The question asks for the sex ratio of Kerala according to the Census of India 2011. This requires recalling specific demographic data from the 2011 Census.
Correct Option: A) 1084 is the correct sex ratio for Kerala as per the Census of India 2011.
If 4 women or 7 girls can complete a piece of work in 58 days, then how much time will 12 women and 8 girls take to complete the same work?
This problem involves the concept of work and time, specifically dealing with different groups of workers (women and girls) and their combined work rate. The key is to establish a relationship between the work efficiency of women and girls, then calculate the total work units, and finally determine the time taken by the new group.
Establish the relationship between women and girls' work efficiency:
Given that 4 women or 7 girls can complete a piece of work in 58 days, it implies that the work done by 4 women is equal to the work done by 7 girls in the same amount of time.
\[ 4 \text{ Women} = 7 \text{ Girls} \]From this, we can find the equivalent number of girls for 1 woman:
\[ 1 \text{ Woman} = \frac{7}{4} \text{ Girls} \]Calculate the total work units:
Let's consider the work done by girls. 7 girls complete the work in 58 days. If we assume the work done by 1 girl in 1 day is 1 unit, then the total work is:
\[ \text{Total Work} = 7 \text{ Girls} \times 58 \text{ days} = 406 \text{ units} \]Convert the new group (12 women and 8 girls) into an equivalent number of girls:
We have 12 women and 8 girls. Convert the women into an equivalent number of girls using the relationship established in step 1:
\[ 12 \text{ Women} = 12 \times \frac{7}{4} \text{ Girls} = 3 \times 7 \text{ Girls} = 21 \text{ Girls} \]Now, add this to the existing number of girls:
\[ \text{Total equivalent girls} = 21 \text{ Girls} + 8 \text{ Girls} = 29 \text{ Girls} \]Calculate the time taken by the new group:
The total work is 406 units, and the new group is equivalent to 29 girls. If 1 girl does 1 unit of work per day, then 29 girls do 29 units of work per day.
\[ \text{Time taken} = \frac{\text{Total Work}}{\text{Work rate of new group}} = \frac{406 \text{ units}}{29 \text{ units/day}} = 14 \text{ days} \]B) 14 days
To find the difference between the place values of two digits in a number, we first need to determine the place value of each digit and then subtract the smaller place value from the larger one.
Correct Option: C) 79600 is the correct difference between the place values of 8 and 4 in the number 683479.
The question asks to identify the recipient of the Dronacharya Award in Table Tennis for the year 2018. This requires knowledge of the Dronacharya Award winners for that specific year and sport.
The Dronacharya Award is presented by the Ministry of Youth Affairs and Sports, Government of India, for excellence in sports coaching. In 2018, A. Srinivasa Rao was one of the recipients of this prestigious award for his contributions to Table Tennis coaching.
A) A Srinivasa Rao — A. Srinivasa Rao was indeed awarded the Dronacharya Award in 2018 for his coaching in Table Tennis.
The question asks for the year of execution of Banda Singh Bahadur, a significant figure in Sikh history. To answer this, one needs to recall the historical timeline of his life and death.
Correct Option: B) 1716 is the correct year when Banda Singh Bahadur was executed by the Mughals.
The question asks to identify the President of India known as the "Missile Man." This requires knowledge of prominent Indian personalities and their associated titles or contributions.
Correct Option: A) Dr. APJ Abdul Kalam is famously known as the "Missile Man of India" due to his pivotal role in the development of ballistic missile and nuclear weapons programs. He served as the 11th President of India.
The volume of a cylinder is 5500 cm³. If its curved surface area is 4400 sq.cm, then find its height.
This problem involves finding the height of a cylinder given its volume and curved surface area. We will use the standard formulas for the volume and curved surface area of a cylinder, set up equations, and solve for the height.
The volume of a cylinder (\(V\)) is given by:
\[ V = \pi r^2 h \]where \(r\) is the radius of the base and \(h\) is the height.
The curved surface area of a cylinder (\(CSA\)) is given by:
\[ CSA = 2 \pi r h \]Given Volume \(V = 5500 \text{ cm}^3\).
So, \( \pi r^2 h = 5500 \quad \text{(Equation 1)}\)
Given Curved Surface Area \(CSA = 4400 \text{ cm}^2\).
