The value of \( \frac{56}{5} \) + 5 \( \frac{1}{10} \) ÷ 3 \( \frac{2}{5} \) is:
10 \( \frac{7}{12} \)
12 \( \frac{7}{10} \)
8 \( \frac{4}{7} \)
9 \( \frac{1}{4} \)
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS). First, convert all mixed fractions to improper fractions. Then, perform the division operation, which involves multiplying by the reciprocal of the divisor. Finally, perform the addition.
The expression becomes:
\[ \frac{56}{5} + \frac{51}{10} \div \frac{17}{5} \]Dividing by a fraction is equivalent to multiplying by its reciprocal.
\[ \frac{51}{10} \div \frac{17}{5} = \frac{51}{10} \times \frac{5}{17} \]Now, simplify the multiplication:
\[ \frac{51}{10} \times \frac{5}{17} = \frac{51 \times 5}{10 \times 17} \]We know that \(51 = 3 \times 17\) and \(10 = 2 \times 5\). So,
\[ \frac{(3 \times 17) \times 5}{(2 \times 5) \times 17} = \frac{3 \times 17 \times 5}{2 \times 5 \times 17} \]Cancel out common terms (17 and 5):
\[ \frac{3}{2} \]Now substitute the result of the division back into the original expression:
\[ \frac{56}{5} + \frac{3}{2} \]To add these fractions, find a common denominator, which is 10.
\[ \frac{56 \times 2}{5 \times 2} + \frac{3 \times 5}{2 \times 5} = \frac{112}{10} + \frac{15}{10} \] \[ \frac{112 + 15}{10} = \frac{127}{10} \]So, \( 12\frac{7}{10} \).
Correct Option: B) \( 12\frac{7}{10} \)
The question asks to identify the country that is NOT a part of the proposed TAPI gas pipeline project. To answer this, one needs to know the countries involved in the TAPI pipeline.
Correct Option: D) Iran is not a part of the proposed TAPI gas pipeline project. The pipeline is designed to transport natural gas from Turkmenistan, through Afghanistan and Pakistan, to India.
This problem can be solved using the fundamental relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers. The product of two numbers is always equal to the product of their HCF and LCM.
Recall the relationship between HCF, LCM, and two numbers:
\[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \]Let the two numbers be \(N_1\) and \(N_2\). We are given:
Substitute the given values into the formula:
\[ N_1 \times N_2 = \text{HCF} \times \text{LCM} \] \[ 148 \times N_2 = 37 \times 740 \]Now, solve for \(N_2\):
\[ N_2 = \frac{37 \times 740}{148} \]Perform the calculation. We can simplify the expression:
Notice that \(148 = 4 \times 37\). So, we can cancel out 37:
\[ N_2 = \frac{37 \times 740}{4 \times 37} \] \[ N_2 = \frac{740}{4} \]Divide 740 by 4:
\[ N_2 = 185 \]C) The other number is 185.
The LCM of \( \frac{2}{3} \), \( \frac{4}{9} \), \( \frac{7}{12} \), \( \frac{3}{5} \) is:
To find the Least Common Multiple (LCM) of fractions, we use the formula:
\[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} \]First, we will find the LCM of the numerators and the HCF (Highest Common Factor) of the denominators separately, and then apply the formula.
Identify the numerators and denominators:
The given fractions are \( \frac{2}{3} \), \( \frac{4}{9} \), \( \frac{7}{12} \), \( \frac{3}{5} \).
Numerators: \(2, 4, 7, 3\)
Denominators: \(3, 9, 12, 5\)
Calculate the LCM of the numerators:
We need to find LCM of \(2, 4, 7, 3\).
To find the LCM, take the highest power of each prime factor present:
\[ \text{LCM}(2, 4, 7, 3) = 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7 = 12 \times 7 = 84 \]So, the LCM of the numerators is \(84\).
Calculate the HCF of the denominators:
We need to find HCF of \(3, 9, 12, 5\).
To find the HCF, take the lowest power of common prime factors. In this case, there are no common prime factors among all four numbers (\(3\), \(9\), \(12\), \(5\)). When there are no common prime factors other than 1, the HCF is \(1\).
\[ \text{HCF}(3, 9, 12, 5) = 1 \]So, the HCF of the denominators is \(1\).
Apply the LCM of fractions formula:
\[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} = \frac{84}{1} = 84 \]Therefore, the LCM of the given fractions is \(84\).
D) 84 is the correct LCM of the given fractions.
The question asks to identify the operating system family to which Ubuntu, Mint, and Fedora belong. This requires knowledge of common operating systems and their distributions.
Correct Option: D) Linux
If \( \frac{a}{b} \) = 0.75, then the value of \(\frac{2a+b}{2a-b}\) + \( \frac{4}{9} \) is:
\( \frac{41}{9} \)
\( \frac{43}{9} \)
\( \frac{47}{9} \)
\( \frac{49}{9} \)
The problem asks us to evaluate an expression involving variables \(a\) and \(b\), given their ratio. We will first convert the decimal ratio to a fraction, then find a relationship between \(a\) and \(b\). Substitute this relationship into the given expression and simplify it. Finally, add the constant fraction to get the result.
We are given \( \frac{a}{b} = 0.75 \).
