This problem can be solved by understanding percentages. If a certain percentage of apples are sold, the remaining apples represent the complementary percentage of the original total. We can set up an equation to find the original number of apples.
Thus, the fruit seller originally had 400 apples.
Correct Option: A) 400
The problem presents a series of three-letter combinations based on the English alphabetical order. We need to identify the pattern for each position (first, second, and third letter) separately and then apply it to find the missing term.
Y (25), P (16), G (7), X (24), ?
Let's find the difference between the positional values:
R (18), I (9), Z (26), Q (17), ?
Let's find the difference between the positional values:
M (13), D (4), U (21), L (12), ?
Let's find the difference between the positional values:
The first letter is O, the second letter is H, and the third letter is C. Therefore, the next term in the series is OHC.
C) OHC is the correct option because, by applying the pattern of subtracting 9 from the alphabetical position for each letter cyclically, we arrive at OHC.
To calculate the work done by a force, we use the formula for work, which is the product of the force applied and the displacement in the direction of the force. Since the displacement is in the same direction as the force, the angle between them is 0 degrees, and the cosine of 0 degrees is 1.
The work done (\(W\)) by a constant force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]Since the displacement is in the direction of the force, \(\theta = 0^\circ\). We know that \(\cos(0^\circ) = 1\).
\[ W = 10 \, \text{N} \times 2 \, \text{m} \times \cos(0^\circ) \]\[ W = 10 \, \text{N} \times 2 \, \text{m} \times 1 \]The unit Newton-meter (N·m) is equivalent to Joule (J).
\[ W = 20 \, \text{J} \]C) 20 joules is the correct answer. The work done is calculated as the product of force and displacement when they are in the same direction.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to find the relationship between the letters within each cluster (e.g., T-X) and between the two clusters in a pair (e.g., TX and RV).
Alphabetical positions:
A) TX-RV
B) SV-MP
C) AD-UX
D) FI-ZC
Let's re-evaluate D) FI-ZC with wrap-around for consistency. The problem implies a linear alphabetical order, but sometimes wrap-around is used. Let's assume the primary pattern is the difference between letters.
Looking at the pattern within clusters for B, C, and D (assuming wrap-around for ZC):
So, in options B, C, and D, the difference between the second and first letter within each cluster is \(+3\).
Now let's check the pattern between the clusters for B, C, and D:
So, the common pattern among B, C, and D is that the difference between the letters within each cluster is \(+3\), and the difference between the corresponding letters of the two clusters is consistent (e.g., \(-6\) for both letters in B, \(+20\) for both letters in C and D).
Now, let's re-examine A) TX-RV:
Option A has a \(\boldsymbol{+4}\) difference within its clusters, while options B, C, and D have a \(\boldsymbol{+3}\) difference within their clusters. All options show a consistent difference between the corresponding letters of the two clusters.
Therefore, the distinguishing factor is the difference within the clusters.
A) TX-RV — In this pair, the difference between the letters within each cluster is \(+4\) (T to X is \(+4\), R to V is \(+4\)). This is different from the other three options where the difference within each cluster is \(+3\).
The question asks for the state where the Vishnupad Temple, for which funds were allocated in the 2024 Union Budget for corridor development, is located. This requires knowledge of prominent religious sites in India and current affairs related to government initiatives.
Correct Option: D) The Vishnupad Temple is located in Gaya, Bihar. The government's allocation of funds for its corridor development in the 2024 Union Budget makes it a relevant current affairs topic.
To determine which element iron is more reactive than, we need to recall the reactivity series of metals. The reactivity series lists metals in order of their decreasing reactivity. A metal higher in the series is more reactive than a metal lower in the series and can displace it from its compounds.
Correct Option: C) copper
This problem involves analyzing statements and conclusions based on the principles of syllogism, often visualized using Venn diagrams. We need to determine which conclusions logically follow from the given statements, treating the statements as absolutely true.
Correct Option: A) Both conclusions (I) and (II) follow.
To find the single equivalent discount for successive discounts, we can assume an initial price (e.g., 100 units) and apply each discount sequentially. Alternatively, a direct formula for equivalent discount can be used.
Let the original price of the item be \(P = 100\).
The first discount is 25%. So, the price after the first discount will be:
\[ P_1 = P - (0.25 \times P) = P(1 - 0.25) = 100 \times 0.75 = 75 \]The second discount is 10%, applied to the discounted price \(P_1\). So, the price after the second discount will be:
\[ P_2 = P_1 - (0.10 \times P_1) = P_1(1 - 0.10) = 75 \times 0.90 = 67.5 \]The total discount is the difference between the original price and the final price:
\[ \text{Total Discount Amount} = P - P_2 = 100 - 67.5 = 32.5 \]Since we started with an original price of 100, the total discount amount directly represents the equivalent single discount percentage.
\[ \text{Equivalent Single Discount} = \frac{\text{Total Discount Amount}}{\text{Original Price}} \times 100\% = \frac{32.5}{100} \times 100\% = 32.5\% \]For two successive discounts of \(d_1\%\) and \(d_2\%\), the equivalent single discount \(D\%\) can be calculated using the formula:
\[ D = \left( d_1 + d_2 - \frac{d_1 \times d_2}{100} \right)\% \]Given \(d_1 = 25\%\) and \(d_2 = 10\%\):
\[ D = \left( 25 + 10 - \frac{25 \times 10}{100} \right)\% \] \[ D = \left( 35 - \frac{250}{100} \right)\% \] \[ D = (35 - 2.5)\% \] \[ D = 32.5\% \]C) 32.5% is the single equivalent discount.
The question asks for the correct age range of puberty in human males and females. Puberty is the process of physical changes through which a child's body matures into an adult body capable of sexual reproduction. The onset and duration of puberty can vary among individuals, but there are generally accepted age ranges for both sexes.
Correct Option: B) 11-17 years
The problem involves finding the breadth of a wall given its volume and the relationships between its dimensions (length, breadth, and height). We will express all dimensions in terms of breadth, then use the formula for the volume of a cuboid to solve for the breadth.
Let the breadth of the wall be \(b\) meters.
According to the problem, the wall is 5 times as high as it is broad. So, the height \(h\) can be expressed as:
\[ h = 5b \]The wall is 8 times as long as it is high. So, the length \(l\) can be expressed as:
\[ l = 8h \]Substitute the expression for \(h\) from step 2 into the equation for \(l\):
\[ l = 8(5b) \]\[ l = 40b \]The volume \(V\) of a cuboid (wall) is given by the formula:
\[ V = l \times b \times h \]Substitute the expressions for \(l\), \(b\), and \(h\) in terms of \(b\) into the volume formula:
\[ V = (40b) \times b \times (5b) \]\[ V = 200b^3 \]We are given that the volume \(V = 12.8\) cubic meters. Set up the equation:
\[ 200b^3 = 12.8 \]Solve for \(b^3\):
\[ b^3 = \frac{12.8}{200} \]\[ b^3 = \frac{128}{2000} \]\[ b^3 = \frac{64}{1000} \]Take the cube root of both sides to find \(b\):
\[ b = \sqrt[3]{\frac{64}{1000}} \]\[ b = \frac{\sqrt[3]{64}}{\sqrt[3]{1000}} \]\[ b = \frac{4}{10} \]\[ b = 0.4 \text{ meters} \]The question asks for the breadth. The options are in meters and centimeters. Convert the breadth from meters to centimeters:
\[ b = 0.4 \text{ meters} \times 100 \frac{\text{cm}}{\text{meter}} \]\[ b = 40 \text{ cm} \]Correct Option: B) 40 cm