So, \( 2 \pi r h = 4400 \quad \text{(Equation 2)}\)
We can divide Equation 1 by Equation 2 to eliminate \(h\) and solve for \(r\):
\[ \frac{\pi r^2 h}{2 \pi r h} = \frac{5500}{4400} \]Simplify the left side:
\[ \frac{r}{2} = \frac{55}{44} \]Further simplify the fraction on the right side by dividing by 11:
\[ \frac{r}{2} = \frac{5}{4} \]Now, solve for \(r\):
\[ r = \frac{5}{4} \times 2 \]\[ r = \frac{10}{4} \]\[ r = 2.5 \text{ cm} \]Using Equation 2: \( 2 \pi r h = 4400 \)
Substitute \(r = 2.5 \text{ cm}\) and use \( \pi = \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times 2.5 \times h = 4400 \]\[ \frac{44}{7} \times 2.5 \times h = 4400 \]\[ \frac{110}{7} \times h = 4400 \]Now, solve for \(h\):
\[ h = \frac{4400 \times 7}{110} \]\[ h = \frac{440 \times 7}{11} \]\[ h = 40 \times 7 \]\[ h = 280 \text{ cm} \]D) 280 cm is the calculated height of the cylinder.
If Ramu, Rohit and Shyam together can finish a piece of work in 8 days, Ramu alone can complete this work in 16 days and Rohit in 24 days, then Shyam alone can finish this work in how many days?
This problem involves work and time. We can solve it by calculating the individual work rates (amount of work done per day) of Ramu, Rohit, and the combined group. Then, we can find Shyam's work rate by subtracting Ramu's and Rohit's work rates from the combined work rate. Finally, the number of days Shyam takes to complete the work alone is the reciprocal of his work rate.
If Ramu, Rohit, and Shyam together can finish the work in 8 days, their combined work rate is:
\[ \text{Combined work rate} = \frac{1}{\text{Time taken together}} = \frac{1}{8} \text{ work per day} \]If Ramu alone can complete the work in 16 days, his work rate is:
\[ \text{Ramu's work rate} = \frac{1}{\text{Time taken by Ramu}} = \frac{1}{16} \text{ work per day} \]If Rohit alone can complete the work in 24 days, his work rate is:
\[ \text{Rohit's work rate} = \frac{1}{\text{Time taken by Rohit}} = \frac{1}{24} \text{ work per day} \]The combined work rate is the sum of individual work rates. So, Shyam's work rate can be found by subtracting Ramu's and Rohit's work rates from the combined work rate:
\[ \text{Shyam's work rate} = \text{Combined work rate} - (\text{Ramu's work rate} + \text{Rohit's work rate}) \]\[ \text{Shyam's work rate} = \frac{1}{8} - \left(\frac{1}{16} + \frac{1}{24}\right) \]First, find a common denominator for 16 and 24, which is 48:
\[ \frac{1}{16} + \frac{1}{24} = \frac{3}{48} + \frac{2}{48} = \frac{3+2}{48} = \frac{5}{48} \]Now, subtract this sum from the combined work rate:
\[ \text{Shyam's work rate} = \frac{1}{8} - \frac{5}{48} \]\[ \text{Shyam's work rate} = \frac{6}{48} - \frac{5}{48} = \frac{6-5}{48} = \frac{1}{48} \text{ work per day} \]The number of days is the reciprocal of Shyam's work rate:
\[ \text{Days taken by Shyam} = \frac{1}{\text{Shyam's work rate}} = \frac{1}{1/48} = 48 \text{ days} \]Correct Option: D) 48
Shyam alone can finish the work in 48 days.
The question asks for the specific date on which Global Tiger Day is celebrated annually. This is a factual question related to environmental awareness and conservation efforts.
Correct Option: D) 29 July
To find the compound interest, we can use the formula for compound amount and then subtract the principal, or we can calculate the interest year by year. Since the interest is compounded yearly, we will calculate the interest for the first year, add it to the principal to get the new principal for the second year, and then calculate the interest for the second year. The sum of interests for both years will be the total compound interest.
Interest for the first year \((I_1)\) is calculated on the initial principal.
\[ I_1 = \frac{P \times R \times 1}{100} \]\[ I_1 = \frac{20000 \times 8 \times 1}{100} \]\[ I_1 = 200 \times 8 \]\[ I_1 = \text{₹}1600 \]Amount after first year \((A_1) = P + I_1\)
\[ A_1 = 20000 + 1600 \]\[ A_1 = \text{₹}21600 \]For compound interest, the principal for the second year is the amount at the end of the first year \((A_1)\).
\[ I_2 = \frac{A_1 \times R \times 1}{100} \]\[ I_2 = \frac{21600 \times 8 \times 1}{100} \]\[ I_2 = 216 \times 8 \]\[ I_2 = \text{₹}1728 \]Total Compound Interest \((CI) = I_1 + I_2\)
\[ CI = 1600 + 1728 \]\[ CI = \text{₹}3328 \]A) ₹3,328.00 is the correct compound interest calculated over two years.