Solve the following:
72 ÷ \( \frac{1}{2} \){15 + 12 - (9 + 6 - (\(\overline{5+7}\)))} = ?
To solve this problem, we need to apply the BODMAS/PEMDAS rule (Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, Subtraction). We will evaluate the expression from the innermost brackets outwards, following the order of operations.
Thus, the final answer is 6.
A) 6 is the correct answer, as derived from the step-by-step application of the BODMAS rule.
Which of the following numbers is irrational?
\(\sqrt[3]{64}\)
\(\sqrt[]{64}\)
\(\sqrt[6]{64}\)
\(\sqrt[4]{64}\)
To determine which number is irrational, we need to simplify each given expression. A number is irrational if it cannot be expressed as a simple fraction \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\). In the context of roots, a number \(\sqrt[n]{x}\) is rational if \(x\) is a perfect \(n^{th}\) power of some rational number; otherwise, it is irrational.
D) \(\sqrt[4]{64}\) is irrational because it simplifies to \(\sqrt[]{8}\), which is not an integer or a simple fraction.
The question asks about the chromosomal combination in a normal human female (girl child). We need to recall the basic human karyotype, which includes autosomes and sex chromosomes, and how they differ between males and females.
A) 44 autosomes + XX — This correctly represents the chromosomal composition of a normal human female (girl child), with 44 autosomes and two X sex chromosomes.
To calculate the percentage of water of crystallisation in washing soda, we need to determine the molecular mass of washing soda (\(\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}\)) and the total mass of water molecules present in one molecule of washing soda. Then, we can use the formula for percentage composition.
Identify the chemical formula of washing soda:
Washing soda is chemically known as sodium carbonate decahydrate, and its formula is \(\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}\).
Determine the atomic masses of the elements involved:
Calculate the molecular mass of anhydrous sodium carbonate (\(\text{Na}_2\text{CO}_3\)):
\[ \text{Mass of } \text{Na}_2\text{CO}_3 = (2 \times 23) + (1 \times 12) + (3 \times 16) \]\[ = 46 + 12 + 48 = 106 \text{ u} \]Calculate the molecular mass of water (\(\text{H}_2\text{O}\)):
\[ \text{Mass of } \text{H}_2\text{O} = (2 \times 1) + (1 \times 16) \]\[ = 2 + 16 = 18 \text{ u} \]Calculate the total mass of water of crystallisation (\(10\text{H}_2\text{O}\)):
\[ \text{Mass of } 10\text{H}_2\text{O} = 10 \times 18 = 180 \text{ u} \]Calculate the total molecular mass of washing soda (\(\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}\)):
\[ \text{Total molecular mass} = \text{Mass of } \text{Na}_2\text{CO}_3 + \text{Mass of } 10\text{H}_2\text{O} \]\[ = 106 + 180 = 286 \text{ u} \]Calculate the percentage of water of crystallisation:
\[ \text{Percentage of water} = \frac{\text{Mass of } 10\text{H}_2\text{O}}{\text{Total molecular mass of washing soda}} \times 100 \]\[ = \frac{180}{286} \times 100 \]\[ = 0.62937 \times 100 \]\[ \approx 62.937 \% \]Round to one decimal place:
The percentage of water of crystallisation is approximately \(62.9\%\).
Correct Option: D) 62.9
The problem asks us to determine if the given statements are sufficient to find the total number of illegal immigrants. We need to analyze each statement individually and then together to see if they provide enough information to calculate a specific numerical value for the total number of illegal immigrants.
Analyze Statement 1: "30% of the total illegal immigrants are from Bangladesh."
Let \(T\) be the total number of illegal immigrants. According to Statement 1, the number of illegal immigrants from Bangladesh is \(0.30 \times T\). This statement gives us a proportion but does not provide any absolute number. We don't know the value of \(T\).
Therefore, Statement 1 alone is not sufficient to find the total number of illegal immigrants.
Analyze Statement 2: "Remaining are from India."
This statement tells us about the origin of the remaining illegal immigrants. However, it does not provide any numerical value or proportion. It simply states that if there are any illegal immigrants not from Bangladesh (as per Statement 1), they are from India. If considered alone, this statement provides no information about the total number of immigrants or any part of it.
