The question asks to identify the Indian state where the Moatsu festival is celebrated. This requires knowledge of the cultural festivals of different states in Northeast India.
Correct Option: A) Nagaland is the correct answer. The Moatsu festival is an annual harvest festival celebrated by the Ao tribe of Nagaland. It is observed in the first week of May after the sowing season, marked by feasting, singing, dancing, and traditional rituals to invoke blessings for a good harvest.
The question involves a two-digit number in which the digit in the tens' place is twice the digit in the units' place. When the digits are interchanged, the resulting number is 9 less than the original number. We can represent the digits using variables, form an algebraic equation based on the given conditions, and solve it to determine the original number.
Identify the given information:
Represent the digits using a variable:
Let the digit in the units' place be \(x\).
Since the tens' digit is twice the units' digit, the tens' digit is \(2x\).
Therefore:
\[ \text{Units' digit}=x \] \[ \text{Tens' digit}=2x \]Form the original two-digit number:
A two-digit number is obtained by multiplying its tens' digit by 10 and adding its units' digit.
\[ \text{Original number}=10(2x)+x \] \[ =20x+x \] \[ =21x \]Form the number after interchanging the digits:
After interchanging the digits, the original units' digit \(x\) becomes the tens' digit, and the original tens' digit \(2x\) becomes the units' digit.
\[ \text{Interchanged number}=10(x)+2x \] \[ =10x+2x \] \[ =12x \]Form an equation using the given condition:
The interchanged number is 9 less than the original number.
\[ \text{Original number}-\text{Interchanged number}=9 \]Substituting the expressions:
\[ 21x-12x=9 \]Solve for \(x\):
\[ 9x=9 \]Dividing both sides by 9:
\[ x=\frac{9}{9} \] \[ x=1 \]Therefore, the units' digit is 1.
Determine the tens' digit:
The tens' digit is twice the units' digit.
\[ 2x=2\times1=2 \]Therefore, the tens' digit is 2.
Calculate the original number:
\[ \text{Original number}=10(2)+1 \] \[ =20+1 \] \[ =21 \]Hence, the original number is 21.
Verify the result:
The original number is 21, and the number obtained by interchanging its digits is 12.
Check the relationship between the digits:
\[ 2=2\times1 \]Check the difference between the numbers:
\[ 21-12=9 \]Both conditions are satisfied. Therefore, the original number is 21.
Correct Option: B) 21 — The units' digit is 1, and the tens' digit is 2, which is twice the units' digit. Interchanging the digits gives 12, which is 9 less than 21. Hence, Option B is the correct answer.
A) 12: This is incorrect because the tens' digit is 1 and the units' digit is 2. The tens' digit is not twice the units' digit. Moreover, interchanging the digits gives 21, which is 9 more than 12, not 9 less.
C) 63: This is incorrect because, although the tens' digit 6 is twice the units' digit 3, interchanging the digits gives 36. The difference is \(63-36=27\), not 9. Therefore, it does not satisfy the second condition.
D) 42: This is incorrect because, although the tens' digit 4 is twice the units' digit 2, interchanging the digits gives 24. The difference is \(42-24=18\), not 9. Therefore, it does not satisfy the given condition.
The ratio of the numbers of ₹10 notes, ₹20 notes and ₹50 notes in a box is given as 3 : 5 : 7. The total amount of cash in the box is ₹3,360. Find the number of ₹20 notes in that box.
We are given the ratio of the number of ₹10, ₹20, and ₹50 notes and the total cash amount. We need to find the number of ₹20 notes. We can represent the number of notes using a common multiplier, calculate the total value in terms of this multiplier, and then solve for the multiplier. Finally, we use the multiplier to find the number of ₹20 notes.
Let the common ratio be \(x\). Then the number of notes are:
The total amount of cash in the box is ₹3,360. So, we sum the values from each denomination:
\[ 30x + 100x + 350x = 3360 \]
Combine the terms:
\[ 480x = 3360 \]
Divide to find \(x\):
\[ x = \frac{3360}{480} \]
\[ x = 7 \]
The number of ₹20 notes is \(5x\). Substitute the value of \(x\):
\[ \text{Number of ₹20 notes} = 5 \times 7 = 35 \]
Correct Option: B) 35
The question asks to identify an example of a series circuit from the given options. We need to understand the characteristics of a series circuit and a parallel circuit to correctly answer this question.
A) decoration lights — Traditional decoration lights are often wired in series. If one bulb in the string burns out, the circuit is broken, and all the other bulbs in that string will go out. This is a classic example of a series circuit.
To find the power of an electric bulb, we can use the formula relating power, voltage, and current. The given values are the current flowing through the bulb and the voltage of the generator to which it is connected.
The electrical power (\(P\)) is given by the product of voltage (\(V\)) and current (\(I\)).
\[ P = V \times I \]The unit of power is Watts (W).
Correct Option: C) 440 watt
The power of the electric bulb is 440 Watts.
To find the selling price after successive discounts, we can apply each discount one by one to the marked price. Alternatively, we can calculate the effective percentage remaining after each discount and multiply these percentages by the marked price.
