The question asks about the product formed when copper oxide reacts with dilute hydrochloric acid. This is a classic acid-base reaction where a metal oxide (basic in nature) reacts with an acid to form a salt and water. We need to determine the correct oxidation state of copper in the resulting chloride.
\( \text{CuO} (\text{s}) + 2\text{HCl} (\text{aq}) \rightarrow \text{CuCl}_2 (\text{aq}) + \text{H}_2\text{O} (\text{l}) \)
In \(\text{CuCl}_2\), copper has an oxidation state of \(+2\), and chloride ions have an oxidation state of \(-1\).
B) Copper (II) Chloride is formed because copper in copper oxide (\(\text{CuO}\)) is in the \(+2\) oxidation state, and this oxidation state is retained in the salt formed with hydrochloric acid.
The work done in moving a charge +Q across two points having a potential difference K is:
The problem asks for the work done in moving a charge between two points with a given potential difference. The fundamental definition of potential difference relates it directly to the work done per unit charge.
Thus, the work done in moving a charge \(+Q\) across two points having a potential difference \(K\) is \(QK\).
The question asks for the venue of the Fifth Global Standards Symposium (GSS-24). This requires knowledge of recent international events hosted in India, specifically related to telecommunications and digital standards.
Correct Option: C) The Fifth Global Standards Symposium (GSS-24) was held in New Delhi, India. This event, along with the World Telecommunication Standardization Assembly (WTSA-24), marked a significant occasion for India in the global telecommunications sector.
A scheme like 'Buy 5, Get 6' on the same kind of articles with the same marked price offers a _____ discount.
20%
16 \( \frac{2}{3} \)%
11 \( \frac{1}{9} \)%
17.5%
This problem involves calculating the percentage discount offered in a "Buy X, Get Y free" type of scheme. The key is to understand that the discount is calculated on the total number of articles received, not just the ones paid for.
B) 16 \( \frac{2}{3} \)% is the correct discount percentage.
This problem involves calculating the cost price based on a given selling price and profit percentage. We need to find out how many toffees were bought for a rupee, given that selling 10 toffees for a rupee resulted in a 20% profit.
Let the Selling Price (SP) of 10 toffees be 1 rupee.
\[ \text{SP of 10 toffees} = ₹1 \]The vendor gained 20%. The formula relating SP, Cost Price (CP), and profit percentage is:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]Substitute the given values into the formula:
\[ ₹1 = \text{CP} \times \left(1 + \frac{20}{100}\right) \] \[ ₹1 = \text{CP} \times \left(1 + 0.20\right) \] \[ ₹1 = \text{CP} \times 1.20 \]Now, calculate the Cost Price (CP) of 10 toffees:
\[ \text{CP} = \frac{₹1}{1.20} \] \[ \text{CP} = \frac{100}{120} \text{ rupees} \] \[ \text{CP} = \frac{5}{6} \text{ rupees} \]So, the cost price of 10 toffees was \(₹\frac{5}{6}\).
The question asks how many toffees he bought for a rupee. We know that 10 toffees cost \(₹\frac{5}{6}\). We need to find out how many toffees can be bought for \(₹1\).
If \(₹\frac{5}{6}\) buys 10 toffees,
Then \(₹1\) will buy:
\[ \text{Number of toffees} = 10 \times \frac{1}{\frac{5}{6}} \] \[ \text{Number of toffees} = 10 \times \frac{6}{5} \] \[ \text{Number of toffees} = 2 \times 6 \] \[ \text{Number of toffees} = 12 \]Therefore, the vendor bought 12 toffees for a rupee.
B) 12 — As calculated, the cost price of 10 toffees was \(₹\frac{5}{6}\). To find out how many toffees were bought for \(₹1\), we perform the inverse calculation, which gives 12 toffees.
Which of the following options gives the correct expression for y, when \(\frac{\cos^2A}{1-\sin A}\) = y, and sinA ≠ 1?
The problem asks us to simplify the given trigonometric expression \(\frac{\cos^2A}{1-\sin A}\) and find the equivalent expression for \(y\). We will use the fundamental trigonometric identity \(\sin^2A + \cos^2A = 1\) to rewrite \(\cos^2A\) in terms of \(\sin A\) and then factorize the numerator to simplify the fraction.
