The question asks to identify the largest freshwater lake in India from the given options. This requires knowledge of Indian geography, specifically the prominent lakes and their characteristics.
Correct Option: D) Wular Lake is the largest freshwater lake in India. It is located in the Bandipora district of Jammu and Kashmir. The lake basin was formed as a result of tectonic activity and is fed by the Jhelum River. It plays a vital role in the hydrology of the Kashmir Valley.
Manu sold a dozen watches for Rs.1,454.64 per watch and made a profit of 16%. Find the cost price of the watches?
The problem asks us to find the total cost price of a dozen watches given the selling price per watch and the profit percentage. We will first calculate the cost price of a single watch using the selling price and profit percentage, and then multiply it by the number of watches (a dozen) to find the total cost price.
Identify the given information:
Calculate the Cost Price (CP) of one watch:
The formula relating Selling Price, Cost Price, and Profit Percentage is:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]OR\[ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit Percentage}}{100}} \]Substituting the given values:\[ \text{CP per watch} = \frac{1,454.64}{1 + \frac{16}{100}} \]\[ \text{CP per watch} = \frac{1,454.64}{1 + 0.16} \]\[ \text{CP per watch} = \frac{1,454.64}{1.16} \]\[ \text{CP per watch} = 1,254.00 \]So, the cost price of one watch is Rs. 1,254.00.Calculate the total cost price of a dozen watches:
Since there are 12 watches in a dozen, the total cost price will be:
\[ \text{Total CP} = \text{CP per watch} \times \text{Number of watches} \]\[ \text{Total CP} = 1,254.00 \times 12 \]\[ \text{Total CP} = 15,048.00 \]C) 15,048.00 is the total cost price of the watches, which matches our calculation.
The question asks to identify the annual fair famous for its camel trading event. This requires knowledge of prominent Indian fairs and their associated unique features.
Correct Option: D) Pushkar Mela. The Pushkar Mela, held annually in Pushkar, Rajasthan, is one of the world's largest camel fairs. Thousands of camels, horses, and cattle are traded during this event, which also includes various cultural performances, competitions, and religious rituals.
The question asks for the term that describes the rate of change of an object's position with respect to a frame of reference, as a function of time. This is a fundamental definition in kinematics, a branch of physics.
Correct Option: C) Velocity is defined as the rate of change of an object's position (displacement) with respect to time, and it is a vector quantity, meaning it includes both speed and direction.
If DELHI is QRYUV, then BOMBAY is
The problem is a coding-decoding question. We need to identify the pattern used to transform "DELHI" into "QRYUV" and then apply the same pattern to transform "BOMBAY".
Compare the letters of "DELHI" with "QRYUV" based on their alphabetical positions.
Let's find the difference in alphabetical positions for each letter:
The pattern is consistent: each letter is shifted forward by 13 positions in the alphabet. This is also known as a ROT13 cipher.
Now, apply the "add 13" rule to each letter of "BOMBAY". Remember that if the sum exceeds 26, we wrap around the alphabet (e.g., A=1, Z=26, so 27 becomes A, 28 becomes B, etc.).
The coded word for BOMBAY is OBZONL.
Correct Option: D) OBZONL
This is a coding-decoding problem where each letter is assigned a specific digit. We need to identify the pattern of digit assignment for the given words and then apply the same pattern to decode the target word.
From GOING = 38253, we can deduce:
Notice that the last 'G' is also 3, which is consistent.
From CASUAL = 409106, we can deduce:
Notice that the second 'A' is also 0, which is consistent.
Combining these digits, LOGICAL = 6832406.
D) 6832406 is the correct code derived from the established letter-digit mapping.
Manju takes 16 days to complete a work. If she works with her friend Jenny they complete it in 12 days. How many days will it take for Jenny to complete the work alone?
This is a work and time problem. We can solve it by calculating the amount of work done per day (rate of work) by each person or by the combined team. The total work is considered as 1 unit. The rate of work is the reciprocal of the number of days taken to complete the work.
