This problem involves finding an unknown number given the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers, along with one of the numbers. The key concept to solve this is the fundamental relationship between LCM, HCF, and the two numbers: the product of two numbers is equal to the product of their LCM and HCF.
For any two positive integers, say \( a \) and \( b \), the following relationship holds true:
\[ \text{Product of the two numbers} = \text{LCM} \times \text{HCF} \]So, \( a \times b = \text{LCM}(a, b) \times \text{HCF}(a, b) \).
Let the two numbers be 240 and \( x \). Then,
\[ 240 \times x = 1920 \times 16 \]First, calculate the product of LCM and HCF:
\[ 1920 \times 16 = 30720 \]Now, the equation becomes:
\[ 240 \times x = 30720 \]Divide both sides by 240 to find \( x \):
\[ x = \frac{30720}{240} \] \[ x = \frac{3072}{24} \]Performing the division:
\[ x = 128 \]Correct Option: A) 128
The question asks to identify the inventor of the modern mercury thermometer with a standardized scale. This requires knowledge of the history of scientific instruments, specifically thermometers and their development.
Correct Option: C) Daniel Gabriel Fahrenheit is credited with inventing the modern mercury thermometer and developing a standardized scale (the Fahrenheit scale) in the early 18th century. His work was crucial in making temperature measurement accurate and reproducible.
A can complete 25% of a task in 10 days. B can complete 40% of the task in 40 days and C can complete \( \frac{1}{3} \) of the task in 13 days. Who among them has the fastest speed to complete the same task?
To determine who has the fastest speed, we need to calculate the time each person takes to complete the entire task (100% of the task). The person who takes the least amount of time to complete the full task has the fastest speed.
A completes 25% of the task in 10 days.
\[ \text{Time for 100% task (A)} = \frac{10 \text{ days}}{25\%} \times 100\% \]\[ = \frac{10}{0.25} \text{ days} \]\[ = 40 \text{ days} \]B completes 40% of the task in 40 days.
\[ \text{Time for 100% task (B)} = \frac{40 \text{ days}}{40\%} \times 100\% \]\[ = \frac{40}{0.40} \text{ days} \]\[ = 100 \text{ days} \]C completes \(\frac{1}{3}\) of the task in 13 days.
\[ \text{Time for 100% task (C)} = \frac{13 \text{ days}}{\frac{1}{3}} \]\[ = 13 \times 3 \text{ days} \]\[ = 39 \text{ days} \]Since C takes the least amount of time (39 days) to complete the entire task, C has the fastest speed.
B) C is the correct answer because C completes the entire task in 39 days, which is less than A's 40 days and B's 100 days.
The question asks for the birth year of Guru Nanak Dev Ji, the founder of Sikhism, in Rāi Bhoi Kī Talvaṇḍī (now Nankana Sahib).
Correct Option: A) 1469
Guru Nanak Dev Ji was born on 15 April 1469, in Rāi Bhoi Kī Talvaṇḍī, which is now known as Nankana Sahib, located in present-day Pakistan. This date is widely accepted and celebrated as Gurpurab.
The question asks for the financial year in which the Jal Kranti Abhiyan was launched. This requires knowledge of the launch date of this specific government initiative related to water conservation and management.
Correct Option: D) 2015-16
The question asks to identify the organization that launched the "Samwad with Students (SwS)" outreach program on New Year's Day, 2019. This requires knowledge of recent initiatives by prominent Indian scientific and educational organizations.
Correct Option: D) ISRO launched the "Samwad with Students (SwS)" program on New Year's Day, 2019, as part of its outreach efforts to engage and educate young people about space science and technology.
The question asks to identify the finger-like projections found in the inner lining of the small intestine. This is a direct recall question from human biology, specifically related to the digestive system and absorption.
Correct Option: A) villi are the finger-like projections found in the inner lining of the small intestine. They are crucial for increasing the surface area for efficient absorption of nutrients.
