Compute 4923 ÷ 547 – 10.
1
-1
\( \frac{1641}{179} \)
\( \frac{1614}{179} \)
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS). Division should be performed before subtraction. First, divide 4923 by 547, and then subtract 10 from the result.
We need to calculate \(4923 \div 547\).
Let's try multiplying 547 by small integers to see if we can find a direct multiple:
So, \(4923 \div 547 = 9\).
Now, substitute the result of the division back into the original expression:
\[ 9 - 10 \]Subtracting 10 from 9 gives:
\[ 9 - 10 = -1 \]Thus, the final answer is -1.
Correct Option: B) -1
A protruding part of the throat that is responsible for growing voice box in boys is called?
The question asks to identify the specific protruding part of the throat in boys that is associated with the growing voice box. This is a direct recall question related to human anatomy and puberty.
D) Adam's Apple is the common term for the visible protrusion in the throat caused by the enlargement of the larynx during male puberty. It is directly responsible for the deepening of the voice.
Which country is going to organise the FIFA U-17 World cup in the year 2017? (as of 2016)
The question asks about the host country for the FIFA U-17 World Cup in 2017. This is a factual question related to sports events and general knowledge, often covered in current affairs for competitive exams. The key is to recall the host nation for that specific tournament.
D) India
India was the host nation for the FIFA U-17 World Cup in 2017. The tournament was held from 6 to 28 October 2017 across six cities in India.
The mean of the data 1, \( \frac{1}{2} \), \( \frac{1}{2} \), \( \frac{3}{4} \), \( \frac{1}{4} \), 2, \( \frac{1}{2} \), \( \frac{1}{4} \), \( \frac{3}{4} \) is.
\( \frac{15}{18} \)
\( \frac{13}{18} \)
\( \frac{7}{9} \)
\( \frac{8}{9} \)
To find the mean of a given set of data, we need to sum all the data points and then divide by the total number of data points. This is the standard formula for calculating the arithmetic mean.
The given data points are: \[1, \frac{1}{2}, \frac{1}{2}, \frac{3}{4}, \frac{1}{4}, 2, \frac{1}{2}, \frac{1}{4}, \frac{3}{4}\].
There are 9 data points in total.
We need to find the sum \(S\) of all these numbers:
\[ S = 1 + \frac{1}{2} + \frac{1}{2} + \frac{3}{4} + \frac{1}{4} + 2 + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} \]The mean is the sum of data points divided by the number of data points.
\[ \text{Mean} = \frac{S}{\text{Number of data points}} \]\[ \text{Mean} = \frac{\frac{13}{2}}{9} \]\[ \text{Mean} = \frac{13}{2 \times 9} \]\[ \text{Mean} = \frac{13}{18} \]Correct Option: B) \( \frac{13}{18} \)
This problem involves understanding how scaling data affects its variance. If each observation in a dataset is multiplied by a constant, the variance of the new dataset is the original variance multiplied by the square of that constant.
Let the first set of data be \(X = \{x_1, x_2, x_3, x_4, x_5, x_6\}\), where \(X = \{2, 4, 5, 6, 8, 17\}\).
The variance of this data is given as \(Var(X) = 23.33\).
Let the second set of data be \(Y = \{y_1, y_2, y_3, y_4, y_5, y_6\}\), where \(Y = \{4, 8, 10, 12, 16, 34\}\).
Observe the relationship between the two datasets. Each element in the second dataset \(Y\) is twice the corresponding element in the first dataset \(X\). That is, \(y_i = 2x_i\) for all \(i\).
The property of variance states that if a constant \(c\) is multiplied by each observation in a dataset, the new variance will be \(c^2\) times the original variance. Mathematically, if \(Y = cX\), then \(Var(Y) = c^2 Var(X)\).
In this case, \(c = 2\).
Therefore, the variance of the second dataset \(Y\) will be:
\[ Var(Y) = (2)^2 \times Var(X) \] \[ Var(Y) = 4 \times 23.33 \] \[ Var(Y) = 93.32 \]
Rounding to two decimal places, the variance is \(93.32\). Option C is \(93.3333\), which is the most accurate representation.
C) 93.3333
To solve this problem, we first need to determine the cost price (CP) of the bus. We are given the selling price (SP) and the percentage loss. Once we have the cost price, we can calculate the new selling price required to achieve a 15% profit.
Calculate the Cost Price (CP):
Given:
If there is a 15% loss, it means the selling price is \(100\% - 15\% = 85\%\) of the cost price.
