To find the approximate percentage of the class that attended the programme, we need to calculate the number of girls who attended and the number of boys who attended. Then, sum these numbers to get the total attendees and divide by the total number of students in the class, finally multiplying by 100 to express it as a percentage.
Total girls = 50
Percentage of girls who attended = 40%
\[ \text{Number of girls attended} = 40\% \text{ of } 50 = \frac{40}{100} \times 50 = 20 \]Total boys = 70
Percentage of boys who attended = 50%
\[ \text{Number of boys attended} = 50\% \text{ of } 70 = \frac{50}{100} \times 70 = 35 \]The percentage is approximately 46%.
D) 46% is the closest approximation to 45.833...%.
If all the special characters are dropped from the below arrangement, which of the following will be the 10th to the right of X?
3X!B9#F45*1K2$8RS%Z
The problem asks us to identify a specific element in a given alphanumeric arrangement after removing all special characters. We need to first filter the arrangement, then locate 'X', and finally count 10 positions to its right.
A) R is the 10th character to the right of X after removing all special characters.
Select the number from among the given options that can replace the question mark (?) in the following table.
| 5 | 4 | 3 |
| 6 | 5 | 4 |
| 7 | 6 | 5 |
| 384 | 245 | ? |
The question gives a table whose rows are 5, 4, 3; 6, 5, 4; 7, 6, 5; and 384, 245, ?. We need to find how the three numbers at the top of each column produce the number at the bottom and use the same rule for the third column.
Identify the given information:
Find the rule using Column 1:
Multiply the second number by the square of one more than the third number:
\[ 6\times(7+1)^2=6\times64=384 \]Check the rule with Column 2:
\[ 5\times(6+1)^2=5\times49=245 \]The rule holds.
Apply the rule to Column 3:
\[ X=4\times(5+1)^2 \] \[ =4\times36=144 \]Therefore, the missing number is 144.
Correct Option: C) 144 — In each column, the result equals the middle number multiplied by the square of one more than the third number. For the third column, 4 × 6² = 144. Hence, Option C is the correct answer.
A) 269: This is incorrect because the correct value works out to 144; this value cannot be obtained mathematically from the given data.
B) 244: This is incorrect because the correct value works out to 144; this value cannot be obtained mathematically from the given data.
D) 249: This is incorrect because the correct value works out to 144; this value cannot be obtained mathematically from the given data.
The question asks us to find the relationship between the first two terms and apply the same relationship to the third term to find the fourth term. This is a common type of analogy question where we need to identify the functional or locational relationship between the given pairs.
B) parlour — A parlour is the primary place where a beautician provides their professional services, just as a court is the primary place where a lawyer performs their duties.
The question asks for the most appropriate average value for measuring central tendency. We need to evaluate the properties of mean, median, mode, and range to determine which one generally provides the best representation of the center of a dataset.
B) mean — The mean is generally considered the most appropriate measure of central tendency because it takes into account every value in the dataset. It is widely used and understood, and it forms the basis for many other statistical analyses. While it can be affected by outliers, in the absence of specific information suggesting extreme skewness or outliers, it provides the most comprehensive representation of the central value.
The question asks to identify the unit used for measuring the amount of a substance. We need to recall the standard units for various physical quantities as defined in the International System of Units (SI).
A) Mole is the SI unit used to measure the amount of a substance. It represents a specific number of elementary entities (like atoms, molecules, ions, or electrons), approximately \(6.022 \times 10^{23}\) (Avogadro's number).
The numbers 155, 260 and 315 leave remainders 5, 10 and 15 respectively when divided by the same greatest number. We need to subtract each remainder from its number, so that the required divisor divides the results exactly, and then find the HCF of these results.
Identify the given information:
Remove the remainders:
The required number divides each number minus its remainder exactly.
\[ 155 - 5 = 150,\quad 260 - 10 = 250,\quad 315 - 15 = 300 \]Factorise the results:
\[ 150 = 2 \times 3 \times 5^2 \] \[ 250 = 2 \times 5^3 \] \[ 300 = 2^2 \times 3 \times 5^2 \]Find the HCF:
Taking the lowest power of each common prime factor:
\[ \text{HCF} = 2 \times 5^2 = 50 \]Verify the remainders:
\[ 155 = 3 \times 50 + 5,\quad 260 = 5 \times 50 + 10,\quad 315 = 6 \times 50 + 15 \]Each remainder is also less than 50, so 50 is valid.
Correct Option: D) 50 — The HCF of 150, 250 and 300 is 50, which leaves the required remainders. Hence, Option D is the correct answer.
A) 10: This is incorrect because 10 is a common divisor but not the greatest; it also cannot leave remainders 10 and 15, which are not less than 10.
B) 75: This is incorrect because 75 does not divide 250 exactly.
C) 25: This is incorrect because 25 is a common divisor but not the greatest one.
The question asks to identify the author of the historical chronicle 'Rajatarangini'. This requires knowledge of prominent ancient Indian authors and their works.
C) Kalhana — Kalhana is widely recognized as the author of 'Rajatarangini', a historical chronicle of Kashmir, written in Sanskrit in the 12th century CE. It is considered one of the most important historical texts of ancient India.
The simple interest on an amount of ₹3,400 for 4 years is ₹680. The rate of interest is:
To find the rate of simple interest, we will use the standard formula for simple interest: \[\text{Simple Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}\]. We are given the principal amount, the simple interest, and the time period. We need to rearrange the formula to solve for the rate of interest.
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]
Where R is the Rate of Interest.
To find R, we can rearrange the formula as:
\[ \text{R} = \frac{\text{SI} \times 100}{\text{P} \times \text{T}} \]
\[ \text{R} = \frac{680 \times 100}{3400 \times 4} \]
\[ \text{R} = \frac{68000}{13600} \]
\[ \text{R} = 5 \]
So, the rate of interest is 5%.
Correct Option: C) 5%
The problem asks us to find the smallest angle of a rhombus given that its adjacent angles are in the ratio 3:6. We know that in a rhombus, adjacent angles are supplementary (sum up to 180 degrees).
Let the two adjacent angles of the rhombus be \(A\) and \(B\). According to the problem, their ratio is 3:6. So, we can write:
\[ \frac{A}{B} = \frac{3}{6} \]This ratio can be simplified to 1:2. So, let the angles be \(3x\) and \(6x\) for some constant \(x\). Alternatively, we can use \(x\) and \(2x\).
In a rhombus, adjacent angles are supplementary. This means their sum is 180 degrees.
\[ A + B = 180^\circ \]Substitute the expressions for \(A\) and \(B\) in terms of \(x\):
\[ 3x + 6x = 180^\circ \]Combine the terms:
\[ 9x = 180^\circ \]Solve for \(x\):
\[ x = \frac{180^\circ}{9} \]\[ x = 20^\circ \]Now, find the measures of the two adjacent angles:
The angles of the rhombus are \(60^\circ, 120^\circ, 60^\circ, 120^\circ\). The smallest angle among these is \(60^\circ\).
D) The smallest angle of the rhombus is \(60^\circ\).