The question asks to identify the correct statements regarding the Industrial Sector in India. We need to evaluate each statement based on common knowledge about industrial policies, economic principles, and the role of industry in development.
Since all three statements are correct, the option that includes 1, 2, and 3 is the right answer.
Correct Option: B) 1, 2 and 3
This problem involves decoding a relationship expression based on given symbolic codes. We need to break down the expression 'M ÷ N + O × P – Q' step-by-step, determining the relationship between each pair of individuals, and then combine these relationships to find how M is related to Q.
Correct Option: D) Brother's Wife's Father
M is the father of O. O is the wife of P. P is the brother of Q. Therefore, M is the father of (P's wife), and P is Q's brother. So, M is Q's brother's wife's father.
The question asks to identify the Indian leader whose birth anniversary is celebrated as National Youth Day in January. This is a factual question related to important days and personalities in Indian history.
Correct Option: C) Swami Vivekananda
National Youth Day is celebrated every year on January 12th to commemorate the birth anniversary of Swami Vivekananda. The Government of India declared this day as National Youth Day in 1984, stating that "the philosophy of Swamiji and the ideals for which he lived and worked could be a great source of inspiration for the Indian Youth."
This problem involves calculating the combined rate of two taps, one filling and one emptying, to determine the time required to fill a specific fraction of a tank. We will find the individual rates, then the net rate, and finally the time taken for the required volume.
Calculate the filling rate of the first tap:
The first tap fills the cistern in 18 hours. So, in one hour, it fills \(\frac{1}{18}\) of the tank.
Calculate the emptying rate of the second tap:
The second tap empties the full tank in 24 hours. So, in one hour, it empties \(\frac{1}{24}\) of the tank.
Calculate the net filling rate when both taps are open:
Since one tap fills and the other empties, the net rate is the difference between their individual rates.
To subtract these fractions, find a common denominator, which is the least common multiple (LCM) of 18 and 24. The LCM of 18 (2 \(\times\) 3\(\times\) 3) and 24 (2 \(\times\) 2 \(\times\) 2 \(\times\) 3) is 72.
\[ \text{Net filling rate} = \frac{4}{72} - \frac{3}{72} = \frac{1}{72} \]So, when both taps are open, \(\frac{1}{72}\) of the tank is filled in one hour.
Calculate the time to fill the entire tank:
If \(\frac{1}{72}\) of the tank is filled in 1 hour, then the entire tank will be filled in 72 hours.
Calculate the time to fill three-fourth of the tank:
We need to find the time to fill \(\frac{3}{4}\) of the tank. This will be \(\frac{3}{4}\) of the time it takes to fill the whole tank.
C) 54
We are given the sum of three numbers, the sum of their products taken two at a time, and their product. We need to find the sum of their cubes. We will use the algebraic identity for the sum of cubes of three numbers, which relates these given values.
Identify the given information:
Recall the algebraic identity for the sum of cubes:
The relevant identity is:
Find the value of \(a^2 + b^2 + c^2\):
We know that \((a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)\).
Rearranging this, we get:
Substitute the given values into the expression for \(a^2 + b^2 + c^2\):
\[ a^2 + b^2 + c^2 = (5)^2 - 2(-2) \]\[ a^2 + b^2 + c^2 = 25 - (-4) \]\[ a^2 + b^2 + c^2 = 25 + 4 \]\[ a^2 + b^2 + c^2 = 29 \]Substitute all known values into the main identity for \(a^3 + b^3 + c^3\):
From step 2, we have:
Plug in the values:
So, the equation becomes:
\[ a^3 + b^3 + c^3 - 3(3) = (5)(29 - (-2)) \]\[ a^3 + b^3 + c^3 - 9 = (5)(29 + 2) \]\[ a^3 + b^3 + c^3 - 9 = (5)(31) \]\[ a^3 + b^3 + c^3 - 9 = 155 \]Solve for \(a^3 + b^3 + c^3\):
\[ a^3 + b^3 + c^3 = 155 + 9 \]\[ a^3 + b^3 + c^3 = 164 \]Correct Option: A) 164
The problem presents a numerical series, and we need to find the missing term. We will analyze the differences between consecutive terms to identify a pattern. Once the pattern is established, we will apply it to find the next term in the series.
D) 912 is the correct answer because the pattern of differences between consecutive terms is an increasing sequence of even numbers (2, 4, 6, 8, ...). The next difference is 10, so \(922 - 10 = 912\).
The problem presents a series of letter-number clusters. To find the missing cluster, we need to identify the pattern in the letters and the numbers separately.
B (2), E (5), H (8), K (11)
The pattern is an increment of 3 in alphabetical position:
Following this pattern, the next letter will be \(11 + 3 = 14\), which corresponds to the letter N.
I (9), L (12), O (15), R (18)
The pattern is an increment of 3 in alphabetical position:
Following this pattern, the next letter will be \(18 + 3 = 21\), which corresponds to the letter U.
16, 24, 32, 40
The pattern is an increment of 8:
Following this pattern, the next number will be \(40 + 8 = 48\).
The next cluster in the series is NU48.
B) NU48 is the correct option as it follows all the identified patterns for the first letter, second letter, and the number.
To find the speed of the boat in still water, we first need to calculate the speed upstream and the speed downstream. We can then use these two speeds to find the speed of the boat and the speed of the current.
The speed of the boat in still water is 10 km/hr.
D) 10 km/hr is the correct answer, as calculated above.
The question asks about specific amendments introduced in 2024 to the Companies Act concerning Corporate Social Responsibility (CSR) transparency in India. To answer this, one needs to be aware of the recent regulatory changes in the CSR framework.
A) Mandatory quarterly CSR reporting accompanied by independent audits. This measure directly addresses the enhancement of transparency by requiring more frequent and verified disclosures of CSR activities and expenditures. Such a requirement ensures that stakeholders have up-to-date information and that the reported activities are credible, thereby significantly improving accountability and transparency in CSR spending.
The question asks to identify the option that best describes the principle of 'collective executive responsibility' as it applies to the Council of Ministers in India. This is a fundamental concept in parliamentary democracy, enshrined in the Indian Constitution.
C) All ministers share full responsibility for government decisions. This option correctly encapsulates the principle of collective executive responsibility, where the Council of Ministers acts as a team, and all members are jointly accountable for the government's policies and actions before the Parliament.