So, we can write the equation:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \] \[ 22,100 = \text{CP} \times \left(1 - \frac{15}{100}\right) \] \[ 22,100 = \text{CP} \times \left(\frac{85}{100}\right) \]Now, solve for CP:
\[ \text{CP} = \frac{22,100 \times 100}{85} \] \[ \text{CP} = \frac{2,210,000}{85} \] \[ \text{CP} = 26,000 \]So, the cost price of the bus is Rs. 26,000.
Calculate the Selling Price for 15% Profit:
We want to achieve a 15% profit on the cost price.
New Selling Price (\(\text{SP}_{\text{new}}\)) = \[\text{CP} \times \left(1 + \frac{\text{Profit \%}}{100}\right)\]
\[ \text{SP}_{\text{new}} = 26,000 \times \left(1 + \frac{15}{100}\right) \] \[ \text{SP}_{\text{new}} = 26,000 \times \left(\frac{115}{100}\right) \] \[ \text{SP}_{\text{new}} = 260 \times 115 \] \[ \text{SP}_{\text{new}} = 29,900 \]Therefore, the bus should be sold for Rs. 29,900 to get a profit of 15%.
Correct Option: D) 29,900
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate each conclusion based on these diagrams. We need to find the conclusions that logically follow from the statements.
Based on the statements, we can draw a possible Venn diagram. Note that for "some" statements, there might be multiple possible diagrams, but a conclusion is only valid if it holds true for ALL possible diagrams.
D) Only IV follows
Conclusion IV directly follows from the first statement: "All pens are pencils." If all pens are pencils, it logically means that there are some pencils that are pens.
Which is the correct ascending order of the given numbers?
\( \frac{2}{3} \),\( \frac{5}{6} \), \( \frac{3}{4} \)
\( \frac{3}{4} \),\( \frac{2}{3} \), \( \frac{5}{6} \)
\( \frac{2}{3} \),\( \frac{3}{4} \), \( \frac{5}{6} \)
\( \frac{5}{6} \),\( \frac{3}{4} \), \( \frac{2}{3} \)
To arrange fractions in ascending order, we need to compare their values. This can be done by converting them to decimals or by finding a common denominator and comparing their numerators.
Correct Option: C) \( \frac{2}{3} \),\( \frac{3}{4} \), \( \frac{5}{6} \)
If tan A = \( \frac{15}{8} \) and tan B = \( \frac{7}{24} \), then cos (A + B) = ?
\( \frac{87}{425} \)
\( \frac{304}{425} \)
\( \frac{297}{425} \)
\( \frac{416}{425} \)
To find \( \cos(A+B) \), we will first find the values of \( \sin A \), \( \cos A \), \( \sin B \), and \( \cos B \) using the given \( \tan A \) and \( \tan B \) values. We can use the Pythagorean identity \( \sin^2 \theta + \cos^2 \theta = 1 \) or construct right-angled triangles. Once these values are known, we apply the cosine addition formula: \( \cos(A+B) = \cos A \cos B - \sin A \sin B \).
Find \( \sin A \) and \( \cos A \):
Given \( \tan A = \frac{15}{8} \). We can consider a right-angled triangle where the opposite side is 15 and the adjacent side is 8. The hypotenuse \( h_A \) can be found using the Pythagorean theorem:
Find \( \sin B \) and \( \cos B \):
Given \( \tan B = \frac{7}{24} \). Similarly, for a right-angled triangle, the opposite side is 7 and the adjacent side is 24. The hypotenuse \( h_B \) is:
Apply the cosine addition formula:
The formula for \( \cos(A+B) \) is:
Substitute the values we found:
\[ \cos(A+B) = \left(\frac{8}{17}\right) \left(\frac{24}{25}\right) - \left(\frac{15}{17}\right) \left(\frac{7}{25}\right) \]Perform the multiplications:
\[ \cos(A+B) = \frac{8 \times 24}{17 \times 25} - \frac{15 \times 7}{17 \times 25} \]\[ \cos(A+B) = \frac{192}{425} - \frac{105}{425} \]Subtract the fractions:
\[ \cos(A+B) = \frac{192 - 105}{425} = \frac{87}{425} \]A) \( \frac{87}{425} \) is the correct result obtained from the calculation.
Which country among the following voted in 2015 to be the first country to allow three-parent in-vitro fertilization?
The question asks to identify the country that first legalized three-parent in-vitro fertilization (IVF) in 2015. This is a factual question related to biomedical ethics and legislation, often covered in current affairs or science and technology sections of competitive exams.
A) Britain — In February 2015, the UK House of Commons and House of Lords voted to approve regulations allowing mitochondrial donation, making Britain the first country to legally permit the creation of babies using this three-parent IVF technique.