The problem states that after pouring 51 litres of petrol into an empty tank, the tank is still 1% empty. This means that the 51 litres of petrol represent 99% of the tank's total capacity. We can set up a simple equation to find the total capacity.
If the tank is 1% empty, then it is \(100\% - 1\% = 99\%\) full.
The 51 litres of petrol poured into the tank represent 99% of its total capacity.
Let \(C\) be the total capacity of the storage tank in litres. Then, 99% of \(C\) is equal to 51 litres.
\[ 0.99 \times C = 51 \]Divide both sides by 0.99 to find the total capacity.
\[ C = \frac{51}{0.99} \]Rounding 51.5151... to two decimal places gives 51.52 litres.
Correct Option: C) 51.52
When numbers are divided by a common divisor and leave the same remainder, the difference between any two of these numbers must be divisible by that common divisor. We will use this property to find the greatest common divisor (x) and then determine the remainder (y).
Let the given numbers be \(N_1 = 1063\), \(N_2 = 2815\), and \(N_3 = 3451\). When these numbers are divided by the greatest number \(x\), the remainder in each case is \(y\).
This can be written as:
\[ 1063 = q_1 x + y \]\[ 2815 = q_2 x + y \]\[ 3451 = q_3 x + y \]Subtracting the remainder \(y\) from each number makes them perfectly divisible by \(x\). So, \( (1063 - y) \), \( (2815 - y) \), and \( (3451 - y) \) are all divisible by \(x\).
The difference between any two of these numbers will also be divisible by \(x\). This is a key property when the remainder is the same.
Calculate the differences:
\[ 2815 - 1063 = 1752 \]\[ 3451 - 2815 = 636 \]\[ 3451 - 1063 = 2388 \]The greatest number \(x\) is the HCF (Highest Common Factor) of these differences: \(1752\), \(636\), and \(2388\).
First, find the HCF of \(1752\) and \(636\) using the Euclidean algorithm:
The HCF of \(1752\) and \(636\) is \(12\).
Now, find the HCF of \(12\) and \(2388\):
The HCF of \(12\) and \(2388\) is \(12\).
So, \(x = 12\).
Now that we have \(x = 12\), we can find the remainder \(y\) by dividing any of the original numbers by \(12\).
Let's divide \(1063\) by \(12\):
\[ 1063 = 12 \times 88 + 7 \]\[ 1063 \div 12 = 88 \text{ with a remainder of } 7 \]So, \(y = 7\).
Finally, calculate the value of \( (3x - 14y) \):
\[ 3x - 14y = 3(12) - 14(7) \]\[ = 36 - 98 \]\[ = -62 \]C) \(-62\) is the correct value for \( (3x - 14y) \).
The question asks about the critical factors determining the effectiveness of synaptic transmission. This involves understanding the basic mechanism of how a signal crosses the synapse from the presynaptic neuron to the postsynaptic neuron.
Correct Option: C) The concentration of neurotransmitter and the number of receptors in the postsynaptic membrane
This option directly addresses the two most critical factors for successful chemical synaptic transmission. A higher concentration of neurotransmitter ensures more molecules are available to bind, and a greater number of receptors ensures that more binding events can occur, leading to a stronger postsynaptic potential.
The problem presents a pattern based on rearranging letters within a four-letter word to form two subsequent words. We need to identify the specific rearrangement rule and then apply it to the given options to find the one that follows the same logic.
Correct Option: C) FOWL - LWFO - FWOL
To find the arithmetic mean of a set of observations, we need to sum all the observations and then divide the sum by the total number of observations.
Correct Option: D) 60
The question asks to identify the caves where the 'Reclining Statue of Lord Vishnu' is located. This requires knowledge of prominent cave architecture and their associated sculptures in India.
Correct Option: B) The Undavalli Caves, located in Guntur district, Andhra Pradesh, are famous for their rock-cut architecture, particularly the four-storied cave temple. One of its most prominent features is a massive monolithic statue of Lord Vishnu in a reclining posture (Anantashayana Vishnu) carved from a single granite block inside the second floor of the main cave.
Simplify the following:
47 + \( \frac{49}{7} \) + 65 − 27
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform Division first, then Addition and Subtraction from left to right.
The given expression is:
\[ 47 + \frac{49}{7} + 65 - 27 \]According to BODMAS/PEMDAS, division should be performed first.
\[ \frac{49}{7} = 7 \]Substitute this value back into the expression:
\[ 47 + 7 + 65 - 27 \]Now, perform the additions and subtractions in the order they appear from left to right.
