This problem involves compound interest. We are given the amounts after two different time periods and need to find the rate of interest. The key idea is that the amount after \(n\) years becomes the principal for the \((n+1)\)-th year when interest is compounded annually. Therefore, the amount after 2 years acts as the principal for the 3rd year, and the difference between the amount after 3 years and the amount after 2 years is the interest earned in the 3rd year.
Let the principal be \(P\) and the rate of interest be \(R\) per annum. The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]According to the problem statement:
We can write these as equations:
\[ 9680 = P \left(1 + \frac{R}{100}\right)^2 \quad \text{(Equation 1)} \]\[ 10648 = P \left(1 + \frac{R}{100}\right)^3 \quad \text{(Equation 2)} \]Divide Equation 2 by Equation 1:
\[ \frac{10648}{9680} = \frac{P \left(1 + \frac{R}{100}\right)^3}{P \left(1 + \frac{R}{100}\right)^2} \]\[ \frac{10648}{9680} = \left(1 + \frac{R}{100}\right) \]Calculate the value of the left side:
\[ \frac{10648}{9680} = 1.1 \]Now, equate this to the expression for the rate:
\[ 1.1 = 1 + \frac{R}{100} \]Solve for \(\frac{R}{100}\):
\[ \frac{R}{100} = 1.1 - 1 \]\[ \frac{R}{100} = 0.1 \]Solve for \(R\):
\[ R = 0.1 \times 100 \]\[ R = 10\% \]Correct Option: D) 10%
The question asks about the deity to whom the Virupaksha temple at Hampi is dedicated. This is a factual question related to Indian history and architecture, specifically the Vijayanagara Empire period.
Correct Option: B) Lord Shiva. The Virupaksha temple at Hampi is dedicated to Lord Shiva, in his manifestation as Virupaksha. It is one of the most important and active temples in the Hampi complex.
The question asks to identify a nuclear research reactor operated by the Bhabha Atomic Research Centre (BARC) from the given options. This requires knowledge of India's nuclear research facilities and their specific names.
Correct Option: A) Dhruva is a 100 MWt (megawatts thermal) nuclear research reactor located at the Bhabha Atomic Research Centre (BARC) in Trombay, Mumbai. It became operational in 1985 and is India's largest research reactor. It plays a crucial role in producing radioisotopes for medical, agricultural, and industrial applications, as well as for advanced research in nuclear physics and material science.
We are given two conditions relating two unknown numbers. We can set up a system of two linear equations based on these conditions and solve for the numbers. Alternatively, we can test the given options to see which pair satisfies both conditions.
C) 34 and 5 satisfies both conditions: 25% of 34 is 8.5, and 30% of 5 is 1.5. \(8.5 = 1.5 + 7\). The difference \(34 - 5 = 29\).
To solve this problem, we need to test each option by interchanging the specified signs in the given equation and then evaluating the expression using the BODMAS/PEMDAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction). The goal is to find which interchange makes the equation true, i.e., the left-hand side equals 3.
The original equation is: \(3 + 3 \times 3 - 3 \div 3 = 3\)
The equation becomes: \(3 + 3 \div 3 - 3 \times 3\)
Since \(-5 \neq 3\), this option is incorrect.
The equation becomes: \(3 \div 3 \times 3 - 3 + 3\)
Since \(3 = 3\), this option is correct.
B) + and ÷ is the correct option because when these signs are interchanged, the equation \(3 \div 3 \times 3 - 3 + 3\) evaluates to 3, making the original equation correct.
The question asks to identify the ISRO mission designed to study the Sun. This requires knowledge of ISRO's current and past space missions.
Aditya L1 is indeed ISRO's first dedicated mission to study the Sun. It is designed to observe the Sun from a halo orbit around the Lagrange Point 1 (L1) of the Sun-Earth system, which is about 1.5 million kilometers from Earth. This position provides an uninterrupted view of the Sun.
The question asks about the winner of the inaugural ICC Men's T20 Cricket World Cup. To answer this, one needs to recall the history of the tournament and its first edition's outcome.
Correct Option: A) India won the first ICC Men's T20 Cricket World Cup title in 2007.
The question asks to identify which of the given options contains Chlorofluorocarbons (CFCs). We need to recall the common applications and sources of CFCs.
Correct Option: D) Refrigerants
The question asks to identify the second highest constitutional office in India. This requires knowledge of the Indian constitutional hierarchy and the order of precedence of various dignitaries.
A) Vice President — The Vice President of India is the second highest constitutional office, ranking just below the President in the Indian Order of Precedence.
The problem presents a series of letter-clusters. To find the next cluster in the series, we need to identify the pattern in how the letters change from one cluster to the next. We will analyze the progression of each letter's position in the alphabet.
Correct Option: D) FGK