The question asks for the SI unit of force. To answer this, we need to recall the standard units of measurement in the International System of Units (SI) for various physical quantities, specifically for force.
Correct Option: B) Newton
The question asks to identify the part of the Indian Constitution that deals with Fundamental Rights. This requires knowledge of the structure and contents of the Constitution of India.
Correct Option: C) Part 3 of the Constitution of India contains the Fundamental Rights of the citizens of India. These rights are enshrined in Articles 12 to 35 and are considered a cornerstone of the Indian democracy.
The question asks for the botanical name of the banyan tree. This requires knowledge of common botanical names for well-known plants.
Correct Option: A) Ficus benghalensis is the botanical name for the banyan tree. It is also the national tree of India.
The question asks for the term that describes buying or selling goods electronically. We need to identify the specific term from the given options that accurately defines this activity.
Correct Option: B) e-commerce
E-commerce, short for electronic commerce, specifically refers to the buying and selling of goods and services, or the transmitting of funds or data, over an electronic network, primarily the internet. This perfectly matches the description in the question.
To find the greatest number less than 500 that is divisible by 6, 14, and 28, we first need to find the Least Common Multiple (LCM) of these three numbers. Any number divisible by 6, 14, and 28 must be a multiple of their LCM. Once we have the LCM, we will find the largest multiple of the LCM that is less than 500.
Find the prime factorization of each number:
Calculate the LCM:
The LCM is found by taking the highest power of all prime factors present in the numbers.
So, the LCM is:
\[ \text{LCM}(6, 14, 28) = 2^2 \times 3 \times 7 = 4 \times 3 \times 7 = 12 \times 7 = 84 \]Find the greatest multiple of the LCM less than 500:
We need to find the largest multiple of 84 that is less than 500. Let this multiple be \(84k\), where \(k\) is an integer.
Calculate the number:
Substitute \(k=5\) into \(84k\):
B) 420 is the greatest number less than 500 that is divisible by 6, 14, and 28.
This problem involves calculating the marked price of an article given its cost price, the profit percentage, and the discount percentage. We will use the formulas relating cost price, selling price, marked price, profit, and discount.
Calculate the Selling Price (SP):
The cost price (CP) is ₹500, and the shopkeeper makes a profit of 8%.
\[ \text{Profit} = \text{CP} \times \frac{\text{Profit Percentage}}{100} \]So,
\[ \text{Profit} = 500 \times \frac{8}{100} = \text{₹}40 \]The Selling Price (SP) is the Cost Price plus the Profit.
\[ \text{SP} = \text{CP} + \text{Profit} = 500 + 40 = \text{₹}540 \]Calculate the Marked Price (MP):
The shopkeeper allows a discount of 20% on the Marked Price (MP) to arrive at the Selling Price (SP).
This means that the Selling Price is 100% - 20% = 80% of the Marked Price.
\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right) \]We know SP = ₹540 and Discount Percentage = 20%.
\[ 540 = \text{MP} \times \left(1 - \frac{20}{100}\right) \]\[ 540 = \text{MP} \times \left(1 - 0.20\right) \]\[ 540 = \text{MP} \times 0.80 \]Now, solve for MP:
\[ \text{MP} = \frac{540}{0.80} \]\[ \text{MP} = \frac{540}{\frac{80}{100}} = \frac{540 \times 100}{80} \]\[ \text{MP} = \frac{54000}{80} = \frac{5400}{8} \]\[ \text{MP} = 675 \]The marked price of the article is ₹675.
D) ₹675 is the correct marked price calculated based on the given profit and discount percentages.
To find the average speed for the whole journey, we need to calculate the total distance traveled and the total time taken. The average speed is then the total distance divided by the total time. It's important to note that average speed is not simply the average of the two speeds when the times taken for each part of the journey are different.
D) 60 km/h is the correct average speed calculated by dividing the total distance by the total time.
The question asks to identify the president of the Indian National Congress in the year 1931. This requires knowledge of the history of the Indian National Congress and its presidential sessions.
Correct Option: A) Vallabhbhai J Patel was the president of the Indian National Congress in 1931, presiding over the Karachi Session.
The horizontal distance between two towers is 40\(\sqrt{3}\) m. The angle of depression of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 130 m, find the height of the first tower.
This problem involves trigonometry, specifically angles of depression. We need to visualize the scenario as a right-angled triangle formed by the difference in heights of the towers and the horizontal distance between them. We will use the tangent function to relate the angle of depression, the opposite side (difference in height), and the adjacent side (horizontal distance).
Let the height of the first tower be \(h_1\) and the height of the second tower be \(h_2\).
Given:
When observing the top of the first tower from the top of the second tower, the angle of depression is formed by the horizontal line from the top of the second tower and the line of sight to the top of the first tower. This creates a right-angled triangle where:
Using the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]\[ \tan(30^\circ) = \frac{h_2 - h_1}{d} \]Substitute the given values:
\[ \frac{1}{\sqrt{3}} = \frac{130 - h_1}{40\sqrt{3}} \]Now, solve for \(h_1\):
\[ 40\sqrt{3} \times \frac{1}{\sqrt{3}} = 130 - h_1 \]\[ 40 = 130 - h_1 \]\[ h_1 = 130 - 40 \]\[ h_1 = 90 \text{ m} \]Thus, the height of the first tower is 90 m.
D) 90 m — The calculation shows that the height of the first tower is 90 m.
This problem involves substituting given symbol transformations into mathematical equations and then evaluating them using the order of operations (BODMAS/PEMDAS) to find the correct equation.
The given symbol transformations are:
We will apply these transformations to each option and then evaluate the resulting expression.
Original equation: \(36 − 6 + 3 × 5 ÷ 3 = 74\)
Applying the symbol transformations:
The equation becomes:
\[ 36 \times 6 \div 3 + 5 - 3 \]Now, evaluate using the order of operations (BODMAS/PEMDAS):
Since the result is \(74\), which matches the right-hand side of the equation, option A is correct.