Given the expression:
\[ y = \frac{\cos^2A}{1-\sin A} \]We know the fundamental trigonometric identity:
\[ \sin^2A + \cos^2A = 1 \]From this identity, we can express \(\cos^2A\) as:
\[ \cos^2A = 1 - \sin^2A \]Substitute this expression for \(\cos^2A\) into the original equation:
\[ y = \frac{1 - \sin^2A}{1 - \sin A} \]The numerator \(1 - \sin^2A\) is in the form of \(a^2 - b^2\), which can be factored as \((a-b)(a+b)\). Here, \(a=1\) and \(b=\sin A\). So, \(1 - \sin^2A = (1 - \sin A)(1 + \sin A)\).
Substitute the factored form into the expression for \(y\):
\[ y = \frac{(1 - \sin A)(1 + \sin A)}{1 - \sin A} \]Given that \(\sin A \neq 1\), we know that \(1 - \sin A \neq 0\). Therefore, we can cancel out the common term \((1 - \sin A)\) from the numerator and the denominator:
\[ y = 1 + \sin A \]Rearranging the terms, we get:
\[ y = \sin A + 1 \]C) \(\sin A + 1\) is the correct expression for \(y\) after simplifying the given trigonometric expression.
The question asks about the system responsible for removing nitrogenous waste products generated by metabolic activities in human beings. We need to identify the organ system specifically designed for this function.
Correct Option: B) the excretory system is responsible for filtering blood and removing metabolic waste products, including nitrogenous wastes, from the body.
The problem asks us to analyze two statements and determine their relationship: whether they are independent causes, effects of independent causes, or if one is the cause of the other. We need to evaluate each statement for its potential as a cause or effect and see if a logical connection exists between them.
B) Both I and II are effects of independent causes. Statement I (teachers leaving) is likely an effect of issues related to school management, compensation, or opportunities. Statement II (football team winning) is an effect of factors like good coaching, player talent, and training. There is no direct causal link between the two events, and their underlying reasons are distinct.
The problem presents a number series and asks us to find the missing term. We need to identify the pattern or rule governing the series to determine the missing number.
The term before the question mark is 25. Applying the rule:
\[ \text{Missing Term} = 25 \times 2 - 1 = 50 - 1 = 49 \]If the missing term is 49, let's check if the next term (97) follows the rule:
\[ 49 \times 2 - 1 = 98 - 1 = 97 \]This matches the given term 97.
Let's check the last term (193):
\[ 97 \times 2 - 1 = 194 - 1 = 193 \]This also matches the given term 193.
Correct Option: B) 49
All 36 people are standing in a row, facing north. Aman is 11th from the left end, while Pratha is 12th from the right end. How many people are there between Aman and Pratha?
The problem asks us to find the number of people between Aman and Pratha in a row of 36 people. We are given Aman's position from the left and Pratha's position from the right. We need to determine if their positions overlap or not, and then calculate the number of people between them.
The position of a person from the right end can be found using the formula:
\[ \text{Position from right} = \text{Total people} - \text{Position from left} + 1 \]For Aman:
\[ \text{Aman's position from right} = 36 - 11 + 1 = 26 \]So, Aman is 26th from the right end.
The position of a person from the left end can be found using the formula:
\[ \text{Position from left} = \text{Total people} - \text{Position from right} + 1 \]For Pratha:
\[ \text{Pratha's position from left} = 36 - 12 + 1 = 25 \]So, Pratha is 25th from the left end.
Aman is 11th from the left. Pratha is 25th from the left. Since Aman's position (11th) is less than Pratha's position (25th) from the left, Aman is to the left of Pratha. There is no overlap in their counting from opposite ends.
To find the number of people between two individuals when their positions are known from the same end (e.g., from the left), we use the formula:
\[ \text{People between} = \text{Position of rightmost person} - \text{Position of leftmost person} - 1 \]Using their positions from the left:
Number of people between Aman and Pratha:
\[ 25 - 11 - 1 = 14 - 1 = 13 \]Alternatively, we can sum their individual counts and subtract from the total:
\[ \text{Total people} - (\text{Aman's position from left} + \text{Pratha's position from right}) \] \[ 36 - (11 + 12) = 36 - 23 = 13 \]Both methods yield the same result.
D) 13. There are 13 people between Aman and Pratha.