First addition:
\[ 47 + 7 = 54 \]The expression becomes:
\[ 54 + 65 - 27 \]Second addition:
\[ 54 + 65 = 119 \]The expression becomes:
\[ 119 - 27 \]Finally, subtraction:
\[ 119 - 27 = 92 \]Therefore, the simplified value of the expression is 92.
Correct Option: A) 92
The question asks about the sector associated with the Tonnage Tax Scheme, specifically mentioned in the Union Budget 2025-26. This requires knowledge of tax policies related to specific industries.
Correct Option: D) Shipping activities
This is a logical reasoning problem involving seating arrangements or, in this case, floor arrangements. We need to deduce the exact floor on which each person lives based on the given clues and then answer the question about the number of people between N and P.
List the floors: There are 6 floors, numbered 1 to 6.
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | |
| 4 | |
| 3 | |
| 2 | |
| 1 |
Clue 1: O lives on an even numbered floor but not on floor number 4.
Possible floors for O: 2 or 6.
Clue 2: Only two people live between O and Z.
Case 1: If O is on floor 2, then Z must be on floor 5 (2 people between 2 and 5 are on floors 3 and 4).
Case 2: If O is on floor 6, then Z must be on floor 3 (2 people between 6 and 3 are on floors 4 and 5).
Clue 3: Y lives on an odd numbered floor but not on the lowermost floor (floor 1).
Possible floors for Y: 3 or 5.
Clue 4: Only two people live between Y and M.
Clue 5: P lives immediately below Y.
Let's combine clues 3, 4, and 5. If Y is on floor 3, then P must be on floor 2. If Y is on floor 5, then P must be on floor 4.
Now let's try to fit these into the main cases for O and Z.
Let's re-evaluate the combination of clues. It seems I made an error in my deduction. Let's restart the filling process carefully.
We have floors 1 to 6.
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | |
| 4 | |
| 3 | |
| 2 | |
| 1 |
From Clue 1: O lives on an even numbered floor but not on floor 4. So O is on floor 2 or 6.
From Clue 3: Y lives on an odd numbered floor but not on floor 1. So Y is on floor 3 or 5.
From Clue 5: P lives immediately below Y.
From Clue 4: Only two people live between Y and M.
From Clue 2: Only two people live between O and Z.
Let's try to combine these possibilities:
Possibility 1: O on Floor 2.
If O is on Floor 2, then Z must be on Floor 5 (two people between them, floors 3 and 4).
Now, let's consider Y and P. If Y is on Floor 3, P is on Floor 2. But O is already on Floor 2. So this is not possible.
Therefore, Y must be on Floor 5. But Z is already on Floor 5. So this is also not possible.
This means O cannot be on Floor 2.
Possibility 2: O on Floor 6.
If O is on Floor 6, then Z must be on Floor 3 (two people between them, floors 4 and 5).
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | |
| 4 | |
| 3 | Z |
| 2 | |
| 1 |
Now consider Y and P. Y can be on floor 3 or 5. But Z is on floor 3, so Y cannot be on floor 3. Thus, Y must be on Floor 5.
If Y is on Floor 5, then P lives immediately below Y, so P is on Floor 4.
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | Y |
| 4 | P |
| 3 | Z |
| 2 | |
| 1 |
Now, from Clue 4: Only two people live between Y and M.
Y is on Floor 5. Two people between Y and M means M must be on Floor 2 (floors 3 and 4 are between them). Alternatively, M could be on floor 8 (5 + 2 + 1), but there are only 6 floors. So M is on Floor 2.
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | Y |
| 4 | P |
| 3 | Z |
| 2 | M |
| 1 |
The only remaining person is N, and the only remaining floor is 1. So, N lives on Floor 1.
| Floor No. | Person |
|---|---|
| 6 | O |
| 5 | Y |
| 4 | P |
| 3 | Z |
| 2 | M |
| 1 | N |
All conditions are met.
Answer the question: How many people live between N and P?
N is on Floor 1.
P is on Floor 4.
The people living between N (Floor 1) and P (Floor 4) are on Floor 2 (M) and Floor 3 (Z).
There are two people (M and Z) between N and P.
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This stands for Brackets/Parentheses, Orders/Exponents, Division/Multiplication (from left to right), and Addition/Subtraction (from left to right).
Thus, the simplified value of the expression is \(-34\).
C) \(-34\) is the correct answer, as derived by following the order of operations.