The problem asks us to identify symbols in a given series that satisfy two conditions: they must be immediately preceded by a number and immediately followed by another symbol. We need to scan the series from left to right and check each symbol against these conditions.
C) Two. There are two symbols, '*' and '&', that are immediately preceded by a number and immediately followed by another symbol.
The problem describes a relationship between a whole number and its two parts. We need to set up an algebraic equation based on the given conditions and then solve for the ratio of the second part to the first part.
Let the whole number be \(N\).
Let the two parts be \(x\) and \(y\). So, \(N = x + y\).
According to the problem statement, "5 times the first part added to 14 times the second part makes 7 times the whole". We can write this as an equation:
\[ 5x + 14y = 7N \]Substitute \(N = x + y\) into the equation:
\[ 5x + 14y = 7(x + y) \]Expand the right side of the equation:
\[ 5x + 14y = 7x + 7y \]Rearrange the terms to group \(x\) terms on one side and \(y\) terms on the other side. Subtract \(5x\) from both sides:
\[ 14y = 7x + 7y - 5x \]\[ 14y = 2x + 7y \]Subtract \(7y\) from both sides:
\[ 14y - 7y = 2x \]\[ 7y = 2x \]The question asks for the ratio of the second part to the first part, which is \(\frac{y}{x}\). To find this ratio, divide both sides by \(x\) (assuming \(x \neq 0\)) and then divide by 7:
\[ \frac{7y}{x} = \frac{2x}{x} \]\[ \frac{7y}{x} = 2 \]\[ \frac{y}{x} = \frac{2}{7} \]The ratio of the second part to the first part is \(2:7\).
B) 2 : 7 — As derived from the algebraic equation, the ratio of the second part (\(y\)) to the first part (\(x\)) is \(2:7\).
The question asks about the characteristics and functions of trichomes found on the stem. We need to evaluate each option based on the known biological properties of trichomes in plants.
Based on this analysis, option B provides an accurate description of some common characteristics of trichomes.
Correct Option: B) They are multicellular and may be secretory.
The problem asks us to identify a sequence of numbers that follows the same mathematical operation pattern as two given sets of numbers. We need to analyze the relationship between consecutive numbers in the given sets to find the underlying rule.
D) 6 - 12 - 24 - 48
This option perfectly matches the identified rule of multiplying by 2 for each step.
This problem requires us to substitute the given symbols with their corresponding mathematical operators and then evaluate each expression following the order of operations (BODMAS/PEMDAS) to find which one results in 5.
First, let's list the symbol-operator mappings:
Now, we will evaluate each option:
Substitute the operators:
\[ 96 + 12 \times 45 \div 3 - 14 \]The result is 262, not 5.
Substitute the operators:
\[ 96 \times 12 - 45 \div 3 + 14 \]The result is 1151, not 5.
Substitute the operators:
\[ 96 \div 12 - 45 + 3 \times 14 \]The result is 5.
Substitute the operators:
\[ 96 - 12 + 45 \times 3 \div 14 \]The result is approximately 93.64, not 5.
Correct Option: C) 96 A 12 D 45 C 3 B 14
To find the correct average weight, we first need to calculate the initial total weight based on the given average. Then, we identify the errors in reading the weights and adjust the total weight accordingly. Finally, we divide the corrected total weight by the number of boys to get the correct average.
Calculate the initial total weight:
Given that the average weight of 10 boys is 70 kg.
Identify the errors and calculate the correction needed:
There are two types of errors:
Let's calculate the total error:
Now, calculate the net correction:
\[ \text{Net Correction} = (2 \times (54 - 44)) - (40 - 35) \]\[ \text{Net Correction} = (2 \times 10) - 5 \]\[ \text{Net Correction} = 20 - 5 = 15 \text{ kg} \]Calculate the correct total weight:
Add the net correction to the initial total weight.
Calculate the correct average weight:
Divide the correct total weight by the number of boys.
B) 71.5 kg is the correct average weight of the 10 boys.
The question asks about the integration of co-operatives into India's planning initiatives after independence. We need to identify the overarching framework that guided India's economic and social development, within which co-operatives played a significant role.
Correct Option: C) Five-Year Plans — Co-operatives were explicitly recognized and promoted as a key strategy for economic development and social justice within the framework of India's Five-Year Plans, right from the First Five-Year Plan onwards.
The question asks to identify the factor that does NOT significantly contribute to the degradation of the Thar Desert ecosystem. We need to evaluate each option based on its known impact on desert environments.
Therefore, increased plantation of native trees is the factor that does NOT contribute much to the degradation of the Thar Desert ecosystem; in fact, it helps in its restoration.
Correct Option: D) Increased plantation of native trees
The question asks to identify the personality known as the 'Father of the Indian Renaissance' based on their contributions to social reform, literary works, and patriotism. This requires knowledge of prominent figures in Indian history and their specific roles during the 19th century reform movements.
D) Raja Ram Mohan Roy is widely regarded as the 'Father of the Indian Renaissance' and the 'Father of Modern India'. He was a towering figure who initiated significant social reforms, including the abolition of Sati, advocating for women's rights, and promoting modern education. His literary works and journalistic endeavors played a crucial role in shaping public opinion and fostering a spirit of reform and patriotism in India.
The given series is a numerical series where each subsequent number is obtained by subtracting a progressively increasing odd number from the previous term. We need to identify the pattern of subtraction to find the missing term.
The differences are 1, 3, 5, 7. This is a sequence of consecutive odd numbers.
Following the pattern of odd numbers (1, 3, 5, 7), the next odd number is 9.
Subtract the next difference (9) from the last given term (485):
\[ 485 - 9 = 476 \]The missing term in the series is 476.
D) 476 — As determined by following the pattern of subtracting consecutive odd numbers (1, 3, 5, 7, 9) from the preceding terms.