Therefore, Statement 2 alone is not sufficient to find the total number of illegal immigrants.
Analyze Statements 1 and 2 together:
From Statement 1, 30% of the total illegal immigrants are from Bangladesh.
From Statement 2, the remaining immigrants are from India. This implies that if 30% are from Bangladesh, then \(100\% - 30\% = 70\%\) of the total illegal immigrants are from India.
So, we know that:
Even with both statements, we only have the proportions of immigrants from Bangladesh and India relative to the total. We still do not have any absolute number (e.g., the number of immigrants from Bangladesh, or the number of immigrants from India, or any other specific count). Without at least one absolute number, we cannot calculate the total number of illegal immigrants \(T\).
Therefore, both statements 1 and 2 together are not sufficient to answer the question.
Correct Option: C) Neither 1 nor 2 is sufficient to answer the question.
Who is the Bengali writer who won the 31st Moortidevi Award for the year 2017?
Joy Goswami
Taslima Nasreen
Subhro Bandhopadhyay
Baby Halder
The question asks to identify the Bengali writer who received the 31st Moortidevi Award for the year 2017. This requires knowledge of prominent literary awards and their recipients, specifically the Moortidevi Award.
A) Joy Goswami is the correct answer. He was awarded the 31st Moortidevi Award for 2017 for his poetry collection "Du Dondo Phowara Matro".
Based on the given table, the overall percentage increase in salary from 2001 to 2006 was _____ (round off to the nearest integer).
| Year | Items of Expenditure | |||
| Salary | Food | Medicine | Tax | |
| 2001 | ₹ 1,500 | ₹ 200 | ₹ 500 | ₹ 100 |
| 2002 | ₹ 2,600 | ₹ 300 | ₹ 600 | ₹ 200 |
| 2003 | ₹ 3,200 | ₹ 150 | ₹ 700 | ₹ 150 |
| 2004 | ₹ 4,100 | ₹ 250 | ₹ 650 | ₹ 125 |
| 2005 | ₹ 5,000 | ₹ 200 | ₹ 800 | ₹ 150 |
| 2006 | ₹ 5,200 | ₹ 100 | ₹ 750 | ₹ 175 |
To find the overall percentage increase in salary from 2001 to 2006, we need to identify the salary in 2001 (initial salary) and the salary in 2006 (final salary) from the given table. Then, we will use the percentage increase formula: \[\frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\].
Correct Option: B) 247
To determine the nature of the acid and base that form NaCl, we need to identify the parent acid and base from which NaCl is derived and classify them as strong or weak.
Correct Option: C) Strong acid and strong base
This problem involves calculating the sum of numbers based on their mean and then using these sums to find the mean of a subset of numbers. We will use the formula: \[\text{Mean} = \frac{\text{Sum of numbers}}{\text{Count of numbers}}\].
Calculate the sum of the 5 smallest numbers:
Given that the mean of the 5 smallest numbers is 15.
Calculate the sum of all 13 numbers in the group:
Given that the mean of all 13 numbers is 17.
Calculate the sum of the 8 largest numbers:
The group consists of 13 numbers. If we remove the 5 smallest numbers, the remaining numbers are the 8 largest numbers. Therefore, the sum of the 8 largest numbers can be found by subtracting the sum of the 5 smallest numbers from the sum of all 13 numbers.
Calculate the mean of the 8 largest numbers:
Now, we have the sum of the 8 largest numbers and their count (which is 8).
Correct Option: D) 18.25
A and B together can do a piece of work in 10 days. If A can do the work in 15 days, find in how many days B alone can do the same work. Given below are the steps involved in solving the above problem. Arrange them in sequential order.
A) One day's work of B is \( \frac{1}{10} \) - \( \frac{1}{15} \)
B) One day's work of A and B is \( \frac{1}{10} \) and one day's work of A is \( \frac{1}{15} \)
C) B alone can do the work in 30 days
D) One day's work of B is \( \frac{1}{30} \)
This problem involves calculating the time taken by an individual to complete a work, given the time taken by two individuals together and one individual alone. The key concept is to use the 'one day's work' method, where the amount of work done in one day is the reciprocal of the total time taken to complete the work.
The sequential order of the steps is B, A, D, C.
A) BADC is the correct sequence as derived from the step-by-step explanation.