The problem requires us to apply specific letter transformation rules to the word "FRIENDLY" and then identify the letter at a particular position in the resulting sequence. We need to classify each letter as a vowel or a consonant and apply the corresponding rule: vowels change to the next letter, and consonants change to the previous letter in the English alphabet.
The letter in the second position from the right is K.
Correct Option: A) K is the letter in the second position from the right in the new group of letters.
This is a blood relation problem where symbols represent relationships. We need to decode the given expression step-by-step to determine the relationship between M and T.
B) Father's brother's wife's mother. As derived, M is the mother of N, who is the wife of P. P is the brother of S, who is the father of T. Therefore, M is the mother of T's father's brother's wife, which means M is T's father's brother's wife's mother.
The problem asks us to identify a set of three numbers that follows the same logical rule as the given sets: (9, 6, 56) and (7, 8, 58). We need to find a mathematical relationship between the first two numbers and the third number in each set.
Let the numbers be \(A\), \(B\), and \(C\). So, \(A=9\), \(B=6\), \(C=56\).
We need to find a pattern that relates 9 and 6 to 56. Let's try common arithmetic operations:
Here, \(A=7\), \(B=8\), \(C=58\).
Using the proposed rule \( (A \times B) + 2 = C \):
\[ (7 \times 8) + 2 = 56 + 2 = 58 \]This matches the third number in the set. So, the rule \( (A \times B) + 2 = C \) is consistent with both given sets.
B) (5, 11, 57)
This problem can be solved by applying Ohm's Law, which describes the relationship between voltage, current, and resistance in an electrical circuit. We need to determine how current changes when resistance is increased, assuming voltage remains constant.
Recall Ohm's Law: Ohm's Law states that the voltage (\(V\)) across a conductor is directly proportional to the current (\(I\)) flowing through it, provided all physical conditions and temperature remain constant. The relationship is given by:
\[ V = I \times R \]Rearrange for Current: To find out how current changes, we can rearrange Ohm's Law to express current in terms of voltage and resistance:
\[ I = \frac{V}{R} \]Identify Given Conditions: The problem states that the voltage (\(V\)) remains constant. The resistance (\(R\)) is increased to three times its original value. Let the original resistance be \(R_1\) and the new resistance be \(R_2\). So, \(R_2 = 3R_1\).
Calculate Original Current: Let the original current be \(I_1\). Using Ohm's Law:
\[ I_1 = \frac{V}{R_1} \]Calculate New Current: Let the new current be \(I_2\). Using the new resistance \(R_2 = 3R_1\) and constant voltage \(V\):
\[ I_2 = \frac{V}{R_2} = \frac{V}{3R_1} \]Compare New Current with Original Current: We can rewrite the expression for \(I_2\) by substituting \(I_1 = \frac{V}{R_1}\):
\[ I_2 = \frac{1}{3} \times \left(\frac{V}{R_1}\right) \]\[ I_2 = \frac{1}{3} \times I_1 \]Thus, the new current is one third of the original current.Correct Option: C) one third
We need to determine the seating arrangement of seven people (A, B, C, D, E, F, G) in a row facing north based on the given clues. Once the arrangement is established, we can find the number of people between A and F.
Clue 1: Only five people sit between F and D.
Since there are 7 people in total, and 5 people are between F and D, F and D must be at the extreme ends of the row. This means F and D are at positions 1 and 7 (or 7 and 1).
Case 1: F _ _ _ _ _ D
Case 2: D _ _ _ _ _ F
Clue 2: G sits third to the right of F.
If F is at the extreme right (position 7), G cannot sit to its right. So, F must be at the extreme left (position 1).
Thus, Case 1 is the correct one: F _ _ _ _ _ D
Now, place G third to the right of F:
F (1) _ (2) G (3) _ (4) _ (5) _ (6) D (7)
Clue 3: E is the immediate neighbour of C and D.
D is at position 7. E must be next to D. So, E is at position 6. E is also an immediate neighbour of C, so C must be at position 5.
F (1) _ (2) G (3) _ (4) C (5) E (6) D (7)
Clue 4: B is not the immediate neighbour of G.
The remaining positions are 2 and 4. The remaining people are A and B.
