To find the ratio of the two numbers, we first need to express them in terms of a third number. We can assume the third number to be 100 for easy percentage calculations. Then, we calculate the values of the two numbers based on the given percentages and form their ratio.
Let the third number be \(C\).
\[ C = 100 \]The first number (\(A\)) is 30% more than the third number.
\[ A = C + 30\% \text{ of } C \]\[ A = C \left(1 + \frac{30}{100}\right) \]\[ A = 100 \left(1 + \frac{30}{100}\right) \]\[ A = 100 \left(\frac{100+30}{100}\right) \]\[ A = 100 \times \frac{130}{100} \]\[ A = 130 \]The second number (\(B\)) is 18% more than the third number.
\[ B = C + 18\% \text{ of } C \]\[ B = C \left(1 + \frac{18}{100}\right) \]\[ B = 100 \left(1 + \frac{18}{100}\right) \]\[ B = 100 \left(\frac{100+18}{100}\right) \]\[ B = 100 \times \frac{118}{100} \]\[ B = 118 \]The ratio of the first number to the second number is \(A : B\).
\[ A : B = 130 : 118 \]Both numbers are divisible by 2.
\[ \frac{130}{2} : \frac{118}{2} \]\[ 65 : 59 \]Correct Option: C) 65 : 59
The question asks about the body primarily exercising powers delegated through Article 243W of the Indian Constitution. This article is part of Part IXA of the Constitution, which deals with Municipalities. Understanding the scope of Part IXA is key to identifying the correct answer.
Correct Option: B) Municipal Corporations. Article 243W of the Indian Constitution, introduced by the 74th Amendment Act, deals with the powers, authority, and responsibilities of Municipalities, which include Municipal Corporations, Municipal Councils, and Nagar Panchayats. Therefore, Municipal Corporations primarily exercise the powers delegated through this article.
The problem describes a coding-decoding relationship based on the English alphabetical order. We need to identify the pattern between the given pairs of words and then apply the same pattern to find the related word for "SCLQ".
B) WYPM is the correct option as it follows the established \((+4, -4, +4, -4)\) pattern.
The question asks for the approximate number of farmer IDs generated under the Digital Agriculture Mission as of a specific date (28 March 2025). This requires knowledge of recent government initiatives and their progress, which is a common topic in competitive exams. The key is to recall the most up-to-date figures released by official sources regarding this mission.
A) 4.85 crore is the correct answer. As of recent official statements and reports regarding the Digital Agriculture Mission, approximately 4.85 crore farmer IDs have been generated. This initiative is a crucial part of the government's efforts to modernize agriculture and enhance farmer welfare through digital means.
To find the median of a set of observations, we first need to arrange the observations in ascending or descending order. Once ordered, the median is the middle value if the number of observations is odd. If the number of observations is even, the median is the average of the two middle values.
The given observations are 49, 91, 24, 46, 90, 20, 21, 14, 66, 32, and 92.
Counting them, we find there are 11 observations. Let \(n\) be the number of observations, so \(n = 11\).
14, 20, 21, 24, 32, 46, 49, 66, 90, 91, 92
Since \(n = 11\) (an odd number), the median will be the \(\left(\frac{n+1}{2}\right)^{\text{th}}\) observation.
\[\text{Median position} = \frac{11+1}{2} = \frac{12}{2} = 6^{\text{th}}\]The 6th observation in the sorted list is 46.
14, 20, 21, 24, 32, 46, 49, 66, 90, 91, 92
Thus, the median is 46.
A) 46 is the correct median as it is the 6th value in the ascending ordered list of 11 observations.
The question asks to identify the first Indian recipient of the Ramsar Award for 'Wetland Wise Use' in March 2025. This requires specific knowledge of environmental awards and their recipients.
In March 2025, Dr. Jayshree Vencatesan was announced as the first Indian to receive the Ramsar Award for 'Wetland Wise Use'. She is a conservationist known for her work with the Care Earth Trust in Chennai, focusing on wetland conservation and restoration.
C) Jayshree Vencatesan — Dr. Jayshree Vencatesan is indeed the first Indian to receive the Ramsar Award for 'Wetland Wise Use', an announcement made in March 2025. Her work with Care Earth Trust has been instrumental in wetland conservation in India.
