The question asks about the presentation of the audit report of an apex co-operative society. This falls under the regulatory and oversight mechanisms for co-operative societies, which are primarily governed by state laws in India. Understanding the hierarchy of accountability for such organizations is key.
B) State Legislature — The audit report of an apex co-operative society, being a state-level organization, is presented to the State Legislature. This ensures legislative oversight, transparency, and accountability to the public through their elected representatives. This is a standard practice for bodies operating under state jurisdiction and often receiving state government support or having significant public impact.
What is the mode of the data given below? [Give your answer correct to 2 decimal places.]
| Age in years | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 | 75-85 |
| No. of patients | 14 | 32 | 39 | 38 | 10 | 36 | 22 |
To find the mode for grouped data, we first identify the modal class, which is the class interval with the highest frequency. Then, we use the formula for the mode of grouped data, which involves the lower limit of the modal class, the class size, and the frequencies of the modal class, the class preceding it, and the class succeeding it.
Correct Option: C) 43.75
When four numbers are in proportion, the product of the extremes is equal to the product of the means. We will set up the proportion and solve for the unknown variable \(y\).
Identify the given numbers: 48, 96, 20, and \(y\).
Understand the definition of proportion: If four numbers \(a, b, c, d\) are in proportion, it means that the ratio of the first two is equal to the ratio of the last two. Mathematically, this is expressed as \(a:b :: c:d\) or \[\frac{a}{b} = \frac{c}{d}\].
Apply the proportion rule to the given numbers:
\[ \frac{48}{96} = \frac{20}{y} \]
Cross-multiply to solve for \(y\):
\[ 48 \times y = 96 \times 20 \]
Isolate \(y\) by dividing both sides by 48:
\[ y = \frac{96 \times 20}{48} \]
Simplify the expression. We can notice that 96 is twice 48:
\[ y = \frac{2 \times 48 \times 20}{48} \]
\[ y = 2 \times 20 \]
\[ y = 40 \]
Correct Option: D) 40
Which of the following was the theme of National Science Day 2025, celebrated on the 28th of February?
Fostering Scientific Excellence through Youth-Driven Research and Innovation in India
Building a Developed Nation through Scientific Thinking and Modern Technology
Empowering Indian Youth for Global Leadership in Science and Innovation for Viksit Bharat
Advancing Scientific Vision through Innovation and Collaborative Growth in Bharat
The question asks for the theme of National Science Day 2025. National Science Day is celebrated annually on February 28th in India. To answer this, one needs to know the official theme declared for the specific year.
The official theme for National Science Day 2025 is "Empowering Indian Youth for Global Leadership in Science and Innovation for Viksit Bharat".
C) Empowering Indian Youth for Global Leadership in Science and Innovation for Viksit Bharat is the correct theme for National Science Day 2025. This theme emphasizes the role of youth in scientific advancement and innovation, aligning with the vision of a developed India (Viksit Bharat).
The question asks about the primary script used for inscriptions during the Mauryan period. This requires knowledge of ancient Indian scripts and their historical usage, particularly during the reign of Emperor Ashoka.
B) Brahmi — The Brahmi script was the most widely used script for Mauryan inscriptions, particularly the edicts of Emperor Ashoka. It is the ancestor of most modern Indian scripts.
The question asks about the time period when the Indus Valley Civilization (IVC) flourished. This requires knowledge of the established chronological timeline for this ancient civilization.
Correct Option: A) 2500–1800 BCE
This problem involves finding the LCM of two numbers given their HCF division method quotients and the last divisor. We will work backward from the last step of the Euclidean algorithm to find the two numbers, and then use the formula \(\text{Product of two numbers} = \text{HCF} \times \text{LCM}\) to find the LCM.
Understand the Euclidean Algorithm (Division Method):
The Euclidean algorithm for finding the HCF of two numbers \(a\) and \(b\) (where \(a > b\)) works as follows:
In this problem, the last divisor is 57, which means the HCF is 57. The quotients are 1, 5, and 8. Let the two numbers be \(A\) and \(B\).
Work backward to find the numbers:
Let the quotients be \(q_1 = 1\), \(q_2 = 5\), \(q_3 = 8\).
The last divisor is 57. This means the HCF is 57. In the last step of the division, the remainder is 0.
The division process can be represented as:
From the last step, \(r_1 = r_2 \times q_3 + 0\). We know that the last non-zero remainder (which is \(r_2\)) is the HCF, which is 57. And \(q_3 = 8\).
So, \(r_1 = 57 \times 8 + 0 = 456\).
Now, move to the second last step:
\(B = r_1 \times q_2 + r_2\)
Substitute \(r_1 = 456\), \(q_2 = 5\), and \(r_2 = 57\):
\(B = 456 \times 5 + 57\)
\(B = 2280 + 57\)
\(B = 2337\)
Finally, move to the first step:
\(A = B \times q_1 + r_1\)
Substitute \(B = 2337\), \(q_1 = 1\), and \(r_1 = 456\):
\(A = 2337 \times 1 + 456\)
\(A = 2337 + 456\)
\(A = 2793\)
So, the two numbers are 2793 and 2337.
Calculate the LCM:
We know the relationship between HCF, LCM, and the two numbers:
\[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \]Therefore,
\[ \text{LCM} = \frac{\text{Product of two numbers}}{\text{HCF}} \]Substitute the values:
\[ \text{LCM} = \frac{2793 \times 2337}{57} \]First, simplify by dividing one of the numbers by the HCF:
\[ \text{LCM} = \frac{2793}{57} \times 2337 \]Divide 2793 by 57:
\[ \frac{2793}{57} = 49 \]Now, multiply 49 by 2337:
\[ \text{LCM} = 49 \times 2337 \]\[ \text{LCM} = 114513 \]
Correct Option: D) 114513
The question asks to identify the country developing the 'Gelephu Mindfulness City' project, which aims to promote economic growth, wellness, and sustainability. This is a factual question related to current affairs and international development projects.
B) Bhutan — Bhutan is indeed developing the 'Gelephu Mindfulness City'. This ambitious project was announced by the King of Bhutan and aims to create a sustainable economic hub rooted in the country's unique philosophy of Gross National Happiness, focusing on economic growth, wellness, and sustainability.
To find the missing number in the series, we need to identify the pattern of differences between consecutive terms. We will calculate the differences between the given numbers and observe if there is a consistent arithmetic progression or another recognizable sequence in these differences.
The complete series with differences is:
356 \(\xrightarrow{-23}\) 333 \(\xrightarrow{-33}\) 300 \(\xrightarrow{-43}\) 257 \(\xrightarrow{-53}\) 204 \(\xrightarrow{-63}\) 141
C) 257