The question asks for the budget allocation for the Ministry of Rural Development for the fiscal year 2023-24. This requires knowledge of the Union Budget presented for that specific fiscal year.
According to the Union Budget 2023-24, the Ministry of Rural Development was allocated ₹1,59,964 crore.
Correct Option: C) ₹1,59,964 crore is the correct budget allocation for the Ministry of Rural Development for the fiscal year 2023-24.
This is a circular seating arrangement problem. We need to deduce the positions of all seven people (P, Q, R, S, T, U, V) around a circular table based on the given clues and then answer the specific question about the number of people between S and U.
Let's draw the circular arrangement. Assume all are facing the center.
Let's place T at the bottom. Since R is to the immediate left of T, R is to the right of T's position (when looking from the center).
\[ \text{Arrangement 1:}\]
\[ \text{_ _ _}\]
\[ \text{R T}\]
V is third to the left of T. Counting left from T: T-1st-2nd-V. So, there are two people between T and V.
\[ \text{_ _ V}\]
\[ \text{_ _ _}\]
\[ \text{R T}\]
Q and V are immediate neighbours of S. So, S must be next to V. Given the circular arrangement, S can be to the left or right of V. Let's try placing S to the immediate right of V (when looking from the center).
\[ \text{_ S V}\]
\[ \text{_ _ _}\]
\[ \text{R T}\]
Now, Q is also an immediate neighbour of S. So Q must be to the immediate right of S.
\[ \text{Q S V}\]
\[ \text{_ _ _}\]
\[ \text{R T}\]
The remaining two spots are between T and Q. The people left are P and U. The arrangement is: T, R, (empty), (empty), V, S, Q.
Let's list the positions clockwise starting from T:
T, R, P, U, V, S, Q (This is one possibility for P and U)
T, R, U, P, V, S, Q (This is another possibility for P and U)
Now apply Clue 4: U is not an immediate neighbour of V.
In the arrangement T, R, P, U, V, S, Q: U is an immediate neighbour of V. This is incorrect.
In the arrangement T, R, U, P, V, S, Q: U is NOT an immediate neighbour of V (P is between U and V). This is correct.
So the final arrangement in clockwise order is: T, R, U, P, V, S, Q.
Let's verify all conditions:
1. Q and V are immediate neighbours of S: Yes, V-S-Q.
2. V sits third to the left of T: Counting left from T: T-R-U-V. Yes, V is third to the left of T.
3. R sits to the immediate left of T: Yes, R is to the immediate left of T.
4. U is not an immediate neighbour of V: Yes, P is between U and V.
The question asks: How many people sit between S and U when counted from the right of S?
From the right of S (clockwise direction): S -> Q -> T -> R -> U.
Between S and U, we have Q, T, R. That's 3 people.
Let's re-check the counting. From the right of S means moving clockwise from S. The sequence is S, Q, T, R, U. The people between S and U are Q, T, R. There are 3 people.
Let's re-draw the circle and count carefully.
\[ \text{ U P }\]
\[ \text{R V}\]
\[ \text{T S}\]
\[ \text{ Q }\]
Counting from the right of S (clockwise):
S - (Q) - (T) - (R) - U
The people between S and U are Q, T, R. There are 3 people.
C) 4 is incorrect. Let's re-count. S, Q, T, R, U. People between S and U (from right of S) are Q, T, R. This is 3 people.
Wait, I made a mistake in the final count. Let's re-draw the circle and count carefully. Let's assume T is at position 1. 1. T 2. R (immediate left of T) 3. U (from T-R-U-P-V-S-Q) 4. P 5. V (third to the left of T) 6. S (immediate neighbour of V, and Q is other immediate neighbour) 7. Q (immediate neighbour of S)
The arrangement clockwise from T is: T - R - U - P - V - S - Q.
Now, count from the right of S. Right of S means clockwise from S. S -> Q (1st person) -> T (2nd person) -> R (3rd person) -> U (4th person).
The people between S and U are Q, T, R. That is 3 people.
Let's re-check the question: "How many people sit between S and U when counted from the right of S?"
If we count from the right of S (clockwise): S, Q, T, R, U. The people between S and U are Q, T, R. There are 3 people.
Let's verify the solution given in the prompt, which states C (4 people) is correct. This implies my interpretation of "between
This problem involves analyzing logical statements and drawing conclusions based on them. We will use Venn diagrams to represent the relationships between the categories (warriors, politicians, leaders, knights) and then evaluate each conclusion.
Correct Option: A) Only conclusion (II) follows.
The question asks about the functional groups involved in peptide bond formation. Recall the basic structure of an amino acid and how peptide bonds are formed during protein synthesis (condensation reaction).
Correct Option: A) Carboxyl and amino groups
To determine which number is divisible by 71, we can perform division for each given option. A number is divisible by another if the remainder of their division is zero.
Correct Option: A) 5609 is divisible by 71 because \(5609 \div 71 = 79\) with a remainder of 0.
This problem involves calculating the combined work rate of two pipes, one filling and one emptying. We will determine the individual rates of filling and emptying, then find the net rate when both operate together. Finally, we will use the net rate to find the total time required to fill the tank.
D) 10 — As calculated, the net filling rate is \(\frac{1}{10}\) tank per minute, meaning it will take 10 minutes to fill the entire tank.
