values. For example, if we try to complete the square for \(n\):
\[ (n^2 - 2n + 1) + x^2 + y^2 - 3 - 1 = 0 \] \[ (n - 1)^2 + x^2 + y^2 - 4 = 0 \] \[ (n - 1)^2 = 4 - x^2 - y^2 \]The value of \(n\) depends on the values of \(x\) and \(y\). Since \(x\) and \(y\) are not given, \(n\) cannot be determined uniquely. Therefore, statement 2 is not sufficient.
Based on the analysis, only statement 1 is sufficient to find the value of 'n'.
Correct Option: B) Only statement 1 is sufficient
This question asks us to identify which assumptions are implicit in the given statement. An implicit assumption is something that is not directly stated but must be true for the statement to make sense or be logically consistent. We need to evaluate each assumption based on the information provided in the statement.
B) Only assumption I is implicit
Assumption I is directly supported by the statement that he consumes "only healthy food." If he consumes only healthy food, he cannot consume junk food. Assumption II is not supported by the statement. The statement says he walks 4 km "every day," which includes weekends, and there's no information to suggest he walks more on weekends.
This problem involves calculating changes in average age. When one person is replaced by another, and the average age decreases, it means the new person's age is less than the person who left. We can calculate the total decrease in age and subtract it from the age of the girl who left to find the age of the new girl.
Since 1 year = 12 months, a decrease of 2 months is \(\frac{2}{12}\) years or \(\frac{1}{6}\) years.
The total decrease in the sum of ages is the number of girls multiplied by the decrease in average age.
\[ \text{Total decrease in age} = \text{Number of girls} \times \text{Decrease in average age} \] \[ \text{Total decrease in age} = 20 \times 2 \text{ months} = 40 \text{ months} \]Since 1 year = 12 months:
\[ 40 \text{ months} = 3 \times 12 \text{ months} + 4 \text{ months} = 3 \text{ years } 4 \text{ months} \]The age of the new girl will be the age of the girl who left minus the total decrease in age.
\[ \text{Age of new girl} = \text{Age of old girl} - \text{Total decrease in age} \] \[ \text{Age of new girl} = 18 \text{ years} - 3 \text{ years } 4 \text{ months} \]To subtract, we can borrow 1 year (12 months) from 18 years:
\[ \text{Age of new girl} = (17 \text{ years } 12 \text{ months}) - (3 \text{ years } 4 \text{ months}) \] \[ \text{Age of new girl} = (17 - 3) \text{ years } (12 - 4) \text{ months} \] \[ \text{Age of new girl} = 14 \text{ years } 8 \text{ months} \]Correct Option: D) The age of the new girl is 14 years 8 months.
The question asks to identify the oldest public-sector bank in India among the given options. This requires knowledge of the establishment dates of major Indian banks.
Correct Option: B) Allahabad Bank was established in 1865, making it the oldest public-sector bank in India among the choices provided. It was one of the 14 major banks nationalized by the Government of India in 1969. In 2020, it was merged with Indian Bank.
\(\frac{1120}{\sqrt{x}}\) = 80 then x =?
To solve for \(x\), we need to isolate \(\sqrt{x}\) first and then square both sides of the equation to find \(x\).
Multiply both sides by \(\sqrt{x}\):
\[ 1120 = 80 \times \sqrt{x} \]Divide both sides by 80:
\[ \sqrt{x} = \frac{1120}{80} \]Correct Option: D) 196