To determine which assumptions are implicit in the advertisement, we need to analyze the statement "Buy pure and natural honey of company Z" and consider what must be true for such an advertisement to make sense or be effective. An implicit assumption is something that is not stated directly but is taken for granted or necessarily implied by the statement.
Based on this analysis, only Assumption I is implicitly conveyed by the advertisement.
Correct Option: B) Only assumption I is implicit.
The problem involves properties of tangents drawn from an external point to a circle. We are given the length of the tangents and the angle between them. We need to find the length of the chord connecting the points of tangency. We will use the property that tangents from an external point are equal in length, which forms an isosceles triangle. Then, we will use the given angle to determine the type of triangle formed.
Correct Option: A) The length of the chord AB is 12 cm because the triangle formed by the external point and the points of tangency is an equilateral triangle.
The question asks for the city where the Human Space Flight Centre (HSFC) was inaugurated by Dr. K. Kasturirangan in 2019. This is a factual question related to India's space program, specifically ISRO's human spaceflight initiative.
Correct Option: C) Bangalore
The question asks about the origin of the 'Five-Year Plan' feature in the Indian Constitution. This requires knowledge of the sources of various provisions of the Indian Constitution, a common topic in Indian competitive exams.
Correct Option: D) USSR
The concept of Five-Year Plans for economic development was adopted by India from the Constitution of the Union of Soviet Socialist Republics (USSR). The USSR was the first country to implement nationwide Five-Year Plans to achieve rapid industrialization and economic growth. India, under its first Prime Minister Jawaharlal Nehru, was greatly influenced by the Soviet model of planned economy and adopted it to guide its own post-independence development, although with a democratic framework.
To find the Highest Common Factor (HCF) of two algebraic expressions, we need to find the HCF of their numerical coefficients and the HCF of their variable parts separately. For the variable parts, the HCF is formed by taking the lowest power of each common variable present in both expressions.
Correct Option: B) \( 14 p^{3}q^{2} \)
As calculated, the HCF of \( 28 p^{5}q^{2} \) and \( 70 p^{3}q^{4} \) is \( 14 p^{3}q^{2} \).
To determine the effect of increasing each entry of a data set by a constant value on its arithmetic mean, we can use the definition of the arithmetic mean. We will consider a general set of data points, calculate its initial mean, and then calculate the mean after each data point is increased by 7.
Let the given data set be \(x_1, x_2, x_3, \dots, x_n\), where \(n\) is the number of entries.
The arithmetic mean (let's call it \(\bar{X}\)) of this data set is given by the formula:
\[ \bar{X} = \frac{x_1 + x_2 + \dots + x_n}{n} = \frac{\sum_{i=1}^{n} x_i}{n} \]
According to the problem, each entry of the data is increased by 7. So, the new data set will be:
\[ (x_1 + 7), (x_2 + 7), \dots, (x_n + 7) \]
Let the new arithmetic mean be \(\bar{X}'\). It is calculated as the sum of the new entries divided by the number of entries:
\[ \bar{X}' = \frac{(x_1 + 7) + (x_2 + 7) + \dots + (x_n + 7)}{n} \]
We can rearrange the terms in the numerator:
\[ \bar{X}' = \frac{(x_1 + x_2 + \dots + x_n) + (7 + 7 + \dots + 7 \text{ (n times)})}{n} \]
\[ \bar{X}' = \frac{\sum_{i=1}^{n} x_i + n \times 7}{n} \]
Now, we can split the fraction:
\[ \bar{X}' = \frac{\sum_{i=1}^{n} x_i}{n} + \frac{n \times 7}{n} \]
From step 1, we know that \(\frac{\sum_{i=1}^{n} x_i}{n} = \bar{X}\).
Substituting this into the equation for \(\bar{X}'\):
\[ \bar{X}' = \bar{X} + 7 \]
This shows that the new arithmetic mean is equal to the original arithmetic mean plus 7.
Correct Option: C) increases by 7
The question asks to identify which of the given countries is NOT a Permanent Member of the United Nations Security Council. This requires knowledge of the composition of the UN Security Council.
Correct Option: B) Canada is not a Permanent Member of the Security Council. It serves as a non-permanent member from time to time, elected for two-year terms by the General Assembly.
To find the correct mean, we first need to calculate the incorrect sum of observations. Then, we adjust this sum by subtracting the wrongly noted value and adding the correct value. Finally, we divide the corrected sum by the total number of observations to get the correct mean.
Calculate the incorrect sum of observations:
The mean of 20 observations is 22.5. The formula for the mean is:
So, the incorrect sum of observations can be calculated as:
\[ \text{Incorrect Sum} = \text{Mean} \times \text{Number of observations} \]Given:
Adjust the sum for the error:
One observation was wrongly noted as \(-25\) instead of \(25\). To correct the sum, we need to subtract the wrong value and add the correct value.
Given:
This simplifies to:
\[ \text{Correct Sum} = 450 + 25 + 25 \]So,
\[ \text{Correct Sum} = 450 + 50 = 500 \]Calculate the correct mean:
Now, divide the correct sum by the number of observations.
Given:
Correct Option: B) 25
The question asks to identify the state among the given options that has more than one seat in the Lok Sabha. This requires knowledge of the number of Lok Sabha constituencies allocated to each state in India.
Based on this information, Meghalaya is the only state among the options with more than one Lok Sabha seat.
C) Meghalaya — Meghalaya has 2 Lok Sabha seats, which is more than one.
The question asks about Clement Attlee's visit to India as a member of a specific commission or mission. To answer this, we need to recall the historical context of British commissions and missions sent to India and identify which one included Clement Attlee before he became Prime Minister.
B) Simon Commission — Clement Attlee was one of the seven members of the Simon Commission, which arrived in India in 1928 to study constitutional reforms.