Manju takes 16 days to complete the work alone.
\[ \text{Manju's 1-day work} = \frac{1}{16} \text{ of the total work} \]Manju and Jenny together complete the work in 12 days.
\[ \text{Manju and Jenny's 1-day work} = \frac{1}{12} \text{ of the total work} \]The combined daily work rate is the sum of their individual daily work rates. So, to find Jenny's daily work rate, subtract Manju's daily work rate from their combined daily work rate.
\[ \text{Jenny's 1-day work} = (\text{Manju and Jenny's 1-day work}) - (\text{Manju's 1-day work}) \]\[ \text{Jenny's 1-day work} = \frac{1}{12} - \frac{1}{16} \]The least common multiple (LCM) of 12 and 16 is 48.
\[ \text{Jenny's 1-day work} = \frac{4}{48} - \frac{3}{48} \]\[ \text{Jenny's 1-day work} = \frac{4 - 3}{48} \]\[ \text{Jenny's 1-day work} = \frac{1}{48} \text{ of the total work} \]If Jenny completes \(\frac{1}{48}\) of the work in one day, she will take 48 days to complete the entire work alone.
\[ \text{Days for Jenny alone} = \frac{1}{\text{Jenny's 1-day work}} \]\[ \text{Days for Jenny alone} = \frac{1}{\frac{1}{48}} = 48 \text{ days} \]A) 48 is the correct answer. Jenny will take 48 days to complete the work alone.
Solve: \( 10^{9} \) × \( 10^{2} \) ÷ \( 10^{3} \)
\( 10^{8} \)
\( 10^{6} \)
\( 10^{2} \)
\( 10^{5} \)
This problem involves simplifying an expression with exponents. We will use the rules of exponents for multiplication and division with the same base.
The expression is \(10^9 \times 10^2 \div 10^3\).
First, multiply \(10^9 \times 10^2\):
\[ 10^9 \times 10^2 = 10^{9+2} = 10^{11} \]Now, divide the result by \(10^3\):
\[ 10^{11} \div 10^3 = 10^{11-3} = 10^8 \]The expression can be written as:
\[ 10^9 \times 10^2 \times 10^{-3} \]\[ 10^{9+2-3} = 10^{11-3} = 10^8 \]Correct Option: A) \(10^8\) is the correct simplification of the given expression.
If the circumference of a circle is 22 cm, find the area of the semicircle.
To find the area of a semicircle, we first need to determine the radius of the circle. The radius can be calculated from the given circumference of the circle. Once the radius is known, we can calculate the area of the full circle and then divide it by two to get the area of the semicircle.
The formula for the circumference of a circle is \(C = 2\pi r\), where \(C\) is the circumference and \(r\) is the radius. We are given that the circumference \(C = 22 \text{ cm}\).
\[ 2\pi r = 22 \]\[ 2 \times \frac{22}{7} \times r = 22 \]Divide both sides by \(2 \times \frac{22}{7}\):
\[ r = \frac{22}{2 \times \frac{22}{7}} \]\[ r = \frac{22 \times 7}{2 \times 22} \]\[ r = \frac{7}{2} \text{ cm} \]\[ r = 3.5 \text{ cm} \]The formula for the area of a circle is \(A = \pi r^2\).
\[ A = \frac{22}{7} \times \left(\frac{7}{2}\right)^2 \]\[ A = \frac{22}{7} \times \frac{49}{4} \]\[ A = \frac{22 \times 7}{4} \]\[ A = \frac{11 \times 7}{2} \]\[ A = \frac{77}{2} \text{ cm}^2 \]\[ A = 38.5 \text{ cm}^2 \]The area of a semicircle is half the area of the full circle.
\[ \text{Area of semicircle} = \frac{1}{2} \times \text{Area of circle} \]\[ \text{Area of semicircle} = \frac{1}{2} \times 38.5 \]\[ \text{Area of semicircle} = 19.25 \text{ cm}^2 \]B) 19.25 cm2 is the correct area of the semicircle, as calculated.
Find the interest on Rs.25,000 at 12% p.a. compounded annually for 3 years.
To find the interest compounded annually, we first calculate the total amount after 3 years using the compound interest formula. Then, we subtract the principal amount from the total amount to find the compound interest.
Identify the given values:
Use the compound interest formula to calculate the total amount (\(A\)):
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Substitute the given values into the formula:
\[ A = 25000 \left(1 + \frac{12}{100}\right)^3 \]\[ A = 25000 \left(1 + 0.12\right)^3 \]\[ A = 25000 \left(1.12\right)^3 \]Calculate \((1.12)^3\):
\[ (1.12)^3 = 1.12 \times 1.12 \times 1.12 \]\[ (1.12)^2 = 1.2544 \]\[ (1.12)^3 = 1.2544 \times 1.12 = 1.404928 \]Calculate the total amount (\(A\)):
\[ A = 25000 \times 1.404928 \]\[ A = 35123.20 \]Calculate the compound interest (\(CI\)):
\[ CI = A - P \]\[ CI = 35123.20 - 25000 \]\[ CI = 10123.20 \]C) The calculated compound interest is Rs. 10,123.20.