To find the greatest four-digit number that is a perfect square, we need to identify the largest integer whose square is a four-digit number. A four-digit number ranges from 1000 to 9999. We will find the square root of the largest four-digit number and then check the square of the integer part of that square root.
C) 9801 is the greatest four-digit number that is a perfect square, as \(99^2 = 9801\).
The question asks to identify the author of the Hindi novels 'Rangbhumi', 'Godan', 'Gaban', and 'Vardaan'. This is a direct knowledge-based question about famous literary works and their authors in Hindi literature.
D) Munshi Prem Chand — Munshi Prem Chand (1880–1936) was a pioneer of modern Hindi and Urdu fiction. His novels 'Godan', 'Gaban', 'Rangbhumi', 'Karmabhumi', and 'Nirmala' are considered masterpieces of Indian literature. 'Vardaan' is also one of his notable works. He is known for his realistic and insightful portrayal of Indian society, especially the rural masses, and his critique of social evils.
A can do a piece of work alone in 32 days, while together with B she can do the work in 24 days. If C alone can do the work in 64 days, in how many days can B and C together do the work?
38 \( \frac{2}{5} \) days
38 \( \frac{3}{5} \) days
37 \( \frac{4}{5} \) days
38 \( \frac{4}{5} \) days
This problem involves work and time, where we need to calculate the combined work rate of B and C. We will first determine the individual work rates of A, A+B, and C. Then, we will use these to find B's individual work rate. Finally, we will combine B's and C's work rates to find the time they take to complete the work together.
To subtract these fractions, find a common denominator, which is 96.
\[ \text{B's work rate} = \frac{4}{96} - \frac{3}{96} = \frac{1}{96} \text{ part of the work per day} \]So, B alone can do the work in 96 days.
To add these fractions, find a common denominator, which is 192.
\[ (\text{B} + \text{C})\text{'s work rate} = \frac{2}{192} + \frac{3}{192} = \frac{5}{192} \text{ part of the work per day} \]Convert the improper fraction to a mixed number:
\[ \frac{192}{5} = 38 \frac{2}{5} \text{ days} \]A) 38 \( \frac{2}{5} \) days — This matches our calculated result.
To find out when the traffic lights will change simultaneously again, we need to find the least common multiple (LCM) of the time intervals at which each light changes. The LCM will give us the smallest time after which all three events (lights changing) will coincide.
Correct Option: C) 10 minutes 30 seconds
The question asks to identify which of the given options is NOT an operating system. To answer this, we need to understand what an operating system is and then evaluate each option.
C) Microsoft Office is a suite of application software, not an operating system. It runs on top of an operating system (like Windows or macOS) to perform specific tasks such as word processing, spreadsheet management, and presentations.
The question asks to identify the country with the largest total area among the given options. This requires knowledge of the geographical areas of these countries.
Here are the approximate total areas for the countries listed:
Comparing these values, Canada has the largest total area among the options provided.
Correct Option: D) Canada has a total area of approximately \(9.98 \text{ million km}^2\), making it the largest among the given choices. In fact, Canada is the second-largest country in the world by total area, after Russia.
The question asks about the historical event commemorated by Russia's Victory Day Parade, specifically the 75th anniversary of the Soviet victory over a particular country in June 2020. This requires knowledge of World War II history and the significance of Victory Day in Russia.
D) Germany — Victory Day in Russia commemorates the Soviet Union's victory over Nazi Germany in World War II. The 75th anniversary in 2020 specifically marked this historic triumph.
The question asks for the four main tax rates under the Goods and Services Tax (GST) regime in India. Understanding the standard GST slabs is crucial for competitive exams.
D) 5%, 12%, 18% and 28% are the four standard tax rates under GST in India. These slabs categorize goods and services based on their nature and essentiality.
The question asks to identify the largest gold-producing country in 2019. This requires knowledge of global mineral production statistics, which are often covered in economic geography and current affairs sections of competitive exams.
Correct Option: B) China
China has been the world's largest gold producer for over a decade. In 2019, its gold output significantly surpassed that of other nations, making it the top producer.
Solve the following.
108 ÷ (36 × \( \frac{1}{4} \)) + \( \frac{2}{5} \) × 3 \( \frac{1}{4} \) = ?
13 \( \frac{3}{10} \)
\( \frac{130}{10} \)
\( \frac{132}{10} \)
\( \frac{13}{10} \)+ 11
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS): Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. We will simplify the expression step-by-step, starting with operations inside brackets, then division and multiplication, and finally addition.
First, simplify the expression inside the first bracket:
\[ 36 \times \frac{1}{4} = \frac{36}{4} = 9 \]Now, substitute this value back into the original expression:
\[ 108 \div 9 + \frac{2}{5} \times 3 \frac{1}{4} \]Perform the division:
\[ 108 \div 9 = 12 \]Convert the mixed fraction to an improper fraction:
\[ 3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]Now, perform the multiplication:
\[ \frac{2}{5} \times \frac{13}{4} = \frac{2 \times 13}{5 \times 4} = \frac{26}{20} \]Simplify the fraction \(\frac{26}{20}\) by dividing both numerator and denominator by their greatest common divisor, which is 2:
\[ \frac{26}{20} = \frac{13}{10} \]Now, add the results of the division and multiplication:
\[ 12 + \frac{13}{10} \]To add these, find a common denominator. Here, the common denominator is 10:
\[ 12 = \frac{12 \times 10}{10} = \frac{120}{10} \]Add the fractions:
\[ \frac{120}{10} + \frac{13}{10} = \frac{120 + 13}{10} = \frac{133}{10} \]Convert the improper fraction \(\frac{133}{10}\) to a mixed fraction:
\[ \frac{133}{10} = 13 \frac{3}{10} \]Thus, the final answer is \(13 \frac{3}{10}\).
A) \(13 \frac{3}{10}\) is the correct answer, as derived from the step-by-step calculation.