This problem involves calculating the total time taken by a boat to travel a certain distance downstream and then return the same distance upstream. We need to determine the effective speed of the boat in both directions using the speed of the boat in still water and the speed of the stream, and then use the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) for each leg of the journey.
Identify given values:
Calculate the speed downstream:
When the boat travels downstream, its speed is the sum of its speed in still water and the speed of the stream.
\[ \text{Speed downstream} = v_b + v_s = 7 \text{ km/hr} + 5 \text{ km/hr} = 12 \text{ km/hr} \]Calculate the time taken to travel downstream (\(T_d\)):
\[ T_d = \frac{D}{\text{Speed downstream}} = \frac{52.8 \text{ km}}{12 \text{ km/hr}} \]\[ T_d = 4.4 \text{ hours} \]Calculate the speed upstream:
When the boat travels upstream, its speed is the difference between its speed in still water and the speed of the stream.
\[ \text{Speed upstream} = v_b - v_s = 7 \text{ km/hr} - 5 \text{ km/hr} = 2 \text{ km/hr} \]Calculate the time taken to travel upstream (\(T_u\)):
\[ T_u = \frac{D}{\text{Speed upstream}} = \frac{52.8 \text{ km}}{2 \text{ km/hr}} \]\[ T_u = 26.4 \text{ hours} \]Calculate the total time taken:
The total time is the sum of the time taken to travel downstream and the time taken to travel upstream.
\[ \text{Total time} = T_d + T_u = 4.4 \text{ hours} + 26.4 \text{ hours} \]\[ \text{Total time} = 30.8 \text{ hours} \]D) 30.8
The problem requires us to modify a given number based on specific rules for its odd and even digits, then find the difference between the highest and lowest digits in the newly formed number.
C) The difference between the highest (8) and lowest (0) digits in the new number is \(8 - 0 = 8\).
The problem involves finding the price of the cheapest item given the average price of three items and their price ratio. We will first use the average price to find the total price of the three items. Then, we will use the given ratio to determine the individual prices and identify the cheapest one.
Given the average price of three items is ₹15,135.
\[ \text{Total Price} = \text{Average Price} \times \text{Number of Items} \] \[ \text{Total Price} = 15,135 \times 3 = \text{₹}45,405 \]The prices of the three items are in the ratio 3 : 5 : 7. Let the prices be \(3x\), \(5x\), and \(7x\) respectively.
The sum of the individual prices must equal the total price.
\[ 3x + 5x + 7x = 45,405 \] \[ 15x = 45,405 \]The prices are \(3x\), \(5x\), and \(7x\). The cheapest item corresponds to the smallest ratio part, which is \(3x\).
\[ \text{Price of Cheapest Item} = 3x = 3 \times 3,027 \] \[ \text{Price of Cheapest Item} = \text{₹}9,081 \]Correct Option: C) 9,081
The problem presents a series of three-letter combinations. We need to identify the pattern in the alphabetical positions of the letters within each combination and between consecutive combinations to find the missing term.
Let's assign numerical positions to each letter in the English alphabet (A=1, B=2, ..., Z=26).
Combining these, the missing term is XCH.
A) XCH is the correct option because the pattern for each position (first, second, and third letter) consistently involves subtracting 2 from the alphabetical position of the corresponding letter in the previous term.
This problem involves concepts of relative speed and time taken to cross objects. We need to first find the speed of the train using the information about it overtaking a man. Then, we will use this train's speed to calculate the time it takes to cross another train moving in the opposite direction.
Speed of man \(S_m = 9 \text{ km/hr}\). To convert km/hr to m/s, multiply by \(\frac{5}{18}\).
\[ S_m = 9 \times \frac{5}{18} = \frac{5}{2} = 2.5 \text{ m/s} \]Let the speed of the first train be \(S_T\). When the train overtakes a man moving in the same direction, the relative speed is \(S_T - S_m\). The distance covered is the length of the train, \(L_T = 100 \text{ m}\). Time taken \(t_1 = 30 \text{ seconds}\).
\[ \text{Relative Speed} = \frac{\text{Distance}}{\text{Time}} \] \[ S_T - S_m = \frac{L_T}{t_1} \] \[ S_T - 2.5 = \frac{100}{30} \] \[ S_T - 2.5 = \frac{10}{3} \] \[ S_T = 2.5 + \frac{10}{3} = \frac{5}{2} + \frac{10}{3} = \frac{15 + 20}{6} = \frac{35}{6} \text{ m/s} \]The second train has a length \(L_{T2} = 220 \text{ m}\) and moves at a speed of \(S_{T2} = 51 \text{ km/hr}\) in the opposite direction.