If B is not an immediate neighbour of G (who is at position 3), then B cannot be at position 2 or position 4. This is a contradiction, as B must occupy one of these two remaining spots. Let's recheck the interpretation.
Ah, the statement means B cannot be *directly* next to G. So, B cannot be at position 2 or position 4. This implies that A must be at position 2 or 4, and B at the other. But this clue is about B *not* being a neighbour of G. This means B cannot be at position 2 or 4. This is impossible as only positions 2 and 4 are left for A and B.
Let's re-evaluate the interpretation of "B is not the immediate neighbour of G". This means that if G is at position 3, B cannot be at position 2 or position 4. This implies that A must be at position 2 and B at position 4, or vice versa.
Let's consider the available slots: F (1), G (3), C (5), E (6), D (7). The empty slots are 2 and 4. The remaining people are A and B.
If A is at position 2 and B is at position 4:
F (1) A (2) G (3) B (4) C (5) E (6) D (7)
In this arrangement, B (at 4) is an immediate neighbour of G (at 3). This contradicts the clue "B is not the immediate neighbour of G".
Therefore, the only other possibility is A at position 4 and B at position 2:
F (1) B (2) G (3) A (4) C (5) E (6) D (7)
In this arrangement, B (at 2) is an immediate neighbour of G (at 3). This also contradicts the clue "B is not the immediate neighbour of G".
Let's re-read the problem carefully. "Only five people sit between F and D." This means F and D are at the ends. "G sits third to the right of F." This means F is at position 1. So, F _ G _ _ _ D. This is correct.
F _ G _ _ _ D
1 2 3 4 5 6 7
"E is the immediate neighbour of C and D." D is at 7, so E must be at 6. C must be at 5.
F _ G _ C E D
1 2 3 4 5 6 7
The remaining positions are 2 and 4. The remaining people are A and B.
"B is not the immediate neighbour of G." G is at position 3. Its immediate neighbours would be positions 2 and 4. This means B cannot be at position 2 AND B cannot be at position 4. This is impossible, as B must occupy one of these two positions.
Let's re-evaluate the initial placement of F and D. What if the row is not strictly 7 positions, but F and D are just 5 people apart. However, "Seven people... are sitting in a row" implies a fixed length. "Only five people sit between F and D" means F and D are at the ends.
Let's reconsider the wording: "Only five people sit between F and D." This means F and D are at the ends. If F is at position 1, D is at position 7. If D is at position 1, F is at position 7.
Possibility 1: F is at position 1.
1 2 3 4 5 6 7
F _ _ _ _ _ D
G sits third to the right of F. So G is at position 4. (F is 1st, 2nd, 3rd to the right of F is 4th position).
F _ _ G _ _ D
1 2 3 4 5 6 7
E is the immediate neighbour of C and D. D is at 7, so E must be at 6. C must be at 5.
F _ _ G C E D
1 2 3 4 5 6 7
Remaining positions are 2 and 3. Remaining people are A and B.
B is not the immediate neighbour of G (at position 4). So B cannot be at position 3 or position 5. Position 5 is taken by C. Position 3 is available.
If B is at position 3, it is an immediate neighbour of G. This contradicts the clue. So B cannot be at position 3.
Therefore, B must be at position 2. This means A must be at position 3.
F B A G C E D
1 2 3 4 5 6 7
Let's check all conditions for this arrangement:
This arrangement is consistent with all clues.
Now, we need to find how many people sit between A and F.
F B A G C E D
A is at position 3, F is at position 1. The person between A and F is B.
So, 1 person sits between A and F.
B) One
This is a work and time problem. We need to find the individual work rates of a man and a boy. Once we have their individual rates, we can calculate the total work rate of 10 men and 20 boys and then determine the time taken to complete the work.
Let the work done by one man in one day be \(m\) units and the work done by one boy in one day be \(b\) units.
From the first condition: 6 men and 8 boys can do a piece of work in 10 days.
Total work done by (6 men + 8 boys) in 1 day is \((6m + 8b)\) units.
Total work = \((6m + 8b) \times 10\) units.
From the second condition: 26 men and 48 boys can do the same work in 2 days.
Total work done by (26 men + 48 boys) in 1 day is \((26m + 48b)\) units.
Total work = \((26m + 48b) \times 2\) units.