To find the amount after 1 year when interest is compounded half-yearly, we need to adjust the annual interest rate and the number of compounding periods. The annual rate is divided by 2, and the number of years is multiplied by 2 to get the number of half-yearly 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 number of years needs to be multiplied by 2 to get the number of compounding periods.
The formula for the amount (\(A\)) after \(n\) periods is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]The amount after 1 year will be ₹2,904.
Correct Option: B) ₹2,904
To find the amount of water in the cuboid, we need to calculate the volume of the cuboid and subtract the volume of the hemisphere fitted inside it. The hemisphere displaces water, so the remaining volume is the water content.
Calculate the volume of the cuboid:
The dimensions of the cuboid are given as 6 cm × 6 cm × 3 cm.
\[ \text{Volume of cuboid} = \text{length} \times \text{width} \times \text{height} \] \[ \text{Volume of cuboid} = 6 \text{ cm} \times 6 \text{ cm} \times 3 \text{ cm} = 108 \text{ cm}^3 \]Calculate the volume of the hemisphere:
The radius of the hemisphere is given as 3 cm. The formula for the volume of a hemisphere is \(\frac{2}{3} \pi r^3\).
\[ \text{Volume of hemisphere} = \frac{2}{3} \pi (3 \text{ cm})^3 \] \[ \text{Volume of hemisphere} = \frac{2}{3} \times 3.14 \times 27 \text{ cm}^3 \] \[ \text{Volume of hemisphere} = 2 \times 3.14 \times 9 \text{ cm}^3 \] \[ \text{Volume of hemisphere} = 18 \times 3.14 \text{ cm}^3 \] \[ \text{Volume of hemisphere} = 56.52 \text{ cm}^3 \]Calculate the amount of water in the cuboid:
The amount of water is the volume of the cuboid minus the volume of the hemisphere.
\[ \text{Amount of water} = \text{Volume of cuboid} - \text{Volume of hemisphere} \] \[ \text{Amount of water} = 108 \text{ cm}^3 - 56.52 \text{ cm}^3 \] \[ \text{Amount of water} = 51.48 \text{ cm}^3 \]Correct Option: C) 51.48
To solve this problem, we need to use the formula for average speed, which is the total distance covered divided by the total time taken. We will calculate the time taken for each segment of the journey and then sum them up to find the total time. We are given the total distance and the average speed, which will allow us to set up an equation to find the unknown speed 'x'.
The total distance (\(D_{\text{total}}\)) is the sum of all individual distances.
\[ D_{\text{total}} = D_1 + D_2 + D_3 = 100 + 408 + 1460 = 1968 \text{ km} \]The formula for time is \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\).
The total time (\(T_{\text{total}}\)) is the sum of the times for each segment.
\[ T_{\text{total}} = T_1 + T_2 + T_3 = 5 + \frac{408}{x} + 73 = 78 + \frac{408}{x} \text{ hours} \]The average speed is given by \[\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}\].
\[ S_{\text{avg}} = \frac{D_{\text{total}}}{T_{\text{total}}} \]\[ 20 = \frac{1968}{78 + \frac{408}{x}} \]Rearrange the equation to solve for x.
\[ 20 \left(78 + \frac{408}{x}\right) = 1968 \]\[ 1560 + \frac{8160}{x} = 1968 \]\[ \frac{8160}{x} = 1968 - 1560 \]\[ \frac{8160}{x} = 408 \]\[ x = \frac{8160}{408} \]\[ x = 20 \]C) 20
The value of x, which represents the speed for the second segment of the journey, is 20 km/hr. This means that the man traveled at the same speed (20 km/hr) for the first and third segments, and also for the second segment, resulting in an overall average speed of 20 km/hr.
The question asks to identify a common tree species found in the plains of the Thar Desert. This requires knowledge of the typical vegetation adapted to arid and semi-arid desert environments in India.
A) Khejri is famously known as the 'Kalpavriksha' of the Thar Desert due to its immense ecological and economic importance. It is highly adapted to the arid climate, providing fodder, fuel, timber, and shade, and playing a crucial role in soil conservation.