Convert \(S_{T2}\) to m/s:
\[ S_{T2} = 51 \times \frac{5}{18} = \frac{17 \times 5}{6} = \frac{85}{6} \text{ m/s} \]Since they are moving in opposite directions, their relative speed is the sum of their individual speeds:
\[ \text{Relative Speed} = S_T + S_{T2} \] \[ \text{Relative Speed} = \frac{35}{6} + \frac{85}{6} = \frac{120}{6} = 20 \text{ m/s} \]To completely cross each other, the total distance to be covered is the sum of their lengths:
\[ \text{Total Distance} = L_T + L_{T2} = 100 + 220 = 320 \text{ m} \]Correct Option: D) 16
The question asks for the specific keyboard shortcut used to insert a new slide in Microsoft PowerPoint 2019. We need to identify the correct key combination among the given options.
B) Ctrl + M is the standard keyboard shortcut in Microsoft PowerPoint (including version 2019) to insert a new slide into the current presentation. This shortcut adds a new slide with the default layout following the currently selected slide.
To find the gain or loss percentage, we need to determine the Cost Price (CP), Marked Price (MP), and Selling Price (SP). We can assume a convenient Cost Price, then calculate the Marked Price by adding the given percentage, and finally calculate the Selling Price by applying the discount on the Marked Price. Once CP and SP are known, the gain or loss percentage can be calculated.
Let the Cost Price (CP) of the goods be \(₹100\).
The dealer marks his goods at 5% above the cost price.
\[ \text{MP} = \text{CP} + (5\% \text{ of CP}) \] \[ \text{MP} = 100 + \left(\frac{5}{100} \times 100\right) = 100 + 5 = ₹105 \]A discount of 67% is allowed on the Marked Price.
\[ \text{Discount Amount} = 67\% \text{ of MP} \] \[ \text{Discount Amount} = \frac{67}{100} \times 105 = 0.67 \times 105 = ₹70.35 \] \[ \text{SP} = \text{MP} - \text{Discount Amount} \] \[ \text{SP} = 105 - 70.35 = ₹34.65 \]Since SP (\(₹34.65\)) is less than CP (\(₹100\)), there is a loss.
\[ \text{Loss} = \text{CP} - \text{SP} \] \[ \text{Loss} = 100 - 34.65 = ₹65.35 \]The dealer incurs a loss of 65.35%.
C) 65.35% loss
To evaluate the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets (Parentheses), Orders (Exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). We will start from the innermost bracket and work our way outwards.
First, evaluate the innermost parentheses: \((22 - 22 \times 4)\).
According to BODMAS, multiplication comes before subtraction.
\[ 22 \times 4 = 88 \]\[ 22 - 88 = -66 \]Substitute this value back into the expression:
\[ 22 - [22 - \{22 - (-66)\}] \]Next, evaluate the curly braces: \(\{22 - (-66)\}\).
Subtracting a negative number is equivalent to adding the positive number.
\[ 22 - (-66) = 22 + 66 = 88 \]Substitute this value back into the expression:
\[ 22 - [22 - 88] \]Now, evaluate the square brackets: \([22 - 88]\).
\[ 22 - 88 = -66 \]Finally, substitute this value back into the expression and perform the last subtraction:
\[ 22 - (-66) \]\[ 22 - (-66) = 22 + 66 = 88 \]C) 88 is the correct result after following the order of operations.
The question asks to identify the incorrect statement regarding the distribution of elements (metals, non-metals, metalloids) in the periodic table. We need to evaluate each option based on the standard arrangement of elements.
Based on this analysis, statement C is incorrect because metalloids have a specific, non-random placement along the dividing line between metals and non-metals.
C) Metalloids are scattered randomly throughout the table. This statement is incorrect. Metalloids are located along the zig-zag line that separates metals from non-metals in the periodic table, indicating a specific, non-random placement.
To find the area of a parallelogram, we use the formula: Area = base × height. We are given the expressions for the base and height in terms of variables \(x\) and \(y\). We will first substitute the given values of \(x\) and \(y\) into these expressions to find the numerical values of the base and height, and then multiply them to get the area.
Identify the given expressions for base and height:
Substitute the given values of \(x = 3\) and \(y = -2\) into the expression for the base:
\[ b = 4(3)^{2} - 7(3)(-2) + (-2)^{2} \]\[ b = 4(9) - (-42) + 4 \]\[ b = 36 + 42 + 4 \]\[ b = 82 \text{ m} \]Substitute the given values of \(x = 3\) and \(y = -2\) into the expression for the height:
\[ h = 3 + (-2) \]\[ h = 3 - 2 \]\[ h = 1 \text{ m} \]Calculate the area of the parallelogram using the formula Area = base × height:
\[ \text{Area} = b \times h \]\[ \text{Area} = 82 \text{ m} \times 1 \text{ m} \]\[ \text{Area} = 82 \text{ m}^2 \]Correct Option: B) The area of the parallelogram is \(82 \text{ m}^2\). This matches our calculated value.