To determine the number of double bonds in propanone, we need to understand its chemical structure. Propanone is a ketone, and its name provides clues about its carbon chain length and functional group.
\[ \text{CH}_3\text{COCH}_3 \]
Or, more explicitly showing the bonds:
\[ \text{H}_3\text{C} - \text{C}(=\text{O}) - \text{CH}_3 \]
A) 1 — Propanone contains one carbonyl group (\(C=O\)), which consists of a single double bond.
The question asks for the definition of macroeconomics. To answer this, it's essential to understand the fundamental distinction between macroeconomics and microeconomics, which are the two main branches of economics.
Correct Option: D) a branch of economics that studies the behaviour and performance of an economy as a whole.
Macroeconomics deals with aggregate economic indicators such as Gross Domestic Product (GDP), inflation, unemployment rates, and national income. It examines how these factors interact and how government policies can influence them to achieve economic goals like stability and growth. This holistic view of the economy is the defining characteristic of macroeconomics.
The question asks to identify the specific organelle in a plant cell where aerobic respiration occurs, involving the intake of oxygen, release of energy, and production of carbon dioxide from food. This process is characteristic of cellular respiration.
B) mitochondria — Mitochondria are the organelles responsible for cellular respiration, where oxygen is consumed, and food (glucose) is broken down to release energy (ATP) and carbon dioxide as a byproduct. This perfectly matches the description in the question.
This is a logical reasoning problem involving arrangement. We need to deduce the living arrangement of six people (P, Q, R, S, T, U) on six different floors based on the given clues. We will systematically place each person on a floor and eliminate possibilities until the complete arrangement is found.
Identify Fixed Positions:
Current arrangement:
| Floor | Person |
|---|---|
| 6 | R |
| 5 | Q |
| 4 | |
| 3 | |
| 2 | |
| 1 |
Place P:
Current arrangement:
| Floor | Person |
|---|---|
| 6 | R |
| 5 | Q |
| 4 | P |
| 3 | |
| 2 | |
| 1 |
Place S and T:
Current arrangement:
| Floor | Person |
|---|---|
| 6 | R |
| 5 | Q |
| 4 | P |
| 3 | |
| 2 | T |
| 1 | S |
Place the Remaining Person:
Final arrangement:
| Floor | Person |
|---|---|
| 6 | R |
| 5 | Q |
| 4 | P |
| 3 | U |
| 2 | T |
| 1 | S |
Answer the Question: The question asks who lives on floor number 3. From our final arrangement, U lives on Floor 3.
Correct Option: D) U
The question asks to identify the correct statement among the given options regarding the highest peaks of various mountain ranges in India. This requires knowledge of Indian geography, specifically the prominent mountain ranges and their highest points.
Correct Option: A) Dhupgarh is the highest peak of the Satpura Range.
The question asks about contraception methods that can prevent the transmission of HIV. HIV is a sexually transmitted infection (STI). Therefore, the most effective methods for preventing its transmission are those that create a physical barrier to the exchange of bodily fluids during sexual activity.
Correct Option: A) Barrier methods only are effective in preventing the transmission of HIV because they create a physical barrier that prevents the exchange of bodily fluids during sexual activity, which is the primary mode of HIV transmission.
To solve this problem, we first need to find the current ages of K and M 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 determine the new ratio.
Represent current ages:
Let the current age of K be \(7x\) years and the current age of M be \(5x\) years, as their ages are in the ratio of \(7:5\).
Formulate equation for sum of ages:
The sum of their current ages is given as 72 years. So,
\[ 7x + 5x = 72 \]Solve for \(x\):
Combine the terms:
\[ 12x = 72 \]\[ x = \frac{72}{12} \]\[ x = 6 \]Calculate current ages:
Current age of K \( = 7x = 7 \times 6 = 42 \) years.
Current age of M \( = 5x = 5 \times 6 = 30 \) years.
Calculate ages after 9 years:
Age of K after 9 years \( = 42 + 9 = 51 \) years.
Age of M after 9 years \( = 30 + 9 = 39 \) years.
Determine the new ratio:
The ratio of the ages of K and M after 9 years will be:
\[ \text{Ratio} = \frac{\text{Age of K after 9 years}}{\text{Age of M after 9 years}} = \frac{51}{39} \]Simplify the ratio:
Both 51 and 39 are divisible by 3.
\[ \frac{51 \div 3}{39 \div 3} = \frac{17}{13} \]So, the ratio of their ages after 9 years will be \(17:13\).
