The question asks to identify the author of the famous Kannada play 'Tughlaq'. This requires knowledge of prominent Indian playwrights, especially those from Karnataka, and their well-known works.
B) Girish Karnad is the author of the acclaimed Kannada play 'Tughlaq'. This play is a significant work in modern Indian theatre, known for its historical depth and psychological complexity, and has been widely performed and studied across India.
The question asks about the specific location where Mahatma Gandhi was first informed about the Champaran indigo planters' problems and invited to visit the region. This is a factual question related to the early phase of Gandhi's Satyagraha movements in India.
Correct Option: B) Lucknow
The question asks to identify which of the given railway stations is recognized as a UNESCO World Heritage Site. This requires knowledge of specific historical and architectural sites in India that have received this international designation.
D) Chhatrapati Shivaji Maharaj Terminus
The Chhatrapati Shivaji Maharaj Terminus (CSMT) in Mumbai, Maharashtra, India, was inscribed as a UNESCO World Heritage Site in 2004. It is an outstanding example of Victorian Gothic Revival architecture in India, blended with traditional Indian architectural themes. Designed by Frederick William Stevens, it was built in 1887 and originally known as Victoria Terminus.
The question asks for the approximate altitude of the satellites in the Global Positioning System (GPS) constellation. This is a factual recall question related to space technology and navigation systems.
A) 20,000 km is the closest approximate altitude for GPS satellites, which orbit at about 20,200 km.
If each side of a rectangle is increased by 25%, then its area will increase by:
55 \( \frac{1}{4} \) %
56 \( \frac{1}{4} \) %
60 \( \frac{1}{4} \) %
54 \( \frac{1}{4} \) %
To find the percentage increase in the area of a rectangle when its sides are increased by a certain percentage, we can calculate the initial area, then the new dimensions and new area, and finally determine the percentage change. Alternatively, we can use a direct formula for successive percentage changes.
When two successive percentage changes \(x\%\) and \(y\%\) occur, the net percentage change is given by the formula:
\[ \text{Net Change} = \left( x + y + \frac{xy}{100} \right) \% \]
In this case, both length and width are increased by 25%, so \(x = 25\) and \(y = 25\).
\[ \text{Net Change} = \left( 25 + 25 + \frac{25 \times 25}{100} \right) \% \]\[ \text{Net Change} = \left( 50 + \frac{625}{100} \right) \% \]\[ \text{Net Change} = (50 + 6.25) \% \]\[ \text{Net Change} = 56.25\% \]\[ \text{Net Change} = 56 \frac{1}{4} \% \]
Correct Option: B) 56 \( \frac{1}{4} \) %
To find the remainder when \( 11^9 + 7 \) is divided by 10, we can use the properties of modular arithmetic. We need to find the remainder of each term separately when divided by 10 and then combine them.
Find the remainder of \( 11^9 \) when divided by 10:
We know that \( 11 \equiv 1 \pmod{10} \). This means that when 11 is divided by 10, the remainder is 1.
Using the property of modular arithmetic that if \( a \equiv b \pmod{m} \), then \( a^n \equiv b^n \pmod{m} \), we can write:
\[ 11^9 \equiv 1^9 \pmod{10} \] \[ 11^9 \equiv 1 \pmod{10} \]So, the remainder when \( 11^9 \) is divided by 10 is 1.
Find the remainder of \( 7 \) when divided by 10:
When 7 is divided by 10, the remainder is 7.
\[ 7 \equiv 7 \pmod{10} \]Combine the remainders:
Now we need to find the remainder of the sum \( 11^9 + 7 \) when divided by 10. We can add the individual remainders:
\[ (11^9 + 7) \equiv (1 + 7) \pmod{10} \] \[ (11^9 + 7) \equiv 8 \pmod{10} \]Thus, the remainder when \( 11^9 + 7 \) is divided by 10 is 8.
The question asks about the year of the first synchronous census in India. This requires knowledge of the history of census operations in India.
Correct Option: A) 1881 is the year when the first synchronous census was conducted in India.
The question asks about the historical figure responsible for building the 'Shahi' road connecting the Indus Valley to the Sonar Valley. This road is famously known as the Grand Trunk Road. We need to identify the ruler who undertook this significant infrastructure project.
C) Sher Shah Suri — Sher Shah Suri is renowned for his administrative reforms and public works, including the extensive rebuilding and improvement of the Grand Trunk Road, which connected the Indus Valley to the Sonar Valley.
To find the Highest Common Factor (HCF) of three numbers, we can use the prime factorization method or the long division method. The prime factorization method involves finding the prime factors of each number and then multiplying the common prime factors. The long division method involves finding the HCF of two numbers first, and then finding the HCF of the result with the third number.
We can test divisibility by small prime numbers. It's not divisible by 2, 3 (sum of digits \(1+1+8+3=13\)), or 5. Let's try 7:
\[ 1183 \div 7 = 169 \]We know that \(169 = 13^2\). So,
\[ 1183 = 7 \times 13 \times 13 = 7 \times 13^2 \]The prime factorizations are:
The only common prime factor among all three numbers is 13. The lowest power of 13 appearing in any of the factorizations is \(13^1\).
The HCF is the product of the common prime factors raised to their lowest powers.
\[ \text{HCF}(156, 455, 1183) = 13 \]Correct Option: C) 13
The number 0.124\(\overline{64}\) (recurring) in the form \( \frac{p}{q} \) is equal to:
\(\frac{117}{1950}\)
\(\frac{17}{950}\)
\(\frac{617}{4950}\)
\(\frac{67}{4999}\)
To convert a recurring decimal into a fraction of the form \( \frac{p}{q} \), we follow a standard algebraic method. We set the given decimal equal to a variable, multiply it by powers of 10 to shift the decimal point such that the recurring part aligns, and then subtract the equations to eliminate the recurring part.
Let the given number be \( x \):
\[ x = 0.124\overline{64} \]This means \( x = 0.124646464... \)
Multiply \( x \) by a power of 10 such that the non-recurring part before the recurring block is to the left of the decimal point. Here, the non-recurring part is '124'. So, we multiply by \( 1000 \):
\[ 1000x = 124.646464... \quad \text{(Equation 1)} \]Multiply \( x \) by a power of 10 such that the entire non-recurring part and one full recurring block are to the left of the decimal point. The recurring block is '64', which has 2 digits. So, we multiply \( x \) by \( 1000 \times 100 = 100000 \):
\[ 100000x = 12464.646464... \quad \text{(Equation 2)} \]Subtract Equation 1 from Equation 2 to eliminate the recurring part:
\[ 100000x - 1000x = 12464.646464... - 124.646464... \]This simplifies to:
\[ 99000x = 12340 \]Solve for \( x \):
\[ x = \frac{12340}{99000} \]Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. Both are divisible by 10:
\[ x = \frac{1234}{9900} \]Both are divisible by 2:
\[ x = \frac{1234 \div 2}{9900 \div 2} = \frac{617}{4950} \]The number 617 is a prime number, and 4950 is not divisible by 617. So, this is the simplest form.
Correct Option: C) \( \frac{617}{4950} \)