We need to determine who sits on the extreme right end of a line of five people (A, B, C, D, E) facing north. We will analyze each statement individually and then combine them to see if a unique arrangement can be formed.
Analyze Statement I: Exactly three people sit between B and C.
Since there are five people in total, if three people sit between B and C, B and C must be at the ends of the line. The possible arrangements are:
In the first case, B is at the extreme right. In the second case, C is at the extreme right. This statement alone is not sufficient to determine who sits on the extreme right.
Analyze Statement II: A sits immediately to the left of B.
This statement tells us the relative position of A and B: A B. However, it gives no information about C, D, or E, or their positions relative to the ends of the line. Therefore, this statement alone is not sufficient to determine who sits on the extreme right.
Combine Statement I and Statement II.
From Statement I, we have two possibilities:
Case 1: C _ _ _ B
Case 2: B _ _ _ C
From Statement II, we know that A sits immediately to the left of B (A B).
Let's try to fit "A B" into Case 1: C _ _ _ B. If A is immediately to the left of B, the arrangement would be C _ _ A B. This arrangement has 5 positions, and A and B are in the 4th and 5th positions respectively. This is a valid arrangement. In this case, B is at the extreme right.
Let's try to fit "A B" into Case 2: B _ _ _ C. If A is immediately to the left of B, then A must be to the left of the first position, which is impossible as B is at the extreme left. So, this case (B _ _ _ C) is not possible when combined with Statement II.
Therefore, the only possible arrangement is C _ _ A B. The five positions are:
Position 1: C
Position 2: (D or E)
Position 3: (E or D)
Position 4: A
Position 5: B
In this unique arrangement, B sits on the extreme right end.
B) Both Statements I and II put together (and not independently) are sufficient to answer the question.
When both statements are combined, we can uniquely determine the seating arrangement (C, D/E, E/D, A, B), and thus B sits on the extreme right end.
The problem asks us to identify numbers in a given series that are immediately preceded by a number and immediately followed by a number. We need to scan the series from left to right and look for the pattern "Number - Number - Number".
* 5 2 # # 2 2 7 & % 2 \( & 1 3 \) % $ 5 4 $ \(* 5 2: Here, 5 is preceded by a symbol (*) and followed by a number (2). This is not N N N.5 2 #: Here, 2 is preceded by a number (5) but followed by a symbol (#). This is not N N N.# # 2: Here, 2 is preceded by a symbol (#) and followed by a symbol (#). This is not N N N.# 2 2: Here, 2 is preceded by a symbol (#) and followed by a number (2). This is not N N N.2 2 7: Here, 2 is preceded by a number (2) and followed by a number (7). This matches our condition! So, 2 is one such number.2 7 &: Here, 7 is preceded by a number (2) but followed by a symbol (&). This is not N N N.7 & %: Here, & is a symbol.& % 2: Here, 2 is preceded by symbols.% 2 \): Here, 2 is preceded by a symbol (%) and followed by a symbol (\(). This is not N N N.2 \) &: Here, \( is a symbol.\) & 1: Here, 1 is preceded by symbols.& 1 3: Here, 1 is preceded by a symbol (&) and followed by a number (3). This is not N N N.1 3 \(: Here, 3 is preceded by a number (1) but followed by a symbol (\)). This is not N N N.3 \( %: Here, \) is a symbol.\( % \): Here, % is a symbol.% $ 5: Here, 5 is preceded by symbols.$ 5 4: Here, 5 is preceded by a symbol (\() and followed by a number (4). This is not N N N.5 4 \): Here, 4 is preceded by a number (5) but followed by a symbol (\(). This is not N N N.4 \) \(: Here, \) is a symbol.A) 1 — There is only one such number (the second '2' in '2 2 7') that is immediately preceded by a number and immediately followed by a number.
This question asks about the product formed when sodium sulphate solution reacts with barium chloride solution. This is a classic example of a double displacement reaction, specifically a precipitation reaction, where two soluble ionic compounds react to form an insoluble product (precipitate) and another soluble product.
Therefore, the precipitate formed is barium sulphate.
Correct Option: A) barium sulphate — As explained in the step-by-step process, barium sulphate is an insoluble compound formed from the reaction of barium ions and sulphate ions, leading to its precipitation.
The question asks about the nature of demand for an individual firm's product in a monopolistically competitive market. To answer this, we need to understand the characteristics of monopolistic competition, especially regarding product differentiation and the number of firms.
B) Relatively elastic — In monopolistic competition, firms sell differentiated products, giving them some market power and a downward-sloping demand curve. However, because there are many close substitutes available from other firms, consumers are quite sensitive to price changes. If a firm raises its price, many customers will switch to a competitor's product, leading to a relatively large drop in quantity demanded. Therefore, the demand for an individual firm's product is relatively elastic.
An unsaturated hydrocarbon that has a double bond is:
The question asks to identify an unsaturated hydrocarbon with a double bond. Unsaturated hydrocarbons contain at least one double or triple bond between carbon atoms. Specifically, those with a double bond belong to the alkene series. Alkenes follow the general formula \(C_nH_{2n}\).
B) \(C_3H_6\) is an alkene (propene) because it follows the general formula \(C_nH_{2n}\) for \(n=3\). Alkenes are unsaturated hydrocarbons with one carbon-carbon double bond.
A trader lost 10% by selling a shirt for ₹850. He will gain x% by selling it for ₹1,530. The value of x is:
The problem involves calculating profit percentage after an initial loss. We need to first find the Cost Price (CP) using the given Selling Price (SP) and loss percentage. Once the CP is known, we can calculate the new profit percentage when the item is sold at a different SP.
D) 62
Find the mean of the following frequency distribution.
| x | 5 | 6 | 15 | 9 | 8 |
| f | 10 | 5 | 8 | 10 | 9 |
7\( \frac{13}{21} \)
8\( \frac{13}{21} \)
9\( \frac{13}{21} \)
6\( \frac{13}{21} \)
To find the mean of a frequency distribution, we use the formula for the arithmetic mean, which is the sum of the products of each observation (\(x\)) and its corresponding frequency (\(f\)), divided by the sum of the frequencies.
| \(x\) | \(f\) | \(f \times x\) |
|---|---|---|
| 5 | 10 | 50 |
| 6 | 5 | 30 |
| 15 | 8 | 120 |
| 9 | 10 | 90 |
| 8 | 9 | 72 |
B) \(8 \frac{13}{21}\) is the correct mean calculated from the given frequency distribution.
The question asks to identify the Union Minister of Panchayati Raj appointed in June 2024. This is a current affairs question related to recent cabinet appointments in the Indian government.
Correct Option: A) Rajiv Ranjan Singh was appointed as the Union Minister of Panchayati Raj in June 2024. He also holds the portfolio of Minister of Fisheries, Animal Husbandry and Dairying.
The question asks to identify the scientist credited with the discovery of electromagnetic induction. This requires knowledge of fundamental discoveries in physics and their associated scientists.
Correct Option: A) Michael Faraday is widely credited with the discovery of electromagnetic induction in 1831. His experiments demonstrated that a changing magnetic field can induce an electric current.
The question asks why an electric fan becomes warm after continuous use. This phenomenon is related to the principles of electricity and energy conversion. We need to identify the primary reason for heat generation in an electrical appliance.
C) heating effect of the current flowing through the fan
This option correctly identifies the Joule heating effect as the primary reason for the fan becoming warm. The electrical resistance of the motor windings converts electrical energy into heat, especially when used for extended periods.