To find the median of a given set of data, we first need to arrange the data in ascending order. Then, we determine if the number of data points is odd or even. If it's odd, the median is the middle value. If it's even, the median is the average of the two middle values.
11, 15, 16, 17, 18, 22, 33, 51, 71, 75
Correct Option: B) 20
Simplify (32)3 + (23)2
The problem requires simplifying an expression involving exponents. We need to apply the rules of exponents, specifically the power of a power rule \((a^m)^n = a^{m \times n}\) and then perform the addition.
Therefore, the simplified expression is 793.
Correct Option: B) 793
The question asks to identify the hill range where Mawsynram, known as the wettest place on Earth, is located. This is a factual question related to Indian geography.
D) Khasi Hills — Mawsynram is located in the Khasi Hills of Meghalaya, India. This region is famous for receiving the highest average annual rainfall in the world, primarily due to its unique topography that traps monsoon clouds.
To find the percentage increase, we first need to calculate the absolute increase in salary. Then, we divide this increase by the original salary (last year's salary) and multiply by 100 to express it as a percentage.
The increase in salary is the difference between this year's salary and last year's salary.
\[ \text{Increase in salary} = \text{Current salary} - \text{Previous salary} \\ \text{Increase in salary} = 38,640 - 34,500 \\ \text{Increase in salary} = 4,140 \]The percentage increase is calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in salary}}{\text{Previous salary}} \right) \times 100\% \]\[ \text{Percentage Increase} = \left( \frac{4,140}{34,500} \right) \times 100\% \]\[ \text{Percentage Increase} = 0.12 \times 100\% \]\[ \text{Percentage Increase} = 12\% \]Thus, the percentage increase in Ranjan's monthly salary is 12%.
Correct Option: B) 12%
The question asks for the location where GAIL initiated India's first project to blend hydrogen into natural gas systems in January 2022. This is a factual question related to current affairs and infrastructure development in the energy sector.
Correct Option: B) Indore
In January 2022, GAIL (India) Limited commenced India's maiden project of blending hydrogen into the natural gas system at Indore, Madhya Pradesh. This project is a significant step towards a hydrogen-based economy and reducing the carbon footprint of natural gas consumption.
To solve this problem, we need to track Anita's movements step-by-step, considering both the distance walked and the direction. We can represent the movements on a coordinate plane or by keeping track of net displacement in the North-South and East-West directions.
Alternatively, we can sum up the displacements:
Since the net East-West displacement is 0 and the net North-South displacement is \(-100\) m (meaning 100 m South), point B is 100 m South of point A.
Correct Option: B) 100 m, South
To find the missing number in the series, we need to identify the pattern or the rule governing the sequence of numbers. This usually involves looking at the differences between consecutive terms, or the differences of these differences (second-order differences), or some other mathematical operation.
Thus, the missing number is 301.
Correct Option: B) 301
This problem involves analyzing logical statements and conclusions using Venn diagrams or by applying rules of syllogism. We will draw Venn diagrams for the given statements to visualize the relationships between the categories (phones, tablets, calculators, drives) and then check which conclusions logically follow from these diagrams.
A) Only conclusion III follows
The question asks to identify the correct statements regarding the classification of elements. We need to evaluate each statement individually based on the historical development and principles of elemental classification.
Since all three statements (i), (ii), and (iii) are correct, the option that includes all of them is the right answer.
Correct Option: C) i, ii, iii
The I-V graph of three resistances R1, R2, and R3 is shown in the figure below. The correct relation between R1, R2, and R3 is:
R3 < R1 < R2
R3 > R1 > R2
R1 > R2 > R3
R1 < R2 < R3
To determine the correct relationship between the resistances \( R_1 \), \( R_2 \), and \( R_3 \), we need to analyze the slopes of the lines on the I-V graph. The slope of each line represents the inverse of the resistance, as per Ohm's Law \( V = IR \).
Correct Option: A) \( R_3 < R_1 < R_2 \)