To find the median of a given set of data, we first need to arrange the data in ascending or descending order. Then, we identify the middle value. If the number of data points is odd, the median is the single middle value. If the number of data points is even, the median is the average of the two middle values.
The given data set is: 17, 54, 51, 64, 13, 39, 23, 40, 78, 66, 96.
There are 11 data points.
13, 17, 23, 39, 40, 51, 54, 64, 66, 78, 96.
Since the number of data points (\(n = 11\)) is odd, the median is the \(\left(\frac{n+1}{2}\right)^{\text{th}}\) term.
Median position \[= \frac{11+1}{2} = \frac{12}{2} = 6^{\text{th}}\] term.
Looking at the ordered list, the 6th term is 51.
Therefore, the median of the given data is 51.
Correct Option: D) 51
The question asks for the specific name of the angle between the two refracting surfaces (lateral faces) of a triangular glass prism. This is a fundamental definition in optics related to prisms.
Correct Option: C) Angle of the prism
The problem involves finding the age of E by using a series of relationships between the ages of five people (A, B, C, D, E) and a given age for one person (B). We will work backward from the known age of B to find the ages of D, A, and C, and then use the relationship between C and E to find E's age.
The age of B is given as 45.
\[ \text{B} = 45 \]D is one-fifth the age of B.
\[ \text{D} = \frac{1}{5} \times \text{B} \]\[ \text{D} = \frac{1}{5} \times 45 \]\[ \text{D} = 9 \]A is three times the age of D.
\[ \text{A} = 3 \times \text{D} \]\[ \text{A} = 3 \times 9 \]\[ \text{A} = 27 \]C is twice the age of A.
\[ \text{C} = 2 \times \text{A} \]\[ \text{C} = 2 \times 27 \]\[ \text{C} = 54 \]E is equal to the age of C.
\[ \text{E} = \text{C} \]\[ \text{E} = 54 \]Therefore, the age of E is 54.
C) 54 is the correct age for E, derived from the given relationships.
If x is inversely proportional to y, and y = 5 when x = 2, find the value of x, when y = 41.
\( \frac{11}{42} \)
\( \frac{10}{41} \)
\( \frac{10}{42} \)
\( \frac{12}{44} \)
The problem states that two variables, x and y, are inversely proportional. This means their product is a constant. We are given one pair of values for x and y, which allows us to find this constant. Then, using the constant and a new value for y, we can find the corresponding value of x.
Understand Inverse Proportionality: If x is inversely proportional to y, it can be written as:
\[ x \propto \frac{1}{y} \] Or, by introducing a constant of proportionality \(k\):\[ x = \frac{k}{y} \] This implies that the product of x and y is constant:\[ xy = k \]Find the Constant of Proportionality (k): We are given that \(y = 5\) when \(x = 2\). Substitute these values into the equation \(xy = k\):
\[ (2)(5) = k \]\[ k = 10 \]Use the Constant to Find x: Now we need to find the value of x when \(y = 41\). Use the constant \(k = 10\) in the inverse proportionality equation:
\[ xy = k \]\[ x(41) = 10 \]Solve for x: Divide both sides by 41:
\[ x = \frac{10}{41} \]Correct Option: B) \( \frac{10}{41} \)
The question asks to identify the healthcare program that primarily focuses on contraception. We need to evaluate each given option based on its core objectives.
Correct Option: B) Reproductive Health Programme is the healthcare program where contraception is one of the main goals. This program aims to promote responsible sexual behavior, reduce maternal and infant mortality, and provide access to family planning services, including contraception.
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to find a common rule or relationship between the letters in each pair and then identify the option that deviates from this rule. The hint states that the odd one out is not based on the number of consonants/vowels or their position.
Common Pattern: For options A, C, and D, the difference between the sum of the inner two letters and the sum of the outer two letters is 8.
Odd One Out: For option B, the difference is 9.
B) LV-TU is the letter-cluster pair that does not belong to the group because the difference between the sum of the inner two letters and the sum of the outer two letters is 9, whereas for the other options, this difference is 8.
When two parallel lines are intersected by a transversal line, the corresponding angles formed are equal. We are given two expressions for a pair of corresponding angles. By setting these expressions equal to each other, we can form an equation and solve for the unknown variable \(x\).
Correct Option: D) 40
The question asks for the term that describes a material's opposition to the flow of electric charges. We need to identify the correct electrical property from the given options.
Correct Option: A) resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is a fundamental measure of the material's resistance to charge flow.
Find the simple interest (in closest integral ₹) on ₹4,000 at 5.25% per annum rate of interest for the period from 3 February 2024 to 4 April 2024
To find the simple interest, we first need to calculate the number of days for which the interest is accrued. Then, we will use the simple interest formula: \[\text{Simple Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}\], where time is in years. Since the period is given in days, we will convert it to years by dividing by 366 (as 2024 is a leap year).
Calculate the number of days:
Identify the given values:
Apply the Simple Interest formula:
\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]
Substitute the values:
\[ \text{SI} = \frac{4000 \times 5.25 \times \frac{61}{366}}{100} \]
\[ \text{SI} = \frac{4000 \times 5.25 \times 61}{100 \times 366} \]
\[ \text{SI} = \frac{40 \times 5.25 \times 61}{366} \]
We know that \(366 = 6 \times 61\). So, we can simplify:
\[ \text{SI} = \frac{40 \times 5.25}{6} \]
\[ \text{SI} = \frac{210}{6} \]
\[ \text{SI} = 35 \]
Closest integral value:
The calculated simple interest is ₹35, which is an integral value.
B) 35 is the calculated simple interest, which is the closest integral value.
This problem involves calculating the population of a town after successive percentage increases over two decades. We need to apply the percentage increase for each decade sequentially.
A) 501525 is the correct population after two successive 50% increases.