This problem requires the use of the empirical formula relating the mean, median, and mode for a moderately skewed distribution. The formula is: \(\text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean}\). We are given the mode and median, and we need to find the mean.
A) 74.85 is the correct mean calculated using the empirical formula.
The problem asks us to identify symbols 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 count such occurrences.
@ 5 4 £ 8 & © £ * 2 5 9 $ 6 £ 4 * 8 $ 4 % *@: Preceded by nothing, followed by 5. Not a match.5: Number.4: Number.£: Preceded by 4 (number), followed by 8 (number). Match 1: 4 £ 88: Number.&: Preceded by 8 (number), followed by © (symbol). Not a match.©: Preceded by & (symbol), followed by £ (symbol). Not a match.£: Preceded by © (symbol), followed by * (symbol). Not a match.*: Preceded by £ (symbol), followed by 2 (number). Not a match.2: Number.5: Number.9: Number.\(: Preceded by 9 (number), followed by 6 (number). Match 2: 9 \) 66: Number.£: Preceded by 6 (number), followed by 4 (number). Match 3: 6 £ 44: Number.*: Preceded by 4 (number), followed by 8 (number). Match 4: 4 * 88: Number.\(: Preceded by 8 (number), followed by 4 (number). Match 5: 8 \) 44: Number.%: Preceded by 4 (number), followed by * (symbol). Not a match.*: Preceded by % (symbol), followed by nothing. Not a match.C) 5 is the correct answer because there are 5 symbols in the series that are immediately preceded by a number and immediately followed by a number.
This problem involves calculating the work done by pipes filling and emptying a tank. We need to determine the individual rates of filling and emptying, then calculate the amount filled before both pipes are open, and finally, the net rate when both are operating to find the remaining time.
Calculate the filling rate of Pipe A:
Pipe A fills the tank in 9 minutes. So, in 1 minute, Pipe A fills \(\frac{1}{9}\) of the tank.
Calculate the emptying rate of Pipe B:
Pipe B empties the tank in 10 minutes. So, in 1 minute, Pipe B empties \(\frac{1}{10}\) of the tank.
Calculate the amount filled by Pipe A in the first 3 minutes:
Pipe A is opened alone for 3 minutes.
Amount filled by A in 3 minutes \[= 3 \times \frac{1}{9} = \frac{3}{9} = \frac{1}{3}\] of the tank.
Calculate the remaining capacity to be filled:
Remaining capacity \[= 1 - \frac{1}{3} = \frac{2}{3}\] of the tank.
Calculate the net filling rate when both pipes A and B are open:
Pipe A fills and Pipe B empties. So, the net rate is the difference between their individual rates.
Net rate \[= \text{Rate of A} - \text{Rate of B} = \frac{1}{9} - \frac{1}{10}\]
To subtract, find a common denominator, which is 90.
Net rate \[= \frac{10}{90} - \frac{9}{90} = \frac{1}{90}\] of the tank per minute.
Calculate the time required to fill the remaining capacity:
The remaining capacity is \(\frac{2}{3}\) of the tank, and the net filling rate is \(\frac{1}{90}\) of the tank per minute.
Time \[= \frac{\text{Remaining Capacity}}{\text{Net Rate}}\]
Time \[= \frac{\frac{2}{3}}{\frac{1}{90}} = \frac{2}{3} \times 90 = 2 \times 30 = 60\] minutes.
Thus, the remaining tank will be filled completely in 60 minutes.
B) 60
We need to find the measure of \(\angle AEB\) in \(\triangle ABC\). We are given that \(BD \perp AC\), \(\angle DBC = 22°\), and \(\angle CAE = 36°\). We will use the properties of triangles, specifically the sum of angles in a triangle and the concept of exterior angles.
Analyze \(\triangle BDC\):
Given that \(BD \perp AC\), this means \(\angle BDC = 90°\).
In \(\triangle BDC\), the sum of angles is \(180°\):
\[ \angle BCD + \angle DBC + \angle BDC = 180° \]\[ \angle BCD + 22° + 90° = 180° \]\[ \angle BCD + 112° = 180° \]\[ \angle BCD = 180° - 112° \]\[ \angle BCD = 68° \]Find \(\angle ACB\):
From step 1, we found \(\angle BCD = 68°\). Since D is on AC, \(\angle ACB\) is the same as \(\angle BCD\).
\[ \angle ACB = 68° \]Analyze \(\triangle AEC\):
We need to find \(\angle AEB\). Notice that \(\angle AEB\) is an exterior angle to \(\triangle AEC\) at vertex E. However, it's simpler to find \(\angle AEC\) first and then use the linear pair property.
In \(\triangle AEC\), we know \(\angle CAE = 36°\) and \(\angle ACE = \angle ACB = 68°\).
The sum of angles in \(\triangle AEC\) is \(180°\):
\[ \angle AEC + \angle CAE + \angle ACE = 180° \]\[ \angle AEC + 36° + 68° = 180° \]\[ \angle AEC + 104° = 180° \]\[ \angle AEC = 180° - 104° \]\[ \angle AEC = 76° \]Find \(\angle AEB\):
Angles \(\angle AEB\) and \(\angle AEC\) form a linear pair on the line BC.
\[ \angle AEB + \angle AEC = 180° \]\[ \angle AEB + 76° = 180° \]\[ \angle AEB = 180° - 76° \]\[ \angle AEB = 104° \]D) 104° is the correct answer, as calculated in the step-by-step solution.