Convert the decimal to a fraction:
\[ 0.75 = \frac{75}{100} = \frac{3 \times 25}{4 \times 25} = \frac{3}{4} \]From \[\frac{a}{b} = \frac{3}{4}\], we can write \( a = \frac{3}{4}b \).
Substitute \( a = \frac{3}{4}b \) into the numerator:
\[ 2a+b = 2\left(\frac{3}{4}b\right) + b = \frac{3}{2}b + b = \frac{3b+2b}{2} = \frac{5b}{2} \]Substitute \( a = \frac{3}{4}b \) into the denominator:
\[ 2a-b = 2\left(\frac{3}{4}b\right) - b = \frac{3}{2}b - b = \frac{3b-2b}{2} = \frac{b}{2} \]Now, substitute these back into the fraction:
\[ \frac{2a+b}{2a-b} = \frac{\frac{5b}{2}}{\frac{b}{2}} = \frac{5b}{2} \times \frac{2}{b} = 5 \]The full expression is \[\frac{2a+b}{2a-b} + \frac{4}{9}\].
Substitute the value we found:
\[ 5 + \frac{4}{9} \]To add these, find a common denominator:
\[ 5 + \frac{4}{9} = \frac{5 \times 9}{9} + \frac{4}{9} = \frac{45}{9} + \frac{4}{9} = \frac{45+4}{9} = \frac{49}{9} \]D) \( \frac{49}{9} \)
To find the percentage of loss, we need to establish a relationship between the selling price (SP) and the cost price (CP) of the items based on the given condition. We will then calculate the loss and express it as a percentage of the cost price.
Set up the given condition:
The problem states that the selling price of 25 items is equal to the cost price of 20 items. Let \( \text{SP} \) be the selling price of one item and \( \text{CP} \) be the cost price of one item.
\[ 25 \times \text{SP} = 20 \times \text{CP} \]Express SP in terms of CP:
From the equation above, we can find the ratio of SP to CP:
\[ \frac{\text{SP}}{\text{CP}} = \frac{20}{25} = \frac{4}{5} \]This means \( \text{SP} = \frac{4}{5} \times \text{CP} \).
Determine if there is a loss or profit:
Since \( \text{SP} = \frac{4}{5} \times \text{CP} \), and \( \frac{4}{5} < 1 \), it implies that \( \text{SP} < \text{CP} \). Therefore, there is a loss.
Calculate the loss:
Loss is calculated as \( \text{CP} - \text{SP} \).
\[ \text{Loss} = \text{CP} - \frac{4}{5} \times \text{CP} = \left(1 - \frac{4}{5}\right) \times \text{CP} = \frac{1}{5} \times \text{CP} \]Calculate the percentage of loss:
The percentage of loss is calculated as \[\left(\frac{\text{Loss}}{\text{CP}}\right) \times 100\%\].
\[ \text{Percentage of Loss} = \left(\frac{\frac{1}{5} \times \text{CP}}{\text{CP}}\right) \times 100\% \] \[ \text{Percentage of Loss} = \frac{1}{5} \times 100\% = 20\% \]A) 20% is the correct answer. The calculation shows that the loss percentage is 20%.
The value of \(\sqrt{217+\sqrt{50+\sqrt{196}}}\) is:
To solve this problem, we need to evaluate the expression by simplifying it from the innermost square root outwards. We will calculate the square root of perfect squares step-by-step until the entire expression is simplified to a single numerical value.
Start with the innermost square root: \(\sqrt{196}\).
\[ \sqrt{196} = 14 \]Substitute this value back into the expression:
\[ \sqrt{217+\sqrt{50+14}} \]Simplify the expression inside the next square root:
\[ \sqrt{217+\sqrt{64}} \]Calculate the next square root: \(\sqrt{64}\).
\[ \sqrt{64} = 8 \]Substitute this value back into the expression:
\[ \sqrt{217+8} \]Simplify the expression inside the outermost square root:
\[ \sqrt{225} \]Calculate the final square root:
\[ \sqrt{225} = 15 \]Thus, the value of the given expression is 15.
B) 15 — As calculated in the step-by-step solution, the final simplified value of the expression is 15.
The problem is a coding-decoding type where letters are assigned numerical values. We need to identify the pattern used to convert the word "SACHIN" into "19138914" and then apply the same pattern to convert "GEETA". The most common pattern for such problems is assigning the alphabetical position of each letter.
A) 755201 is the correct code for GEETA based on the identified pattern.
Match the following companies with their headquarters.
| Companies | Headquarters |
| A. Bharat Heavy Electricals Limited | 1. Mumbai |
| B. Coal India Limited | 2. Bengaluru |
| C. Bharat Petroleum Corporation Limited | 3. Kolkata |
| D. Bharat Electronics Limited | 4. New Delhi |
A-3, B-2, C-1, D-4
A-4, B-3, C-1, D-2
A-4, B-2, C-1, D-3
A-4, B-3, C-2, D-1
The question requires matching public sector companies with their respective headquarters. This is a factual recall question related to general knowledge about major Indian public sector undertakings.
Combining these matches, we get A-4, B-3, C-1, D-2.
Correct Option: B) A-4, B-3, C-1, D-2