Select the Answer Figure that fits in the blank space in the given Problem Figure.
Problem Figure:
Answer Figures:
The problem figure consists of a 3x3 grid with circles and lines emanating from them. The task is to identify the pattern and select the correct answer figure to complete the sequence.
Correct Option: C) The lines are horizontally oriented, completing the pattern.
How many atoms are present in a (NH4)2SO4 molecule?
To determine the total number of atoms in a molecule, we need to count the atoms of each element present and sum them up. The subscripts in the chemical formula indicate the number of atoms of that element. Parentheses around a group of atoms followed by a subscript mean that the entire group is multiplied by that subscript.
Therefore, there are 15 atoms present in one molecule of \((NH_4)_2SO_4\).
Correct Option: C) 15
This problem can be solved using the empirical relationship between the mean, median, and mode for a moderately skewed distribution. This relationship is given by Karl Pearson's formula.
Recall Karl Pearson's Empirical Formula: For a moderately skewed distribution, the relationship between mean, median, and mode is approximately given by:
\[ \text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean} \]Rearrange the formula: We can rearrange this formula to express the difference between mode and median in terms of the difference between median and mean:
\[ \text{Mode} - \text{Median} \approx 2 \times \text{Median} - 2 \times \text{Mean} \]\[ \text{Mode} - \text{Median} \approx 2 (\text{Median} - \text{Mean}) \]Substitute the given information: The problem states that the difference between the mode and median is 2. So, we have:
\[ 2 = 2 (\text{Median} - \text{Mean}) \]Solve for the required difference: Divide both sides by 2:
\[ \frac{2}{2} = \text{Median} - \text{Mean} \]\[ 1 = \text{Median} - \text{Mean} \]Thus, the difference between the median and mean is 1.
A) 1 — Based on Karl Pearson's empirical formula for moderately skewed distributions, if the difference between the mode and median is 2, then the difference between the median and mean is 1.
We need to analyze the given argument and determine which of the provided assumptions are implicitly made. An implicit assumption is something that is not stated directly but must be true for the argument to hold or make sense. We will evaluate each assumption against the argument's statement.
A) Only assumption 2 is implicit.
The question asks for the definition of momentum. We need to recall the fundamental formula for momentum in physics.
Correct Option: A) Momentum is measured as the product of mass and velocity.
The question asks to determine the total sale of company ABC. We need to evaluate if the given statements individually or together provide enough information to calculate the total sale.
D) Both 1 and 2 are sufficient to answer the question. This is because statement 1 provides the sales figures for soaps, and statement 2 confirms that soaps are the only product, allowing us to calculate the total sale.
The question asks to identify the author of the book 'The Association of Small Bombs', which was shortlisted for the International Dublin Literary Award in 2018. This requires knowledge of contemporary Indian authors and their notable works.
Karan Mahajan is the author of 'The Association of Small Bombs'. This novel was indeed shortlisted for the International Dublin Literary Award in 2018. It tells the story of the aftermath of a small bomb explosion in a Delhi market.
C) Karan Mahajan is the correct answer. He is the author of 'The Association of Small Bombs', which was shortlisted for the International Dublin Literary Award in 2018.
To calculate the simple interest, we use the standard formula which involves the principal amount, the rate of interest, and the time period. We will substitute the given values into this formula to find the interest earned.
The formula for simple interest is:
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]Substitute P = 1600, R = 5, and T = 6 into the formula:
\[ \text{SI} = \frac{1600 \times 5 \times 6}{100} \]First, multiply the numbers in the numerator:
\[ 1600 \times 5 = 8000 \]\[ 8000 \times 6 = 48000 \]Now, divide by 100:
\[ \text{SI} = \frac{48000}{100} = 480 \]The simple interest earned is Rs. 480.
Correct Option: B) Rs. 480
The question asks to identify the group of plants that do not have a differentiated plant body. This refers to organisms where the body is not clearly divided into roots, stems, and leaves. We need to recall the classification of the plant kingdom and the characteristics of each major group.
Correct Option: D) Thallophyta
Thallophyta is the most primitive group of plants, primarily comprising algae. Their plant body is referred to as a 'thallus' because it is simple and undifferentiated, meaning it lacks true roots, stems, and leaves.