We are given the ratio of the present ages of Maya and Meera and the ratio of their ages after fifteen years. We can set up equations based on these ratios and solve for their present ages.
Let the present age of Maya be \(M\) and the present age of Meera be \(R\).
According to the first condition, the present ages of Maya and Meera are in the ratio of 6 : 5.
\[ \frac{M}{R} = \frac{6}{5} \]From this, we can express \(M\) in terms of \(R\):
\[ M = \frac{6}{5}R \]After fifteen years, Maya's age will be \(M + 15\) and Meera's age will be \(R + 15\).
According to the second condition, after fifteen years, their ages will be in the ratio of 9 : 8.
\[ \frac{M + 15}{R + 15} = \frac{9}{8} \]Now, substitute the expression for \(M\) from step 3 into the equation from step 5:
\[ \frac{\frac{6}{5}R + 15}{R + 15} = \frac{9}{8} \]Cross-multiply to solve for \(R\):
\[ 8 \left( \frac{6}{5}R + 15 \right) = 9 (R + 15) \]\[ \frac{48}{5}R + 120 = 9R + 135 \]Gather terms involving \(R\) on one side and constants on the other:
\[ \frac{48}{5}R - 9R = 135 - 120 \]\[ \frac{48R - 45R}{5} = 15 \]\[ \frac{3R}{5} = 15 \]Solve for \(R\):
\[ 3R = 15 \times 5 \]\[ 3R = 75 \]\[ R = \frac{75}{3} \]\[ R = 25 \]So, Meera's present age is 25 years.
We can also find Maya's present age:
\[ M = \frac{6}{5}R = \frac{6}{5} \times 25 = 6 \times 5 = 30 \]Let's verify the ratios:
B) 25 years is the correct answer. Meera's present age is 25 years.
A) 30 years: This is Maya's present age, not Meera's. The question specifically asks for Meera's age.
C) 20 years: If Meera's age were 20, then Maya's age would be \((6/5) \times 20 = 24\). After 15 years, their ages would be \(24+15=39\) and \(20+15=35\). The ratio \(39:35\) is not \(9:8\).
D) 35 years: This value does not satisfy the given conditions. If Meera's age were 35, then Maya's age would be \((6/5) \times 35 = 42\). After 15 years, their ages would be \(42+15=57\) and \(35+15=50\). The ratio \(57:50\) is not \(9:8\).
This is a coding-decoding problem. We need to find the codes for individual words by comparing the given statements and their corresponding codes. By identifying common words and common codes across different statements, we can deduce the code for each word.
Correct Option: D) mu #
The code for 'Wheels' is 'mu' and the code for 'Car' is '#'. Therefore, 'Wheels car' is coded as 'mu #'.
To find the area of a rhombus, we can use the formula involving its base and height, similar to a parallelogram. The perimeter gives us the side length, and the distance between parallel sides acts as the height.
Understand the properties of a rhombus: A rhombus is a quadrilateral with all four sides equal in length. It can also be considered a special type of parallelogram.
Calculate the side length of the rhombus: Given the perimeter of the rhombus is 120 m. Since all four sides of a rhombus are equal, the perimeter is \(4 \times \text{side}\).
\[ \text{Perimeter} = 4 \times \text{side} \] \[ 120 \text{ m} = 4 \times \text{side} \] \[ \text{side} = \frac{120 \text{ m}}{4} \] \[ \text{side} = 30 \text{ m} \]Identify the height of the rhombus: In a rhombus, the distance between any two parallel sides is its height. Given that this distance is 15 m.
\[ \text{Height} (h) = 15 \text{ m} \]Calculate the area of the rhombus: Since a rhombus is a parallelogram, its area can be calculated using the formula: Area = base \(\times\) height. Here, the side length acts as the base.
\[ \text{Area} = \text{base} \times \text{height} \] \[ \text{Area} = 30 \text{ m} \times 15 \text{ m} \] \[ \text{Area} = 450 \text{ m}^2 \]A) 450 m² is the correct area calculated using the side length as the base and the given distance between parallel sides as the height.