To convert a temperature from Celsius to Kelvin, we use a standard conversion formula. The Kelvin scale is an absolute temperature scale, meaning 0 K represents absolute zero, the lowest possible temperature where all molecular motion ceases.
D) 0 K is the correct answer because -273.15°C is defined as absolute zero, which is 0 K on the Kelvin scale.
By how much is \( \frac{1}{6} \) th of 432 smaller than \( \frac{3}{4} \) th of 216?
To find out by how much one quantity is smaller than another, we need to calculate both quantities first and then subtract the smaller one from the larger one. In this problem, we will calculate "\( \frac{1}{6} \)th of 432" and "\( \frac{3}{4} \)th of 216" separately, and then find their difference.
Correct Option: C) 90
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This rule dictates the sequence in which mathematical operations should be performed: Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, and Subtraction. Division and Multiplication have the same priority and are performed from left to right. Similarly, Addition and Subtraction have the same priority and are performed from left to right.
Correct Option: A) 13
The question asks to identify the substance that undergoes sublimation. Sublimation is a physical process where a substance transitions directly from the solid phase to the gas phase without passing through the liquid phase.
Correct Option: B) Iodine — Iodine is a well-known substance that sublimes. When heated, solid iodine turns directly into a violet gas without first melting into a liquid.
The given series is a sequence of numbers. We need to identify the pattern in the series to find the next two numbers. By observing the numbers, we can determine if they are related by addition, subtraction, multiplication, division, or if they follow a specific mathematical property like being prime numbers, square numbers, etc.
Correct Option: B) 19, 23
To find the ratio A : D, we need to combine the given individual ratios A : B, B : C, and C : D. This can be done by multiplying the ratios or by finding a common value for the intermediate terms (B and C).
Write down the given ratios:
Multiply the ratios to find A : D:
We can find the ratio A : D by multiplying the individual ratios:
Substitute the given values into the multiplication:
\[ \frac{A}{D} = \frac{2}{3} \times \frac{2}{3} \times \frac{3}{4} \]Perform the multiplication:
\[ \frac{A}{D} = \frac{2 \times 2 \times 3}{3 \times 3 \times 4} \]\[ \frac{A}{D} = \frac{12}{36} \]Simplify the resulting fraction:
Divide both the numerator and the denominator by their greatest common divisor, which is 12.
Express the result as a ratio:
\(A : D = 1 : 3\)
Correct Option: C) 1 : 3
The question asks about the origin of the term 'byte'. This is a historical question related to computer science. We need to identify the individual credited with coining this fundamental unit of digital information.
Correct Option: C) Werner Buchholz coined the term 'byte' in 1956 during his work on the IBM Stretch computer. He conceived it as a unit for encoding a character, typically comprising 8 bits, which became a standard.
The question asks for the geographical location of Yellowstone National Park. This is a factual question testing general knowledge about world geography and famous landmarks.
Correct Option: B) USA
Yellowstone National Park is a prominent national park located in the western United States. It was established by the U.S. Congress and signed into law by President Ulysses S. Grant on March 1, 1872, making it the first national park in the U.S. and widely held to be the first national park in the world.
To determine who paid more interest and by what amount, we need to calculate the simple interest paid by Sunil and the compound interest paid by Kamal separately. Then, we will compare these two interest amounts.
Calculate Simple Interest for Sunil:
Principal (P) = ₹40,000
Rate (R) = 11% per annum
Time (T) = 1 year 6 months = \(1.5\) years
The formula for Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]Substitute the values:
\[ \text{SI}_{\text{Sunil}} = \frac{40000 \times 11 \times 1.5}{100} \] \[ \text{SI}_{\text{Sunil}} = 400 \times 11 \times 1.5 \] \[ \text{SI}_{\text{Sunil}} = 4400 \times 1.5 \] \[ \text{SI}_{\text{Sunil}} = \text{₹}6600 \]Calculate Compound Interest for Kamal:
Principal (P) = ₹40,000
Rate (R) = 10% per annum, compounded semi-annually
Time (T) = 1 year 6 months = \(1.5\) years
Since the interest is compounded semi-annually, the effective rate per compounding period will be \(R/2\) and the number of compounding periods will be \(2T\).
Effective rate per period = \(10\%/2 = 5\%\)
Number of periods (n) = \(1.5 \times 2 = 3\) periods
The formula for Amount (A) with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Substitute the values:
\[ A_{\text{Kamal}} = 40000 \left(1 + \frac{5}{100}\right)^3 \] \[ A_{\text{Kamal}} = 40000 \left(1 + 0.05\right)^3 \] \[ A_{\text{Kamal}} = 40000 \left(1.05\right)^3 \] \[ A_{\text{Kamal}} = 40000 \times 1.157625 \] \[ A_{\text{Kamal}} = \text{₹}46305 \]Compound Interest (CI) = Amount - Principal
\[ \text{CI}_{\text{Kamal}} = 46305 - 40000 \] \[ \text{CI}_{\text{Kamal}} = \text{₹}6305 \]Compare the Interests:
Interest paid by Sunil = ₹6600
Interest paid by Kamal = ₹6305
Clearly, Sunil paid more interest.
Calculate the Difference:
Difference = Interest paid by Sunil - Interest paid by Kamal
\[ \text{Difference} = 6600 - 6305 \] \[ \text{Difference} = \text{₹}295 \]So, Sunil paid ₹295 more interest than Kamal.
B) Sunil paid ₹295 more
The question asks for the release year of India's first indigenous supercomputer, PARAM 8000. This is a factual question related to the history of computing in India. Recalling key milestones in India's technological advancements is crucial for such questions.
The PARAM 8000 was developed by C-DAC in Pune, India, and was officially launched in 1991. This project was a significant achievement for India, especially after the country was denied access to supercomputers by other nations.
C) 1991 — The PARAM 8000 supercomputer, India's first indigenous supercomputer, was launched in 1991 by C-DAC.