To find the average speed of an object, we need to calculate the total distance traveled and divide it by the total time taken. The problem provides two segments of travel with their respective distances and times.
The object travels 10 m in the first segment and 14 m in the second segment.
\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 \]
\[ \text{Total Distance} = 10 \text{ m} + 14 \text{ m} = 24 \text{ m} \]
The object takes 4 s for the first segment and 2 s for the second segment.
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 \]
\[ \text{Total Time} = 4 \text{ s} + 2 \text{ s} = 6 \text{ s} \]
Average speed is defined as the total distance divided by the total time.
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
\[ \text{Average Speed} = \frac{24 \text{ m}}{6 \text{ s}} \]
\[ \text{Average Speed} = 4 \text{ m s}^{-1} \]
Correct Option: D) 4 m s⁻¹
The question asks for the term describing molten material mixed with gases found within the Earth's mantle. This requires knowledge of basic geological terms related to the Earth's interior and volcanic processes.
Correct Option: A) Magma is the molten material, including dissolved gases, found beneath the Earth's surface, particularly in the mantle and crust. When this material erupts onto the surface, it is called lava.
The question asks about the number of groups and periods in the Modern Periodic Table. This is a fundamental concept in chemistry, directly related to the organization of elements based on their atomic number and electron configurations. We need to recall the standard structure of the Modern Periodic Table.
Therefore, the Modern Periodic Table has 18 groups and 7 periods.
Correct Option: C) 18 groups and 7 periods
To find the sum of the reciprocals of the zeroes of a cubic polynomial, we can use Vieta's formulas, which relate the coefficients of a polynomial to the sums and products of its roots (zeroes). For a cubic polynomial \(ax^3 + bx^2 + cx + d = 0\), if \(\alpha\), \(\beta\), and \(\gamma\) are its zeroes, then:
We need to find the sum of the reciprocals, which is \[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}\]. We can express this in terms of the standard sums and products.
Identify the coefficients of the given polynomial:
The given polynomial is \(6x^3 + 3x^2 - 5x + 1\).
Comparing it with the standard form \(ax^3 + bx^2 + cx + d\), we have:
Express the sum of reciprocals in terms of elementary symmetric polynomials:
Let the zeroes of the polynomial be \(\alpha\), \(\beta\), and \(\gamma\). We need to find \[\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}\].
To sum these fractions, find a common denominator:
\[ \frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = \frac{\beta\gamma + \alpha\gamma + \alpha\beta}{\alpha\beta\gamma} \]Apply Vieta's formulas:
From Vieta's formulas for the given polynomial:
Substitute the values into the expression for the sum of reciprocals:
\[ \frac{\beta\gamma + \alpha\gamma + \alpha\beta}{\alpha\beta\gamma} = \frac{\frac{-5}{6}}{\frac{-1}{6}} \]Calculate the final value:
\[ \frac{\frac{-5}{6}}{\frac{-1}{6}} = \frac{-5}{6} \times \frac{6}{-1} = \frac{-5}{-1} = 5 \]D) The sum of the reciprocals of the zeroes is 5.
Find the odd one out
| A | B | C | D |
| O15 | C3 | G7 | N15 |
To determine the valency of copper in cuprous oxide, we need to know the chemical formula of cuprous oxide and the known valency of oxygen. Valency represents the combining capacity of an element.
D) 1 is the correct valency of copper in cuprous oxide (\(\text{Cu}_2\text{O}\)). Copper can also exhibit a valency of 2 in cupric compounds (e.g., cupric oxide, \(\text{CuO}\)).
To find out how many more marbles Aman got compared to Ashok, we first need to determine the total number of parts in the given ratio. Then, we can calculate the number of marbles each person received and find the difference.
Alternatively, we can find the difference in ratio parts first:
A) 84 is the correct answer. Aman received 147 marbles and Ashok received 63 marbles. The difference is \(147 - 63 = 84\).
The question asks to identify the compound that does NOT contain a carbonyl group. A carbonyl group is a functional group consisting of a carbon atom double-bonded to an oxygen atom (\(C=O\)). We need to examine the structure of each given option to determine the presence or absence of this group.
Based on this analysis, ethanol is the only compound among the options that does not contain a carbonyl group.
Correct Option: D) Ethanol does not contain a carbonyl group. Its functional group is a hydroxyl group (\(-OH\)), making it an alcohol.
This problem involves rates of work for pipes filling and emptying a cistern. We will use the concept of work done per hour (rate) to solve it. The total work is considered as 1 unit (the full cistern). We'll set up equations based on the given efficiencies and combined work rates to find the time taken by the less efficient pipe.
Define variables for efficiencies:
Let the rate of the less efficient inlet pipe be \(R_1\) units/hour.
Since the other inlet pipe works twice as efficiently, its rate will be \(R_2 = 2R_1\) units/hour.
Calculate the rate of the drain pipe:
The drain pipe can empty the cistern in 12 hours. So, its emptying rate is:
Formulate the combined work rate equation:
When both inlet pipes and the drain pipe work together, they fill the cistern in 12 hours. The combined rate is the sum of their individual rates:
Substitute known values into the combined rate equation:
Substitute \(R_2 = 2R_1\) and \(R_{\text{drain}} = -\frac{1}{12}\) into the equation:
Solve for \(R_1\):
Combine terms with \(R_1\):
Determine the time taken by the less efficient pipe:
The rate \(R_1 = \frac{1}{18}\) means the less efficient pipe fills \(\frac{1}{18}\) of the cistern in one hour. Therefore, it will take 18 hours to fill the entire cistern by itself.
Correct Option: D) 18
The less efficient inlet pipe has a rate of \(\frac{1}{18}\) of the cistern per hour, meaning it takes 18 hours to fill the cistern by itself.
The Battle of Plassey was fought on ________.
23rd June 1557
23rd June 1657
23rd June 1857
23rd June 1757
The question asks for the exact date of the Battle of Plassey. This requires knowledge of a specific historical event and its precise timing. Recalling key dates in Indian history is crucial for competitive exams.
D) 23 rd June 1757 is the correct date for the Battle of Plassey. This battle was a pivotal event that established the British East India Company's military and political supremacy in Bengal, eventually leading to British rule over much of India.