Question 3:
How many people who like Mars like Jupiter also?
The question asks to find the number of people who like both Mars and Jupiter based on a Venn diagram. We need to identify the region in the Venn diagram that represents the intersection of the 'Mars' and 'Jupiter' categories.
Therefore, 29 people like both Mars and Jupiter.
Correct Option: B) 29 is the correct answer because it represents the total number of people in the intersection of the 'Mars' and 'Jupiter' circles, which includes those who like only Mars and Jupiter, and those who like Mars, Jupiter, and Saturn.
The question asks to identify the capital city of Uganda. This is a factual question related to world geography, specifically the capitals of African countries. To answer this, one needs to recall the correct capital for Uganda and distinguish it from other cities.
Correct Option: B) Kampala is the capital and largest city of Uganda, located in East Africa.
The question asks to identify Madhubani art from the given options. This requires knowledge of Indian folk art forms and their origins.
C) A folk art practiced in Bihar — Madhubani art, also known as Mithila painting, is indeed a renowned folk art form that originated and is widely practiced in the Mithila region of Bihar, India.
What is 'Planet Nine'? (as of 2016)
A planet in the Comet Galaxy
A planet in Andromeda Galaxy
A planet where the 'Star Wars' series took place
A large icy planet proposed in the outer Solar System
The question asks for the definition of 'Planet Nine' as understood around 2016. This requires knowledge of recent astronomical discoveries and proposals concerning our Solar System.
Correct Option: D) A large icy planet proposed in the outer Solar System
This option accurately describes 'Planet Nine' as it was understood and proposed in 2016. It is a hypothetical, large, icy planet whose existence was inferred from its gravitational effects on other objects in the distant Solar System.
The question asks to identify which of the given options is NOT an Operating System. We need to understand what an Operating System is and then evaluate each option.
Correct Option: D) C++
C++ is a powerful, general-purpose programming language. It is used for developing operating systems, browsers, games, and many other applications, but it is not an operating system itself. It is a tool used to create software, including operating systems.
To find the smallest 5-digit number exactly divisible by a set of numbers, we first need to find the Least Common Multiple (LCM) of those numbers. Then, we find the smallest multiple of this LCM that is a 5-digit number.
Find the LCM of 12, 24, 48, 60, and 96:
First, find the prime factorization of each number:
To find the LCM, take the highest power of each prime factor present in any of the numbers:
\[ \text{LCM}(12, 24, 48, 60, 96) = 2^5 \times 3^1 \times 5^1 \] \[ \text{LCM} = 32 \times 3 \times 5 = 96 \times 5 = 480 \]Find the smallest 5-digit number:
The smallest 5-digit number is 10000.
Divide the smallest 5-digit number by the LCM:
\[ 10000 \div 480 \]Performing the division:
\[ 10000 = 480 \times 20 + 400 \]Here, the quotient is 20 and the remainder is 400.
Calculate the smallest 5-digit number divisible by the LCM:
If the remainder is 0, then 10000 itself would be divisible. Since the remainder is 400, we need to add \((480 - 400)\) to 10000 to get the next multiple of 480.
The required number is:
\[ 10000 + (480 - 400) = 10000 + 80 = 10080 \]Alternatively, we can find the next multiple by multiplying the LCM by \((quotient + 1)\):
\[ 480 \times (20 + 1) = 480 \times 21 \] \[ 480 \times 21 = 10080 \]Correct Option: D) 10080
Find the cost in rupees for carpeting a room 65 dm × 30 dm at Rs. 45 per m2.
To find the cost of carpeting, we first need to calculate the area of the room. The dimensions are given in decimeters (dm), but the cost is per square meter (m²). Therefore, we must convert the dimensions from decimeters to meters before calculating the area. Once the area is in square meters, we multiply it by the cost per square meter to find the total cost.
Convert dimensions from decimeters (dm) to meters (m):
We know that \(1 \text{ m} = 10 \text{ dm}\). Therefore, to convert dm to m, we divide by 10.
Calculate the area of the room:
The room is rectangular, so its area is given by the product of its length and width.
\[ \text{Area} = L \times W \] \[ \text{Area} = 6.5 \text{ m} \times 3.0 \text{ m} \] \[ \text{Area} = 19.5 \text{ m}^2 \]Calculate the total cost of carpeting:
The cost of carpeting is Rs. 45 per square meter.
\[ \text{Total Cost} = \text{Area} \times \text{Cost per m}^2 \] \[ \text{Total Cost} = 19.5 \text{ m}^2 \times \text{Rs. } 45/\text{m}^2 \] \[ \text{Total Cost} = \text{Rs. } 877.50 \]Correct Option: A) 877.50
What is the most common treatment for bacterial infections in humans?
The question asks for the most common treatment for bacterial infections in humans. We need to identify the class of drugs specifically designed to combat bacteria.
Correct Option: C) Antibiotics are a class of antimicrobial drugs used in the treatment and prevention of bacterial infections. They work by either killing bacteria (bactericidal) or inhibiting their growth (bacteriostatic).
To solve this problem, we first need to determine the current ages of Jai and Joy using the given ratio and sum of their ages. Once their current ages are known, we can calculate their ages after 9 years and then find the new ratio.
Represent current ages:
Let the current age of Jai be \(5x\) and the current age of Joy be \(2x\), based on the given ratio of 5:2.
Formulate an equation using the sum of ages:
The sum of their current ages is 63. So, we have the equation:
\[ 5x + 2x = 63 \]Solve for \(x\):
Combine the terms:
\[ 7x = 63 \]\[ x = \frac{63}{7} \]\[ x = 9 \]Calculate their current ages:
Jai's current age \( = 5x = 5 \times 9 = 45 \) years.
Joy's current age \( = 2x = 2 \times 9 = 18 \) years.
Calculate their ages after 9 years:
Jai's age after 9 years \( = 45 + 9 = 54 \) years.
Joy's age after 9 years \( = 18 + 9 = 27 \) years.
Find the ratio of their ages after 9 years:
The ratio of Jai's age to Joy's age after 9 years will be:
\[ \frac{\text{Jai's age}}{\text{Joy's age}} = \frac{54}{27} \]\[ \frac{54}{27} = \frac{2 \times 27}{1 \times 27} = \frac{2}{1} \]So, the ratio of their ages after 9 years will be 2:1.
B) 2:1 — This is the correct ratio calculated after determining their current ages and adding 9 years to each.
This problem involves calculating the cost price of chocolates based on a given selling price and loss percentage, and then determining the number of chocolates to sell at a new price to achieve a desired profit percentage. We will first find the cost price per chocolate, then the desired selling price per chocolate for a 20% profit, and finally, how many chocolates can be sold for Rs. 96 at this new price.
Calculate the Selling Price (SP) per chocolate:
The trader sells 90 chocolates for Rs. 160.
Calculate the Cost Price (CP) per chocolate:
The trader loses 20% by selling at this price. This means the selling price is 80% of the cost price.
Calculate the desired Selling Price (SP') per chocolate for a 20% profit:
To make a profit of 20%, the new selling price should be 120% of the cost price.
Calculate the number of chocolates to sell for Rs. 96 to make a 20% profit:
If each chocolate is sold for Rs. \( \frac{8}{3} \), then for Rs. 96, the number of chocolates will be:
Correct Option: B) 36