This problem involves compound interest. The key property of compound interest is that if a sum of money multiplies by a certain factor in a given time period, it will multiply by the same factor in an equal subsequent time period. We will use the compound interest formula or this property to solve the problem.
Let the principal amount be \(P\). After 10 years, the amount becomes \(2P\). The formula for compound interest is \(A = P(1 + r)^t\), where \(A\) is the amount, \(P\) is the principal, \(r\) is the annual interest rate, and \(t\) is the time in years.
From the given information, in 10 years, the amount doubles:
\[ 2P = P(1 + r)^{10} \]\[ 2 = (1 + r)^{10} \quad (\text{Equation 1}) \]We need to find the time \(T\) when the amount becomes 16 times the principal, i.e., \(16P\).
\[ 16P = P(1 + r)^T \]\[ 16 = (1 + r)^T \quad (\text{Equation 2}) \]We can express 16 as a power of 2:
\[ 16 = 2^4 \]Substitute Equation 1 into this expression:
\[ 16 = \left((1 + r)^{10}\right)^4 \]\[ 16 = (1 + r)^{10 \times 4} \]\[ 16 = (1 + r)^{40} \]Comparing this with Equation 2, we get:
\[ (1 + r)^T = (1 + r)^{40} \]\[ T = 40 \]Alternatively, using the property of compound interest: If the money doubles in 10 years, it will multiply by the same factor (2) in every subsequent 10-year period.
So, it will take 40 years for the sum to become 16 times itself.
C) 40 — As calculated, the sum will become 16 times itself in 40 years.
The question asks to identify the specific department whose Disaster Management Division organized a conference on 'Experience Sharing and Capacity Building in Disaster Management' in August 2024. This requires knowledge of recent events or the organizational structure related to disaster management within various government bodies.
Correct Option: C) Department of Telecommunications (DoT)
The problem asks us to find a relationship between two sets of letters based on their positions in the English alphabet. We are given two examples of this relationship: CYBS is related to GWFQ, and KUJO is related to OSNM. We need to apply the same logic to SQRK to find its related set of letters.
Correct Option: C) WOVI
The question asks to identify the INCORRECT statement regarding the properties of metals. We need to evaluate each option based on the general characteristics of metals.
Based on this evaluation, the statement about lead and mercury being comparatively good conductors of heat appears to be incorrect.
Correct Option: C) Lead and mercury are comparatively good conductors of heat. — This statement is INCORRECT. While metals are generally good conductors of heat, lead is a relatively poor conductor compared to other common metals. Mercury, being a liquid metal, also has significantly lower thermal conductivity than most solid metals. Therefore, stating they are "comparatively good conductors of heat" is misleading and incorrect in the context of typical metallic conductivity.
The question asks to identify the Indian state from which the dance form 'Garba' originates, especially in the context of its recent recognition by UNESCO as an intangible cultural heritage.
Correct Option: D) Garba is a traditional folk dance from the state of Gujarat, India. Its inscription by UNESCO in 2023 further solidifies its identity with Gujarat.
The question asks to identify the application where Chlorofluorocarbons (CFCs) are NOT used. This requires knowledge of common uses of CFCs and general household/industrial equipment.
Correct Option: B) Grinders are mechanical devices used for crushing or grinding materials. They do not require or use CFCs in their operation.
The problem involves two complementary angles. Complementary angles are two angles whose sum is 90 degrees. We are given a relationship between the larger and smaller angles. We will set up a system of two linear equations based on this information and solve for the measure of the larger angle.
Define variables: Let the smaller angle be \(x\) degrees. Let the larger angle be \(y\) degrees.
Formulate the first equation (complementary angles): Since the two angles are complementary, their sum is 90 degrees.
\[ x + y = 90 \quad \text{(Equation 1)} \]
Formulate the second equation (relationship between angles): The larger angle is 6° less than five times the measure of the smaller angle. This can be written as:
\[ y = 5x - 6 \quad \text{(Equation 2)} \]
Solve the system of equations: Substitute Equation 2 into Equation 1:
\[ x + (5x - 6) = 90 \]
Simplify and solve for \(x\):
\[ 6x - 6 = 90 \] Add 6 to both sides:
\[ 6x = 90 + 6 \] \[ 6x = 96 \] Divide by 6:
\[ x = \frac{96}{6} \] \[ x = 16 \]
So, the smaller angle \(x\) is 16 degrees.
Solve for \(y\) (the larger angle): Substitute the value of \(x\) (16) into Equation 2:
\[ y = 5(16) - 6 \] \[ y = 80 - 6 \] \[ y = 74 \]
The larger angle \(y\) is 74 degrees.
Verify the solution: Smaller angle \(x = 16^\circ\). Larger angle \(y = 74^\circ\). Are they complementary? \(16^\circ + 74^\circ = 90^\circ\). Yes. Is the larger angle 6° less than five times the smaller angle? \(5 \times 16^\circ - 6^\circ = 80^\circ - 6^\circ = 74^\circ\). Yes.
Correct Option: C) 74°
The question asks to identify the partner of IIT Bombay in developing India's first Quantum Diamond Microchip Imager. This is a factual question related to recent technological advancements and collaborations in India.
Based on recent reports, IIT Bombay has indeed partnered with Tata Consultancy Services (TCS) to develop India's first Quantum Diamond Microchip Imager. This collaboration aims to advance quantum sensing technology for various applications.
Correct Option: B) TCS
This is a syllogism question. We need to analyze the given statements and determine which conclusions logically follow. We can use Venn diagrams to represent the relationships between the categories (oceans, rivers, ponds) and then check the validity of each conclusion.
C) Neither conclusion (I) nor (II) follows.
Based on our analysis, neither conclusion can be logically derived from the given statements. Conclusion (I) is too strong, and Conclusion (II) is not necessarily true as there's no direct or indirect information in the statements that guarantees an overlap between 'Oceans' and 'Ponds'.
The question asks to identify the company that partnered with iCreate in 2024 to foster AI startups in India. This is a factual question related to recent developments in technology and entrepreneurship in India.
Correct Option: D) Microsoft
In February 2024, Microsoft signed a Memorandum of Understanding (MoU) with iCreate (International Centre for Entrepreneurship and Technology) to empower AI startups in India. This collaboration aims to provide startups with access to Microsoft's AI tools, platforms, and mentorship, fostering innovation and growth in the AI sector.