The first discount is 5% of the Marked Price.
\[ \text{Amount of first discount} = 5\% \times 1500 = \frac{5}{100} \times 1500 = 5 \times 15 = \text{Rs } 75 \]\[ \text{Price after first discount} = \text{MP} - \text{Amount of first discount} = 1500 - 75 = \text{Rs } 1425 \]The second discount is 12% of the price after the first discount (Rs 1425).
\[ \text{Amount of second discount} = 12\% \times 1425 = \frac{12}{100} \times 1425 \]\[ = \frac{3}{25} \times 1425 = 3 \times 57 = \text{Rs } 171 \]\[ \text{Selling Price (SP)} = \text{Price after first discount} - \text{Amount of second discount} \]\[ = 1425 - 171 = \text{Rs } 1254 \]The selling price will be \(95\%\) of \(88\%\) of the Marked Price.
\[ \text{SP} = 95\% \times 88\% \times \text{MP} \]\[ \text{SP} = \frac{95}{100} \times \frac{88}{100} \times 1500 \]\[ \text{SP} = 0.95 \times 0.88 \times 1500 \]\[ \text{SP} = 0.836 \times 1500 \]\[ \text{SP} = \text{Rs } 1254 \]Correct Option: B) 1,254
This is a circular seating arrangement puzzle. We need to deduce the positions of six persons around a circular table based on the given clues and then answer the final question. We will start by placing one person and then use the relative positions to place others.
50 identical units are purchased at a total price of Rs 550 and \( \frac{1}{5} \) of these units are sold at a loss of 10%. Find the per unit selling price of the remaining units to gain 20% on the whole transaction.
The problem requires us to calculate the per unit selling price of the remaining units to achieve an overall profit percentage on the entire transaction. We will first determine the total cost price, then calculate the selling price of the units sold at a loss. Next, we'll find the desired total selling price for a 20% gain. Finally, we'll subtract the selling price of the units already sold to find the required selling price for the remaining units and then the per unit selling price.
Calculate the total cost price (CP) and per unit CP:
Total number of units = 50
Total cost price (CP) = Rs 550
Per unit CP \[= \frac{\text{Total CP}}{\text{Total units}} = \frac{550}{50} = \text{Rs } 11\]
Calculate the number of units sold at a loss:
Units sold at a loss \( = \frac{1}{5} \times 50 = 10 \text{ units} \)
Calculate the selling price (SP) of units sold at a loss:
Loss percentage = 10%
SP per unit for these 10 units \( = \text{CP per unit} \times (1 - \text{Loss percentage}) \)
\( = 11 \times (1 - 0.10) = 11 \times 0.90 = \text{Rs } 9.90 \)
Total SP for 10 units \( = 10 \times 9.90 = \text{Rs } 99 \)
Calculate the desired total selling price (SP) for the whole transaction:
Desired gain on the whole transaction = 20%
Desired total SP \( = \text{Total CP} \times (1 + \text{Gain percentage}) \)
\( = 550 \times (1 + 0.20) = 550 \times 1.20 = \text{Rs } 660 \)
Calculate the number of remaining units:
Remaining units \( = 50 - 10 = 40 \text{ units} \)
Calculate the required selling price for the remaining units:
Required SP for remaining 40 units \( = \text{Desired total SP} - \text{SP of 10 units} \)
\( = 660 - 99 = \text{Rs } 561 \)
Calculate the per unit selling price of the remaining units:
Per unit SP for remaining units \[= \frac{\text{Required SP for remaining units}}{\text{Number of remaining units}}\]
\( = \frac{561}{40} = \text{Rs } 14.025 \)
Correct Option: D) 14.025
How many integers lie between 8912 and 8922?
To find the number of integers between two perfect squares, \(a^2\) and \(b^2\), where \(b > a\), we need to determine the count of integers strictly greater than \(a^2\) and strictly less than \(b^2\). This can be calculated by subtracting the smaller square from the larger square and then subtracting 1, i.e., \((b^2 - a^2) - 1\). Alternatively, we can use the property that the number of integers between \(n^2\) and \((n+1)^2\) is \(2n\).
Correct Option: A) 1782
Rajesh’s daughter’s age is \( \frac{1}{3} \) of Rajesh’s wife’s age. Rajesh’s wife’s age is \( \frac{3}{4} \) of Rajesh’s age, and Rajesh’s age is \( \frac{3}{5} \) of Rajesh’s father’s age. Find the age of Rajesh’s daughter if Rajesh’s father’s age is 60 years.
To find the age of Rajesh's daughter, we need to work backward from the given age of Rajesh's father. We will use the given fractional relationships between the ages of Rajesh's father, Rajesh, Rajesh's wife, and Rajesh's daughter to calculate each age sequentially.
Find Rajesh's age: It is given that Rajesh's age is \( \frac{3}{5} \) of Rajesh's father's age. Rajesh's father's age is 60 years.
\[ \text{Rajesh's age} = \frac{3}{5} \times \text{Rajesh's father's age} \] \[ \text{Rajesh's age} = \frac{3}{5} \times 60 \] \[ \text{Rajesh's age} = 3 \times 12 \] \[ \text{Rajesh's age} = 36 \text{ years} \]Find Rajesh's wife's age: It is given that Rajesh's wife's age is \( \frac{3}{4} \) of Rajesh's age. We just found Rajesh's age to be 36 years.
\[ \text{Rajesh's wife's age} = \frac{3}{4} \times \text{Rajesh's age} \] \[ \text{Rajesh's wife's age} = \frac{3}{4} \times 36 \] \[ \text{Rajesh's wife's age} = 3 \times 9 \] \[ \text{Rajesh's wife's age} = 27 \text{ years} \]Find Rajesh's daughter's age: It is given that Rajesh's daughter's age is \( \frac{1}{3} \) of Rajesh's wife's age. We found Rajesh's wife's age to be 27 years.
\[ \text{Rajesh's daughter's age} = \frac{1}{3} \times \text{Rajesh's wife's age} \] \[ \text{Rajesh's daughter's age} = \frac{1}{3} \times 27 \] \[ \text{Rajesh's daughter's age} = 9 \text{ years} \]A) 9 years is the correct age of Rajesh's daughter, as calculated through the step-by-step process.