The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to find the positional value of each letter and then look for a consistent mathematical relationship within each pair and between the two clusters of each pair.
Let's analyze each option:
Let's summarize the patterns:
From the summary, we can see that options A, B, and D follow a consistent pattern: the difference between letters within each cluster is 5, and the difference between corresponding letters of the two clusters is 3. Option C, however, has a difference of 4 within each cluster and a difference of 2 between corresponding letters of the two clusters.
Correct Option: C) LP-NR is the odd one out.
The question asks to identify the rhino species most vulnerable to climate change according to the '2024 State of the Rhino' Report by the International Rhino Foundation (IRF). This requires knowledge of the specific findings or highlights of this particular report.
C) Black Rhino: The '2024 State of the Rhino' Report by the International Rhino Foundation (IRF) specifically highlights the Black Rhino as a species that could be severely affected by climate change. Their habitats in arid and semi-arid parts of Africa make them particularly vulnerable to increased droughts, water scarcity, and extreme temperatures, which are exacerbated by climate change.
This problem involves a percentage reduction in price and a corresponding increase in the quantity of goods that can be purchased for a fixed amount of money. We can solve this by first calculating the effective amount of money saved due to the price reduction, which then allows the purchase of the extra quantity. From this, we can find the new price and subsequently the original price.
Calculate the amount saved: The price of sugar is reduced by 20%. The purchaser has ₹160 to spend. The saving in money for the original quantity that could have been bought is 20% of ₹160.
\[ \text{Amount saved} = 20\% \text{ of } \text{₹}160 = \frac{20}{100} \times 160 = \text{₹}32 \]Determine the new price per kg: This saved amount of ₹32 enables the purchaser to obtain 2.5 kg more sugar. Therefore, ₹32 is the cost of 2.5 kg of sugar at the new (reduced) price.
\[ \text{New price per kg} = \frac{\text{Amount saved}}{\text{Extra quantity}} = \frac{\text{₹}32}{2.5 \text{ kg}} = \text{₹}12.80 \text{ per kg} \]Calculate the original price per kg: The new price is 20% less than the original price. This means the new price is \(100\% - 20\% = 80\%\) of the original price.
Let the original price be \(P_{\text{original}}\).
\[ P_{\text{new}} = 80\% \text{ of } P_{\text{original}} \] \[ \text{₹}12.80 = \frac{80}{100} \times P_{\text{original}} \] \[ P_{\text{original}} = \frac{\text{₹}12.80 \times 100}{80} \] \[ P_{\text{original}} = \frac{\text{₹}1280}{80} = \text{₹}16 \text{ per kg} \]B) The original price per kg of sugar is ₹16.
When two trains travel in the same direction and cross each other, their relative speed is the difference between their individual speeds. The total distance covered during the crossing is the sum of their lengths. We will use the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\) to find the unknown length of the second train.
Identify the given values:
Calculate the relative speed:
Since the trains are moving in the same direction, the relative speed is the difference between their speeds.
Convert units to be consistent:
The speeds are in km/h, time in minutes, and lengths in meters. Convert the relative speed to m/s and time to seconds.
Calculate the total distance covered:
When two trains cross each other completely, the total distance covered is the sum of their lengths.
Apply the distance formula:
\[ D = S_{\text{rel}} \times T \]\[ L_1 + L_2 = S_{\text{rel}} \times T \]\[ 125 \text{ m} + L_2 = 5 \text{ m/s} \times 60 \text{ s} \]\[ 125 \text{ m} + L_2 = 300 \text{ m} \]Solve for the length of the second train (\(L_2\)):
\[ L_2 = 300 \text{ m} - 125 \text{ m} \]\[ L_2 = 175 \text{ m} \]Correct Option: A) 175 m
The question describes a specific arrangement of insulated copper wire: many circular turns wrapped closely in the shape of a cylinder. We need to identify the electrical component that matches this description.
Correct Option: B) A solenoid is formed by a coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder. This arrangement is designed to produce a uniform magnetic field inside the coil when current flows through it.
The question asks about the indigenously developed technology used in the AKASH-NG missile's flight test in 2024. This requires knowledge of recent developments in India's missile technology, specifically regarding the AKASH-NG system.
B) Radio Frequency Seeker — The AKASH-NG missile successfully flight-tested its indigenously developed Radio Frequency (RF) Seeker during its trials in 2024. This seeker is a critical technology for the missile's terminal guidance, enabling it to track and intercept targets effectively.
To solve this problem, we need to apply the given rules to each letter in the word MAJESTIC. We will identify each letter as either a consonant or a vowel and then change it according to the specified alphabetical order rules. Finally, we will count the number of vowels in the newly formed group of letters.
Correct Option: B) One
This problem involves work and time concepts. We will use the idea that the amount of work done is inversely proportional to the time taken. If a person completes a work in 'n' days, their one day's work is \(1/n\). We'll set up equations based on the given information and solve for the time B alone takes.