Correct Option: C) 17 : 13
If u − v = 4 and uv = 20, then the value of u³ − v³ is:
The problem asks us to find the value of \(u^3 - v^3\) given the values of \(u - v\) and \(uv\). We can use the algebraic identity for the difference of cubes, which relates \(u^3 - v^3\) to \((u - v)\) and \(uv\).
Recall the algebraic identity for the difference of cubes:
\[ u^3 - v^3 = (u - v)(u^2 + uv + v^2) \]We are given \(u - v = 4\) and \(uv = 20\). We need to find \(u^2 + v^2\) to substitute into the identity. We know another identity that relates \((u - v)^2\) to \(u^2 + v^2\) and \(uv\):
\[ (u - v)^2 = u^2 - 2uv + v^2 \]From this, we can express \(u^2 + v^2\) as:
\[ u^2 + v^2 = (u - v)^2 + 2uv \]Substitute the given values into the expression for \(u^2 + v^2\):
\[ u^2 + v^2 = (4)^2 + 2(20) \]\[ u^2 + v^2 = 16 + 40 \]\[ u^2 + v^2 = 56 \]Now substitute this value back into the difference of cubes identity:
\[ u^3 - v^3 = (u - v)(u^2 + uv + v^2) \]\[ u^3 - v^3 = (u - v)((u^2 + v^2) + uv) \]Substitute the known values:
\[ u^3 - v^3 = (4)(56 + 20) \]\[ u^3 - v^3 = (4)(76) \]Perform the multiplication:
\[ u^3 - v^3 = 304 \]Correct Option: D) 304
In a certain code language, ‘TEMPLE’ is written as ‘QHJSIH’ and ‘MOSQUE’ is written as ‘JRPTRH’. How will ‘SUPREME’ be written in the same code language?
The problem requires us to decipher a coding pattern based on two given examples and then apply that pattern to a new word. We need to analyze the letter-to-letter transformation for 'TEMPLE' and 'MOSQUE' to find a consistent rule, which could be based on alphabetical position, skipping letters, or a combination of these.
A) PXMUBPB is the correct code derived by applying the \(-3, +3\) alternating pattern to each letter of 'SUPREME'.
This problem involves work and time. We can solve it by calculating the amount of work done per day by A and B together, and then using the information about B leaving to find the individual work rate of A and B.
Let the total work be 1 unit.
A and B together can complete the work in 5 days. So, their combined work rate is:
\[ \text{Work rate of (A + B)} = \frac{1}{5} \text{ work/day} \]They worked together for 3 days. The amount of work completed in these 3 days is:
\[ \text{Work done in 3 days} = 3 \times \frac{1}{5} = \frac{3}{5} \text{ of the total work} \]After 3 days, B left. The remaining work is:
\[ \text{Remaining work} = 1 - \frac{3}{5} = \frac{2}{5} \text{ of the total work} \]This remaining work was completed by A alone in 3 more days. So, A's work rate is:
\[ \text{Work rate of A} = \frac{\text{Remaining work}}{\text{Days taken by A}} = \frac{2/5}{3} = \frac{2}{15} \text{ work/day} \]Now we can find B's work rate by subtracting A's work rate from the combined work rate of A and B:
\[ \text{Work rate of B} = \text{Work rate of (A + B)} - \text{Work rate of A} \]\[ \text{Work rate of B} = \frac{1}{5} - \frac{2}{15} \]\[ \text{Work rate of B} = \frac{3}{15} - \frac{2}{15} = \frac{1}{15} \text{ work/day} \]If B alone works at this rate, the time taken by B to complete the entire work (1 unit) is the reciprocal of B's work rate:
\[ \text{Time taken by B alone} = \frac{1}{\text{Work rate of B}} = \frac{1}{1/15} = 15 \text{ days} \]B) 15 days is the correct answer. B alone could do the entire work in 15 days.
A) 7.5 days — This would imply a faster work rate for B, which is not consistent with the given information.
C) 6.5 days — This is a significantly lower number of days, suggesting a much higher work rate for B than calculated.
D) 13 days — This value does not result from the correct calculation of B's individual work rate based on the problem's conditions.