You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
What is the total age of the sisters 10 years from now?
Statements:
1. Lina is 20 years old now.
2. Lina’s sister’s age is twice that of \( \frac{1}{4} \)th of the age of Lina.
Statement 1 alone is sufficient.
Statements 1 and 2 together are not sufficient.
Statement 2 alone is sufficient.
Statements 1 and 2 together are sufficient.
The problem asks us to determine if the given statements are sufficient to find the total age of two sisters (Lina and her sister) 10 years from now. We need to find their current ages first, and then calculate their ages after 10 years.
D) Statements 1 and 2 together are sufficient. As shown in the step-by-step analysis, by combining the information from both statements, we can determine the current ages of both sisters and subsequently calculate their total age 10 years from now.
Who has won the Best Actor award in the 90th Oscar awards 2018?
Gary Oldman
Denzel Washington
Daniel Day-Lewis
Daniel Kaluuya
The question asks to identify the winner of the Best Actor award at the 90th Academy Awards (Oscars) held in 2018. This requires knowledge of major international awards and their recipients for a specific year.
A) Gary Oldman — Gary Oldman won the Best Actor award at the 90th Academy Awards in 2018 for his performance as Winston Churchill in the movie Darkest Hour.
This problem involves calculating the distance to a cliff using the concept of an echo. An echo occurs when sound waves reflect off a surface and return to the listener. The key is to remember that the sound travels to the cliff and then back to the person, covering the distance twice. We will use the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\).
When a person claps and hears an echo, the sound travels from the person to the cliff and then reflects back from the cliff to the person. Therefore, the total distance covered by the sound is twice the distance between the person and the cliff.
Let \(D\) be the distance of the cliff from the person.
The total distance traveled by sound is \(2D\).
The relationship between distance, speed, and time is given by:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]In this case, the total distance traveled by sound is \(2D\), the speed is \(v\), and the time is \(t\).
\[ 2D = v \times t \]Now, divide by 2 to find the distance \(D\):
\[ D = \frac{2076 \text{ m}}{2} \] \[ D = 1038 \text{ m} \]Correct Option: A) 1038 m
To find the acceleration of the car, we need to use the formula for acceleration, which is the change in velocity divided by the time taken. First, we must convert the initial and final velocities from kilometers per hour (km h⁻¹) to meters per second (m s⁻¹) to ensure consistent units with the given time in seconds.
Initial velocity, \(u = 18 \text{ km h}^{-1}\)
To convert km h⁻¹ to m s⁻¹, we multiply by \(\frac{1000 \text{ m}}{1 \text{ km}}\) and \(\frac{1 \text{ h}}{3600 \text{ s}}\).
\[ u = 18 \times \frac{1000}{3600} \text{ m s}^{-1} \]\[ u = 18 \times \frac{5}{18} \text{ m s}^{-1} \]\[ u = 5 \text{ m s}^{-1} \]Final velocity, \(v = 72 \text{ km h}^{-1}\)
\[ v = 72 \times \frac{1000}{3600} \text{ m s}^{-1} \]\[ v = 72 \times \frac{5}{18} \text{ m s}^{-1} \]\[ v = 4 \times 5 \text{ m s}^{-1} \]\[ v = 20 \text{ m s}^{-1} \]Time, \(t = 5 \text{ s}\)
The formula for acceleration (\(a\)) is:
\[ a = \frac{v - u}{t} \]\[ a = \frac{20 \text{ m s}^{-1} - 5 \text{ m s}^{-1}}{5 \text{ s}} \]\[ a = \frac{15 \text{ m s}^{-1}}{5 \text{ s}} \]\[ a = 3 \text{ m s}^{-2} \]The acceleration of the car is \(3 \text{ m s}^{-2}\).
Correct Option: D) 3 m s⁻²
Which of the option figures bears the closest resemblance to the question figure?
Question figure
Option figures
The task is to determine which option figure most closely resembles the question figure. The question figure consists of a hexagon with a diagonal line, an arrow, and a circle. We need to compare these elements with the option figures.
Correct Option: C) Option C closely resembles the question figure with the correct placement of the circle and arrow direction.
To find the percentage of oxygen in aluminum sulfate (Al₂(SO₄)₃), we need to calculate the molar mass of the entire compound and the total mass of oxygen within it. Then, we can use these values to determine the percentage by mass.
Total Molar Mass = Mass of Al + Mass of S + Mass of O
\[ \text{Total Molar Mass} = 53.96 + 96.21 + 192.00 = 342.17 \text{ g/mol} \]Percentage of Oxygen = \[\left( \frac{\text{Total mass of Oxygen}}{\text{Total Molar Mass of Al₂(SO₄)₃}} \right) \times 100\%\]
\[ \text{Percentage of Oxygen} = \left( \frac{192.00}{342.17} \right) \times 100\% \]\[ \text{Percentage of Oxygen} \approx 0.5611 \times 100\% \]\[ \text{Percentage of Oxygen} \approx 56.11\% \]Rounding to one decimal place, the percentage of oxygen is \(56.1\%\).
Correct Option: B) 56.1%
We need to evaluate the strength of each argument based on logical reasoning and general knowledge. A strong argument is one that is factual, relevant, and directly addresses the question with a significant impact. A weak argument is often based on personal preference, incomplete information, or is not directly relevant.
Correct Option: A) Only argument I is strong.
Argument I presents a valid and generally accepted health concern associated with the overuse of air conditioners, making it a strong argument for avoiding overuse. Argument II is based on personal comfort, which is subjective and does not constitute a strong counter-argument against potential negative impacts.
The question asks for the location where Prime Minister Narendra Modi laid the foundation stone for the Char Dham highway development project. This is a factual question related to a significant infrastructure project in India. Recalling the specific event and its location is key to answering this question.
Correct Option: B) Dehradun is the correct answer. Prime Minister Narendra Modi laid the foundation stone of the Char Dham highway development project in Dehradun on December 27, 2016.
The question asks us to identify the relationship between "Pond" and "Water" and then apply the same relationship to "Mountain" to find the missing word. This is a classic analogy question that tests logical reasoning and general knowledge.
A mountain is primarily composed of rocks. Rocks are the fundamental building blocks of mountains, just as water is the fundamental constituent of a pond.
The question asks to identify the first Indian woman to win the Korea Open series in Badminton. This requires knowledge of significant achievements of Indian badminton players.
Correct Option: D) P. V. Sindhu became the first Indian woman to win the Korea Open series in Badminton in 2017.