The problem asks us to identify numbers in a given series that are immediately preceded by a symbol and immediately followed by a symbol. We need to scan the series from left to right and apply this condition to each number.
(Left) 9 # 2 6 7 © 6 8 & © \( & 3 9 1 7 \) 5 # @ * 4 (Right)
D) 1
The number '5' is immediately preceded by the symbol '\)' and immediately followed by the symbol '#'. There is only one such number in the series.
To solve this problem, we need to track Mr. C's movements step-by-step, considering each turn and distance covered. We can represent the movements on a 2D plane using coordinates or by calculating the net displacement in the East-West and North-South directions from the starting point. The shortest distance to return to Point A will be the magnitude of the net displacement from Point A to Point B, and the direction will be opposite to the final displacement from A.
Alternatively, we can calculate net displacement:
So, Point B is 1 km East and 0 km North/South from Point A. This means Point B is 1 km East of Point A. To return to Point A from Point B, Mr. C must drive 1 km towards the West.
Correct Option: A) 1 km towards the West
The question asks how rivers contribute to the formation of a coastal plain. We need to understand the geological processes by which rivers interact with coastal areas to build landforms.
B) By depositing sediments over time — Rivers transport eroded material from upstream areas and deposit it as they reach the coast, especially where their velocity decreases. This continuous deposition of sediments (like silt, sand, and clay) over long periods builds up the land, forming or extending coastal plains. This is a fundamental geological process for coastal plain formation.
To find the compound interest when interest is compounded half-yearly, we need to adjust the annual interest rate and the time period. The annual rate is divided by 2, and the number of years is multiplied by 2 to get the number of compounding periods. Then, we use the compound interest formula.
Since the interest is compounded half-yearly, the annual rate needs to be divided by 2, and the time period needs to be multiplied by 2.
The formula for the amount with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]Compound Interest is the difference between the Amount and the Principal.
\[ \text{CI} = A - P \]\[ \text{CI} = 8,70,038 - 8,20,000 \]\[ \text{CI} = 49,938 \]B) ₹49,938 is the correct compound interest calculated.
The problem asks us to find a relationship between two sets of letters based on their positions in the English alphabet. We need to identify the pattern in the given examples and then apply the same pattern to the target set of letters.
Let's find the position of each letter in the alphabet (A=1, B=2, ..., Z=26).
The pattern here is that each letter in the first word is shifted forward by 4 positions to get the corresponding letter in the second word.
Let's verify if the same pattern holds.
The pattern is consistent: each letter is shifted forward by 4 positions.
Now, we apply the same "+4" shift to each letter in HDJR:
So, HDJR is related to LHNV.
Based on our analysis, HDJR is related to LHNV.
The question asks about recent Supreme Court developments concerning bail under the Prevention of Money Laundering Act (PMLA), 2002. We need to evaluate each statement based on recent judicial pronouncements, particularly those in 2024-25, including the context of the Arvind Kejriwal case.
D) Statements 1 and 2 only
To solve this problem, we need to first identify the even and odd digits in the given number. Then, we apply the rule of adding 1 to each even digit and subtracting 1 from each odd digit. Finally, we form the new number and calculate the sum of its first two and last two digits from the left.
Wait, let's re-read the question carefully. The question states: "If 1 is added to each even digit and each odd digit in the number 57831426...". It does NOT say subtract 1 from odd digits. My bad. Let's re-calculate based on the exact wording.
C) 24 — As calculated, the sum of the first two digits (6 and 8) and the last two digits (3 and 7) of the new number is \(6 + 8 + 3 + 7 = 24\).
Simplify the following:
2(\( \frac{2}{9} \)) × 2(\( \frac{2}{3} \)) × 567 + 8(\( \frac{3}{4} \))
To simplify the given expression, we need to follow the order of operations (BODMAS/PEMDAS). First, convert mixed fractions to improper fractions. Then perform multiplication, and finally addition.
The given expression is \[2\left(\frac{2}{9}\right) \times 2\left(\frac{2}{3}\right) \times 567 + 8\left(\frac{3}{4}\right)\].
Convert \(2\left(\frac{2}{9}\right)\) to an improper fraction:
\[ 2\left(\frac{2}{9}\right) = \frac{(2 \times 9) + 2}{9} = \frac{18 + 2}{9} = \frac{20}{9} \]Convert \(2\left(\frac{2}{3}\right)\) to an improper fraction:
\[ 2\left(\frac{2}{3}\right) = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \]Convert \(8\left(\frac{3}{4}\right)\) to an improper fraction:
\[ 8\left(\frac{3}{4}\right) = \frac{(8 \times 4) + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4} \]So the expression becomes:
\[ \frac{20}{9} \times \frac{8}{3} \times 567 + \frac{35}{4} \]First, multiply the fractions and the whole number:
\[ \frac{20}{9} \times \frac{8}{3} \times 567 \]We can simplify by canceling out common factors. Notice that \(567\) is divisible by \(9\) and \(3\).