Let the time taken by A, B, and C to complete the work alone be \(t_A\), \(t_B\), and \(t_C\) days, respectively.
From the first statement, "A can do a certain work in the same time in which B and C together can do it", we can write their one day's work as:
\[ \frac{1}{t_A} = \frac{1}{t_B} + \frac{1}{t_C} \quad \text{(Equation 1)} \]From the second statement, "A and B together could do it in 10 days", their combined one day's work is:
\[ \frac{1}{t_A} + \frac{1}{t_B} = \frac{1}{10} \quad \text{(Equation 2)} \]From the third statement, "C alone in 50 days", we have:
\[ t_C = 50 \text{ days} \]Substitute the value of \(1/t_C\) into Equation 1:
\[ \frac{1}{t_A} = \frac{1}{t_B} + \frac{1}{50} \quad \text{(Equation 3)} \]Now we have a system of two equations (Equation 2 and Equation 3) with two unknowns (\(t_A\) and \(t_B\)). Substitute Equation 3 into Equation 2:
\[ \left( \frac{1}{t_B} + \frac{1}{50} \right) + \frac{1}{t_B} = \frac{1}{10} \]Combine the terms with \(1/t_B\):
\[ \frac{2}{t_B} + \frac{1}{50} = \frac{1}{10} \]Isolate the term with \(1/t_B\):
\[ \frac{2}{t_B} = \frac{1}{10} - \frac{1}{50} \]Find a common denominator for the right side:
\[ \frac{2}{t_B} = \frac{5}{50} - \frac{1}{50} \]\[ \frac{2}{t_B} = \frac{4}{50} \]\[ \frac{2}{t_B} = \frac{2}{25} \]Solve for \(t_B\):
\[ t_B = 25 \text{ days} \]D) 25 days. Based on our calculations, B alone can complete the work in 25 days.
We need to determine the seating arrangement of seven people (B, C, D, E, F, G, K) in a straight line, all facing north. We will use the given clues to deduce their positions and then identify the person sitting third from the right end.
Clue 1: Only E sits to the right of K.
This is a crucial clue. If only E sits to the right of K, it means K is the second person from the right end, and E is the person at the extreme right end. Since there are 7 people, the arrangement for the last two positions is: _ _ _ _ _ K E
Clue 2: Only one person sits between G and K.
Given the partial arrangement _ _ _ _ _ K E, and knowing that one person sits between G and K, G must be to the left of K. _ _ _ G _ K E
Clue 3: Only two people sit between D and G.
From _ _ _ G _ K E, there are two people between D and G. This means D must be to the left of G. D _ _ G _ K E
Clue 4: C sits at some place to the right of B but at some place to the left of F.
This implies the order B...C...F. The remaining people are B, C, F. The remaining spots are the second, third, and fourth from the left. D (B/C/F) (B/C/F) G (B/C/F) K E
Considering the B...C...F order, the only way to fit them into the remaining three spots (second, third, and fifth from the left) is:D B C G F K E
Final Arrangement:
The complete arrangement from left to right is: D B C G F K E
Identify the person third from the right end:
Counting from the right end:
1st from right: E
2nd from right: K
3rd from right: F
A) F is the person sitting third from the right end of the line.
This problem involves the properties of similar triangles, specifically the relationship between the ratio of their corresponding sides and the ratio of their areas. For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Let the two similar triangles be \(\Delta_1\) (smaller) and \(\Delta_2\) (bigger). Let their corresponding sides be \(s_1\) and \(s_2\), and their areas be \(A_1\) and \(A_2\) respectively.
The problem states that the ratio of the corresponding sides of the two similar triangles is 2 : 3. This means:
\[ \frac{s_1}{s_2} = \frac{2}{3} \]For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. So,
\[ \frac{A_1}{A_2} = \left(\frac{s_1}{s_2}\right)^2 \]Substitute the given ratio of sides into the formula:
\[ \frac{A_1}{A_2} = \left(\frac{2}{3}\right)^2 \]\[ \frac{A_1}{A_2} = \frac{4}{9} \]We are given that the area of the smaller triangle (\(A_1\)) is 36 sq cm. Substitute this value into the equation:
\[ \frac{36}{A_2} = \frac{4}{9} \]Now, solve for \(A_2\) (the area of the bigger triangle):
\[ 4 \times A_2 = 36 \times 9 \]\[ A_2 = \frac{36 \times 9}{4} \]\[ A_2 = 9 \times 9 \]\[ A_2 = 81 \]Therefore, the area of the bigger triangle is 81 sq cm.
C) 81 sq cm is the correct answer, as calculated by applying the property that the ratio of the areas of similar triangles is the square of the ratio of their corresponding sides.