The problem asks us to identify the lightest bag among A, B, C, and D using the given statements. We need to determine if each statement alone or both statements together are sufficient to find the lightest bag.
B) Statements 1 and 2 together are necessary.
As shown in step 3, by combining both statements, we can definitively conclude that A is the lightest bag. Neither statement alone provides enough information.
The question asks to identify the country that won the 2017 Women's Hockey Asia Cup title. This requires knowledge of major sporting event outcomes, which is a common topic in general awareness sections of competitive exams.
C) India won the 2017 Women's Hockey Asia Cup title by defeating China in the final match. This victory also qualified India for the 2018 Women's Hockey World Cup.
To find the median of a set of numbers, we first need to arrange the numbers in ascending order. Then, we determine if the count of numbers is odd or even. If the count is odd, the median is the middle number. If the count is even, the median is the average of the two middle numbers.
Therefore, the median of the given numbers is 13.5.
Correct Option: D) 13.5
The question asks to identify the name given to the celebration of PM Modi's birthday across India. This is a factual question related to current events and national observances.
Correct Option: B) Sewa Diwas — Prime Minister Narendra Modi's birthday, September 17th, is celebrated as "Sewa Diwas" (Service Day) by the BJP and its workers across India. On this day, various social welfare activities, blood donation camps, and cleanliness drives are organized.
The question asks to identify the famous temple built by Chola kings in Thanjavur (Tanjavur). This requires knowledge of prominent Chola architecture and their specific constructions.
B) Brihadeesvara — The Brihadeesvara Temple at Thanjavur is one of the largest and most magnificent Hindu temples, built by Raja Raja Chola I in the 11th century CE. It is a UNESCO World Heritage Site and a masterpiece of Chola architecture, known for its massive vimana (temple tower) and intricate sculptures.
The question asks to identify a major component of Liquefied Petroleum Gas (LPG) alongside butane. This requires knowledge of the chemical composition of LPG, which is a common fuel.
B) Propane — Propane is indeed a major component of LPG. LPG is primarily a mixture of propane and butane. In many regions, LPG is sold as either pure propane, pure butane, or a propane/butane mix.
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, evaluate the innermost bracket \((60 - 36 \div 12 \times 4)\).
Inside this bracket, we follow BODMAS: Division first, then Multiplication, then Subtraction.
\[ 36 \div 12 = 3 \]\[ 3 \times 4 = 12 \]\[ 60 - 12 = 48 \]Substitute this value back into the expression:
\[ 80 \div [48 - \{56 - 48\}] \]Next, evaluate the curly bracket \(\{56 - 48\}\):
\[ 56 - 48 = 8 \]Substitute this value back into the expression:
\[ 80 \div [48 - 8] \]Now, evaluate the square bracket \([48 - 8]\):
\[ 48 - 8 = 40 \]Finally, perform the division:
\[ 80 \div 40 = 2 \]D) The final calculated value is 2, which matches option D.
This is a logical reasoning question where we need to determine which conclusions can be logically derived from the given statement. We must only use the information provided in the statement and avoid making assumptions.
B) Conclusion II alone follows. The statement directly implies Kirti's skill, making her a good player. There is no information to suggest Sajit's interest in cricket.
\(\frac{3}{4}+\left\{\frac{3}{4}+\frac{3}{4}\div\left(\frac{3}{4}+\frac{3}{4}\right)\right\}\)=?
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, Subtraction. We will evaluate the innermost parentheses first and then work our way outwards.
The expression inside the innermost parentheses is \[\left(\frac{3}{4} + \frac{3}{4}\right)\].
\[ \frac{3}{4} + \frac{3}{4} = \frac{3+3}{4} = \frac{6}{4} = \frac{3}{2} \]
The expression becomes:
\[ \frac{3}{4} + \left\{\frac{3}{4} + \frac{3}{4} \div \left(\frac{3}{2}\right)\right\} \]
The division is \[\frac{3}{4} \div \frac{3}{2}\].
\[ \frac{3}{4} \div \frac{3}{2} = \frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2} \]
The expression inside the curly braces becomes:
\[ \frac{3}{4} + \frac{1}{2} \]
To add \(\frac{3}{4}\) and \(\frac{1}{2}\), find a common denominator, which is 4.
\[ \frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{1 \times 2}{2 \times 2} = \frac{3}{4} + \frac{2}{4} = \frac{3+2}{4} = \frac{5}{4} \]
The entire expression now is:
\[ \frac{3}{4} + \frac{5}{4} \]
\[ \frac{3}{4} + \frac{5}{4} = \frac{3+5}{4} = \frac{8}{4} = 2 \]
Thus, the final answer is 2.
Correct Option: C) 2
A water tank is \( \frac{2}{5} \)th full. Inlet A can fill the tank in 12 minutes while an outlet pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
It fills in 4.8 min
It empties in 4.8 min
It fills in 5.6 min
It empties in 5.6 min
This problem involves calculating the combined rate of filling and emptying pipes to determine whether a tank will fill or empty, and how long it will take. We'll find the individual rates, then the net rate, and finally use the initial fill level to calculate the time required.
Calculate the filling rate of pipe A:
Pipe A fills the tank in 12 minutes. So, in 1 minute, it fills \( \frac{1}{12} \) of the tank.
Calculate the emptying rate of pipe B:
Pipe B empties the tank in 6 minutes. So, in 1 minute, it empties \( \frac{1}{6} \) of the tank.
Calculate the net rate when both pipes are open:
Since pipe B is an outlet pipe, its rate is subtracted from the inlet pipe's rate. The net change in the tank's volume per minute is:
\[ \text{Net rate} = \text{Rate of A} - \text{Rate of B} \]\[ \text{Net rate} = \frac{1}{12} - \frac{1}{6} \]\[ \text{Net rate} = \frac{1}{12} - \frac{2}{12} \]\[ \text{Net rate} = -\frac{1}{12} \text{ tank/minute} \]Interpret the net rate:
The negative sign indicates that the tank is emptying. The net emptying rate is \( \frac{1}{12} \) of the tank per minute.
Determine the initial amount of water in the tank:
The tank is initially \( \frac{2}{5} \) th full.
Calculate the time to empty the tank:
Since the net rate is emptying, the tank will empty. We need to empty \( \frac{2}{5} \) of the tank. The time taken to empty a certain fraction of the tank is that fraction divided by the emptying rate.
\[ \text{Time to empty} = \frac{\text{Initial filled fraction}}{\text{Net emptying rate}} \]\[ \text{Time to empty} = \frac{\frac{2}{5}}{\frac{1}{12}} \]\[ \text{Time to empty} = \frac{2}{5} \times 12 \]\[ \text{Time to empty} = \frac{24}{5} \]\[ \text{Time to empty} = 4.8 \text{ minutes} \]Therefore, it will take 4.8 minutes to empty the tank.
B) It empties in 4.8 min