Since the work is the same, we can equate the total work from both conditions:
\[ (6m + 8b) \times 10 = (26m + 48b) \times 2 \]Simplify the equation:
\[ 60m + 80b = 52m + 96b \]\[ 60m - 52m = 96b - 80b \]\[ 8m = 16b \]\[ m = 2b \]This means one man's work rate is equal to the work rate of two boys.
Now, substitute \(m = 2b\) into one of the total work expressions. Let's use the first one:
Total work = \((6m + 8b) \times 10 = (6(2b) + 8b) \times 10 = (12b + 8b) \times 10 = 20b \times 10 = 200b\) units.
We need to find the time taken by 10 men and 20 boys to do the same work.
Work rate of (10 men + 20 boys) = \((10m + 20b)\) units per day.
Substitute \(m = 2b\):
Work rate = \((10(2b) + 20b) = (20b + 20b) = 40b\) units per day.
Time taken = \[\frac{\text{Total Work}}{\text{Work Rate}}\]
\[ \text{Time taken} = \frac{200b}{40b} = 5 \text{ days} \]B) The time taken by 10 men and 20 boys to complete the work is 5 days.
The question asks to identify the individual who received the 2024 Greenaccord International Media Award as the Managing Editor of Mongabay India. This is a current affairs question requiring knowledge of recent awards and the personalities associated with them.
Correct Option: B) S Gopikrishna Warrier is the Managing Editor of Mongabay India and was the recipient of the 2024 Greenaccord International Media Award. This award recognizes his exceptional work in environmental journalism, particularly his focus on climate change, biodiversity, and sustainable development in India.
To find the perimeter of a rectangular plot, we need both its length and width. We are given the diagonal and one side. We can use the Pythagorean theorem to find the other side, and then calculate the perimeter.
Identify the given values:
Apply the Pythagorean theorem:
For a rectangle with length \(l\), width \(w\), and diagonal \(d\), the relationship is given by:
\[ l^2 + w^2 = d^2 \]We need to find the length \(l\). Rearranging the formula:
\[ l^2 = d^2 - w^2 \]Substitute the values and calculate \(l\):
\[ l^2 = (65)^2 - (63)^2 \]Calculate the squares:
\[ 65^2 = 4225 \] \[ 63^2 = 3969 \]Subtract the values:
\[ l^2 = 4225 - 3969 \] \[ l^2 = 256 \]Take the square root to find \(l\):
\[ l = \sqrt{256} \] \[ l = 16 \text{ m} \]So, the length of the rectangular plot is \(16 \text{ m}\).
Calculate the perimeter:
The perimeter \(P\) of a rectangle is given by the formula:
\[ P = 2 \times (l + w) \]Substitute the values of \(l\) and \(w\):
\[ P = 2 \times (16 \text{ m} + 63 \text{ m}) \] \[ P = 2 \times (79 \text{ m}) \] \[ P = 158 \text{ m} \]A) 158 m — This is the correct perimeter calculated using the Pythagorean theorem and the perimeter formula.
To find the acceleration of the car, we need to use the formula for acceleration, which is the rate of change of velocity. Since the car is decreasing its speed, we expect the acceleration to be negative, indicating deceleration.
Identify the given values:
Recall the formula for acceleration (\(a\)):
\[ a = \frac{v - u}{t} \]Substitute the given values into the formula:
\[ a = \frac{20 \text{ m/s} - 40 \text{ m/s}}{5 \text{ s}} \]Calculate the change in velocity:
\[ 20 \text{ m/s} - 40 \text{ m/s} = -20 \text{ m/s} \]Calculate the acceleration:
\[ a = \frac{-20 \text{ m/s}}{5 \text{ s}} = -4 \text{ m/s}^2 \]The negative sign indicates that the car is decelerating or slowing down.
Correct Option: B) −4 m/s²
The question asks for the venue where Nadi Utsav 2024 was inaugurated. This is a factual question related to current affairs and cultural events. Recalling recent news or general knowledge about such festivals and their common venues will lead to the correct answer.
Correct Option: D) Indira Gandhi National Centre for the Arts (IGNCA)
Nadi Utsav 2024, a festival celebrating India's rivers, was inaugurated at the Indira Gandhi National Centre for the Arts (IGNCA) in New Delhi. This institution frequently hosts cultural events, exhibitions, and festivals related to India's heritage and arts.