\(567 \div 9 = 63\)
So, the expression becomes:
\[ 20 \times \frac{8}{3} \times 63 \]Now, \(63\) is divisible by \(3\).
\(63 \div 3 = 21\)
So, the expression further simplifies to:
\[ 20 \times 8 \times 21 \]Calculate the product:
\[ 20 \times 8 = 160 \]\[ 160 \times 21 = 3360 \]Now, add the result from the multiplication to the remaining fraction:
\[ 3360 + \frac{35}{4} \]Convert the fraction to a decimal:
\[ \frac{35}{4} = 8.75 \]Finally, add the numbers:
\[ 3360 + 8.75 = 3368.75 \]C) 3368.75 is the correct simplification of the given expression.
A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/symbol | 7 | % | 2 | 5 | * | $ | 3 | ^ | # | 4 | + | 6 | 9 | 8 |
| Code | U | G | L | F | B | M | C | H | N | D | J | P | E | K |
Conditions:
I) If the first element is a symbol and the last a number, then the codes for these two (the first and the last elements) are to be interchanged.
II) If the first element is an odd number and the last element is an even number, then the first and last elements are to be coded as @.
III) If both the second and third elements are perfect squares, the third element is to be coded as the code for the second element.
What will be the code for 536+8?
The problem requires us to code a given sequence of numbers and symbols based on a provided coding table and a set of conditions. We need to first identify the codes for each element in the sequence, then check if any of the given conditions apply, and finally apply the relevant condition(s) to determine the final coded sequence.
A) @CPJ@ is incorrect. Let's re-evaluate the direct codes. The given codes are: 7-U, %-G, 2-L, 5-F, *-B, $-M, 3-C, ^-H, #-N, 4-D, +-J, 6-P, 9-E, 8-K. My initial transcription was incorrect for 3. The code for 3 is C, not H. Let's re-do the step-by-step with the correct codes.
Correct Option: A) @CPJ@ is the correct code after applying Condition II.
An electric pump can fill a tank in 4 hours. Due to a leakage in the tank, it takes 9(\( \frac{1}{3} \)) hours to fill the tank. How much time will this leak take to empty the full tank if water does not get in or out of the tank through any other point during this period?
This problem involves concepts of work and time, specifically dealing with filling and emptying a tank. We will calculate the rate of work for the pump and the combined rate of the pump and the leak. By finding the difference in these rates, we can determine the rate at which the leak empties the tank and subsequently the time it takes for the leak alone to empty the full tank.
The electric pump can fill the tank in 4 hours. So, in 1 hour, the pump fills \(\frac{1}{4}\) of the tank.
\[ \text{Pump's filling rate} = \frac{1}{4} \text{ tank/hour} \]Due to a leakage, it takes \(9\frac{1}{3}\) hours to fill the tank. Convert the mixed fraction to an improper fraction:
\[ 9\frac{1}{3} = \frac{(9 \times 3) + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3} \text{ hours} \]So, in 1 hour, the pump and leak together fill \[\frac{1}{\frac{28}{3}} = \frac{3}{28}\] of the tank.
\[ \text{Combined filling rate} = \frac{3}{28} \text{ tank/hour} \]The combined rate is the pump's filling rate minus the leak's emptying rate (since the leak works against the pump). Let the leak's emptying rate be \(R_{\text{leak}}\).
\[ \text{Pump's rate} - \text{Leak's rate} = \text{Combined rate} \]\[ \frac{1}{4} - R_{\text{leak}} = \frac{3}{28} \]Now, solve for \(R_{\text{leak}}\):
\[ R_{\text{leak}} = \frac{1}{4} - \frac{3}{28} \]To subtract these fractions, find a common denominator, which is 28:
\[ R_{\text{leak}} = \frac{1 \times 7}{4 \times 7} - \frac{3}{28} \]\[ R_{\text{leak}} = \frac{7}{28} - \frac{3}{28} \]\[ R_{\text{leak}} = \frac{7 - 3}{28} \]\[ R_{\text{leak}} = \frac{4}{28} \]Simplify the fraction:
\[ R_{\text{leak}} = \frac{1}{7} \text{ tank/hour} \]This means the leak can empty \(\frac{1}{7}\) of the tank in 1 hour.
If the leak empties \(\frac{1}{7}\) of the tank in 1 hour, then to empty the full tank (which is 1 unit), it will take the reciprocal of its rate.
\[ \text{Time taken by leak} = \frac{1}{R_{\text{leak}}} = \frac{1}{\frac{1}{7}} = 7 \text{ hours} \]D) 7 hours