To find the average speed, we need to calculate the total distance traveled and the total time taken. The average speed is then the total distance divided by the total time.
Distance \(D_1 = 183\) km
Speed \(S_1 = 61\) km/h
Time \(T_1 = \frac{D_1}{S_1}\)
\[ T_1 = \frac{183 \text{ km}}{61 \text{ km/h}} = 3 \text{ hours} \]Distance \(D_2 = 225\) km
Speed \(S_2 = 45\) km/h
Time \(T_2 = \frac{D_2}{S_2}\)
\[ T_2 = \frac{225 \text{ km}}{45 \text{ km/h}} = 5 \text{ hours} \]Total Distance \(D_{\text{total}} = D_1 + D_2\)
\[ D_{\text{total}} = 183 \text{ km} + 225 \text{ km} = 408 \text{ km} \]Total Time \(T_{\text{total}} = T_1 + T_2\)
\[ T_{\text{total}} = 3 \text{ hours} + 5 \text{ hours} = 8 \text{ hours} \]Average Speed \[S_{\text{avg}} = \frac{D_{\text{total}}}{T_{\text{total}}}\]
\[ S_{\text{avg}} = \frac{408 \text{ km}}{8 \text{ hours}} = 51 \text{ km/h} \]Correct Option: C) 51
The average speed of Anamika is 51 km/h, which matches option C.
This problem involves calculating the combined work rate of two individuals, A and B, to find the total time taken to complete a task when they work together. We will use the concept of work and time, where the amount of work done is inversely proportional to the time taken.
To add these fractions, find a common denominator, which is 40:
\[ \text{Combined work rate} = \frac{10}{40} + \frac{1}{40} \]\[ \text{Combined work rate} = \frac{10 + 1}{40} = \frac{11}{40} \text{ of the work per day} \]C) 3.6 is the correct number of days required to complete the work when A and B work together, rounded to one decimal place.
The question asks to identify the winner of the Irani Cup for the 2024-25 season. This requires knowledge of recent domestic cricket tournament results in India.
Correct Option: A) Mumbai clinched the Irani Cup title for the season 2024-25. They were the Ranji Trophy 2023-24 champions and went on to win the Irani Cup against the Rest of India team.
The problem asks us to find a letter-cluster pair that shares the same relationship as the given pairs: WJT : ZNO and KAK : NEF. We need to identify the pattern of letter shifts between the first and second clusters in the given pairs and then apply that pattern to the options.
A) NKH : QOC
To solve this problem, we need to track Mayank's movements step-by-step, considering each turn and distance covered. We can represent his path on a coordinate plane or by keeping track of his net displacement in the East-West and North-South directions. The final position relative to the starting point A will determine the shortest distance and direction needed to return to A.
C) 6 km to the south. As calculated, Mayank's final position (Point P) is 6 km North of Point A. Therefore, to return to Point A, he must drive 6 km towards the South.
₹3,300 were divided among P, Q and R, such that 4 times of P = 7 times of Q = 2 times of R. Find the share of R.
To find the share of R, we first need to determine the ratio of the shares of P, Q, and R. We are given a relationship between their shares: \(4P = 7Q = 2R\). We can use this relationship to express the shares in terms of a common constant or find their ratios directly by finding the Least Common Multiple (LCM) of the coefficients.
Establish the relationship:
We are given: \(4P = 7Q = 2R\)
Let this common value be \(k\). So, \(4P = k\), \(7Q = k\), and \(2R = k\).
Express P, Q, and R in terms of k:
Find the ratio P : Q : R:
The ratio is \[\frac{k}{4} : \frac{k}{7} : \frac{k}{2}\]. We can cancel \(k\) from all terms (assuming \(k \neq 0\)):
\[P : Q : R = \frac{1}{4} : \frac{1}{7} : \frac{1}{2}\]
Convert the fractional ratio to a whole number ratio:
To do this, find the LCM of the denominators (4, 7, 2). The LCM of 4, 7, and 2 is 28.
Multiply each part of the ratio by the LCM (28):
\[ P : Q : R = \left(\frac{1}{4} \times 28\right) : \left(\frac{1}{7} \times 28\right) : \left(\frac{1}{2} \times 28\right) \]\[ P : Q : R = 7 : 4 : 14 \]Calculate the total sum of the ratio parts:
Sum of ratio parts \( = 7 + 4 + 14 = 25\)
Calculate R's share:
The total amount divided is ₹3,300.
R's share \[= \frac{\text{R's ratio part}}{\text{Total ratio parts}} \times \text{Total amount}\]
\[ \text{R's share} = \frac{14}{25} \times 3300 \]\[ \text{R's share} = 14 \times \frac{3300}{25} \]\[ \text{R's share} = 14 \times 132 \]\[ \text{R's share} = \text{₹}1848 \]D) ₹1,848 — The share of R is ₹1,848, calculated based on the derived ratio of 7:4:14 for P:Q:R.
The angle of elevation of a tower from a point which is at a distance of 44 m from its foot is 60°. Find the height of the tower. (use \(\sqrt{3}\) = 1.73)
This problem involves trigonometry, specifically the tangent function, to find the height of a tower given the angle of elevation and the distance from the base of the tower. We will form a right-angled triangle and use the formula \[\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}\].
In a right-angled triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side.
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]We know that \(\tan(60^\circ) = \sqrt{3}\).
A) 76.12 m is the correct height of the tower calculated using the tangent function and the given values.
This is a coding-decoding problem. We need to find the common words and their corresponding codes across the given statements to deduce the code for 'actor'.
Correct Option: A) st is the code for 'actor' as derived from the common elements in the given coded statements.
The question asks for the term describing the oxidation of metals in the presence of acids or moisture. This process is a common chemical reaction that degrades metals.
A) corrosion is the general term for the degradation of metals (or other materials) due to chemical or electrochemical reactions with their environment, which often involves oxidation in the presence of moisture, acids, or other reactive substances. Rusting is a specific type of corrosion affecting iron.
The question asks to identify the ruler of Gujarat during Humayun's attack in 1532. This requires knowledge of the timeline of the Mughal Empire and the Gujarat Sultanate.
Correct Option: D) Bahadur Shah was the Sultan of Gujarat when Humayun attacked the kingdom in 1532. He was a formidable ruler who had expanded his territory and was a major challenge to Humayun's authority.