The question describes a physical event: a monkey falling from a tree. We need to identify which fundamental physics principle best explains this phenomenon, specifically in terms of energy transformation.
Correct Option: A) Law of conservation of energy. This law states that energy cannot be created or destroyed, but can only be transformed from one form to another. In the case of the falling monkey, its gravitational potential energy is converted into kinetic energy as it falls. The total mechanical energy (potential + kinetic) remains constant if air resistance is ignored.
This problem involves relative speed and the concept of meeting points. We need to determine the speed of the woman such that she encounters the cycles at a reduced time interval compared to their departure interval. This can be solved by considering the distance covered by the first cycle in the time difference and then applying the relative speed concept.
C) 1.5 km/hr is the correct speed for the woman to meet the cycles at an interval of 8 minutes.
We are given the cash difference between two selling prices of an article, corresponding to different profit percentages. We need to find the ratio of these two selling prices. We can assume a Cost Price (CP) for the article and then calculate the two Selling Prices (SP) based on the given profit percentages. Finally, we can use the cash difference to find the actual CP and then the ratio of the selling prices.
Let the Cost Price (CP) of the article be \(P\).
First Selling Price (\(SP_1\)) with 8% profit:
The profit is 8% of the CP. So, the selling price will be \(100\% + 8\% = 108\%\) of the CP.
Second Selling Price (\(SP_2\)) with 10% profit:
The profit is 10% of the CP. So, the selling price will be \(100\% + 10\% = 110\%\) of the CP.
Given difference in selling prices:
The cash difference between the selling prices is Rs. 3. Since \(SP_2\) (10% profit) will be higher than \(SP_1\) (8% profit), we have:
Calculate the Cost Price (P):
\[ 2P = 3 \times 100 \]\[ 2P = 300 \]\[ P = \frac{300}{2} = 150 \]So, the Cost Price of the article is Rs. 150.Calculate the actual Selling Prices:
\[ SP_1 = \frac{108 \times 150}{100} = 108 \times 1.5 = 162 \]\[ SP_2 = \frac{110 \times 150}{100} = 110 \times 1.5 = 165 \]Find the ratio of the two selling prices:
\[ \text{Ratio} = SP_1 : SP_2 = 162 : 165 \]To simplify the ratio, divide both numbers by their greatest common divisor. Both 162 and 165 are divisible by 3.\[ 162 \div 3 = 54 \]\[ 165 \div 3 = 55 \]So, the ratio is \(54 : 55\).B) 54:55 is the correct ratio of the two selling prices.
UN Postal Administration issued a commemorative stamp of __________, the Indian music legend on the 2nd October 2016.
Pandit Ravi Shankar
R.D. Burman
M.S. Subbulakshmi
Ustad Bismillah Khan
The question asks to identify the Indian music legend honored by the UN Postal Administration with a commemorative stamp on October 2, 2016. This is a factual question related to current affairs and general knowledge about prominent Indian personalities and international recognition.
C) M.S. Subbulakshmi — The UN Postal Administration issued a commemorative stamp on October 2, 2016, to honor the legendary Carnatic singer M.S. Subbulakshmi on the occasion of her birth centenary. This makes option C the correct answer.
The question asks for the full form of the acronym TELEX. This is a direct recall question related to common communication technologies and their abbreviations.
Correct Option: B) Teleprinter Exchange
The question asks to identify which factor is NOT used by the UNDP's Human Development Index (HDI) to compare countries. We need to recall the key dimensions and indicators that constitute the HDI.
B) Corporate governance — The Human Development Index (HDI) focuses on three fundamental dimensions: a long and healthy life, knowledge, and a decent standard of living. Corporate governance, while important for economic health and business ethics, is not one of the indicators used by the UNDP in its HDI report to compare countries.
To convert a score into a percentage, we need to express the obtained marks as a fraction of the total marks and then multiply by 100.
The student scored 8 marks.
The total marks for the test were 25.
The fraction representing the student's score is:
\[ \text{Fraction} = \frac{\text{Obtained Marks}}{\text{Total Marks}} = \frac{8}{25} \]To convert a fraction to a percentage, multiply it by 100%.
\[ \text{Percentage} = \left( \frac{8}{25} \right) \times 100\% \]\[ \text{Percentage} = 8 \times \left( \frac{100}{25} \right)\% \]\[ \text{Percentage} = 8 \times 4\% \]\[ \text{Percentage} = 32\% \]Thus, the student's marks in percentage are 32%.
A) 32 — This is the correct percentage calculated by dividing the obtained marks by the total marks and multiplying by 100.
This problem involves substituting given symbols with mathematical operations and then evaluating the resulting expression using the order of operations (BODMAS/PEMDAS).
The given expression is 15 Q 3 R 24 P 12 S 2.
Replacing the symbols, we get:
\[ 15 \div 3 + 24 - 12 \times 2 \]BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Both indicate the correct order of operations.
B) 5 is the correct answer after performing the operations in the correct order.
The question asks to identify the festival celebrated annually in the first week of December in Nagaland. This requires knowledge of major festivals and their locations and timings in India.
B) Hornbill festival — The Hornbill Festival is indeed celebrated annually in Nagaland from December 1st to December 10th. It is a major cultural event showcasing the rich traditions and heritage of the Naga tribes, attracting tourists from all over the world.
To divide a decimal number by 100, we need to shift the decimal point to the left by the number of zeros in 100. Since 100 has two zeros, the decimal point will be shifted two places to the left.
Alternatively, we can write the division as a fraction:
\[ \frac{7.7}{100} \]
To remove the decimal from the numerator, multiply both the numerator and denominator by 10:
\[ \frac{7.7 \times 10}{100 \times 10} = \frac{77}{1000} \]
Now, divide 77 by 1000. When dividing by 1000, the decimal point (which is implicitly after 77, i.e., 77.0) moves three places to the left:
\[ 77 \div 1000 = 0.077 \]
D) 0.077