We need to find the principal amount (sum) given the difference between compound interest (CI) and simple interest (SI) for 3 years at a specified rate. We can use the direct formula for the difference between CI and SI for 3 years or calculate CI and SI separately and then find the principal.
The formula for the difference between CI and SI for 3 years is:
\[ \text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2 \left( \frac{R}{100} + 3 \right) \]Where \(P\) is the Principal, \(R\) is the Rate, and \(T\) is the Time.
We have \(\text{CI} - \text{SI} = 244\), \(R = 5\).
\[ 244 = P \left( \frac{5}{100} \right)^2 \left( \frac{5}{100} + 3 \right) \]Since \(244 = 4 \times 61\):
\[ P = 4 \times 8000 \] \[ P = 32000 \]The sum (principal) is ₹32,000.
Correct Option: A) ₹32,000
The question asks to identify the Indian state with which the food preparation 'Chainsoo' is famously associated. This is a general knowledge question related to the regional cuisines of India.
C) Uttarakhand — Chainsoo is a popular and nutritious dish from the Garhwal region of Uttarakhand. It is a dal-based preparation, typically made from black gram (urad dal) or sometimes other dals, ground into a paste and cooked with spices. It is known for its earthy flavor and is a staple in the local cuisine.
If mean of the following distribution is 26, then what is the value of k?
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 8 | 10 | k | 6 | 12 |
To find the value of 'k', we will use the formula for the mean of a grouped frequency distribution. First, we need to calculate the mid-point (\(x_i\)) for each class interval and then the product of frequency and mid-point (\(f_i x_i\)). With these values, we can set up an equation using the given mean and solve for 'k'.
Correct Option: C) 4
The question asks about the political party that formed the government in Punjab during the 1937 Provincial elections under British India. This requires knowledge of the political landscape and election outcomes of that specific period and region.
Correct Option: D) Unionist party
The Unionist Party, led by Sir Sikandar Hayat Khan, won a decisive victory in the 1937 provincial elections in Punjab and subsequently formed the government. This party was a significant political force in Punjab during the pre-partition era, focusing on inter-communal harmony and agricultural interests.
To find the ratio of the surface areas of two spheres given the ratio of their volumes, we need to establish the relationship between volume, radius, and surface area for a sphere. We will use the formulas for the volume and surface area of a sphere to find the ratio of their radii first, and then use that to find the ratio of their surface areas.
Recall the formulas for volume and surface area of a sphere:
Set up the ratio of volumes:
Let the radii of the two spheres be \(r_1\) and \(r_2\), and their volumes be \(V_1\) and \(V_2\). We are given that the ratio of their volumes is 8 : 27.
\[ \frac{V_1}{V_2} = \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = \frac{r_1^3}{r_2^3} = \left(\frac{r_1}{r_2}\right)^3 \]\[ \frac{V_1}{V_2} = \frac{8}{27} \]Find the ratio of the radii:
From the above, we have:
\[ \left(\frac{r_1}{r_2}\right)^3 = \frac{8}{27} \]\[ \frac{r_1}{r_2} = \sqrt[3]{\frac{8}{27}} \]\[ \frac{r_1}{r_2} = \frac{2}{3} \]Set up the ratio of surface areas:
Let the surface areas of the two spheres be \(A_1\) and \(A_2\). Their ratio is:
\[ \frac{A_1}{A_2} = \frac{4\pi r_1^2}{4\pi r_2^2} = \frac{r_1^2}{r_2^2} = \left(\frac{r_1}{r_2}\right)^2 \]Calculate the ratio of surface areas:
Substitute the ratio of radii we found in Step 3:
\[ \frac{A_1}{A_2} = \left(\frac{2}{3}\right)^2 \]\[ \frac{A_1}{A_2} = \frac{4}{9} \]B) 4 : 9 is the correct ratio of the surface areas of the two spheres.
The question asks about the "Silver Revolution" and what it is concerned with. This is a direct knowledge-based question about various revolutions in India aimed at increasing production in specific sectors.
B) Egg — The Silver Revolution is primarily concerned with the increased production of eggs and poultry in India. This revolution was instrumental in making India one of the largest producers of eggs globally.
The problem presents a series of alphanumeric terms, each consisting of a letter, a number, and another letter. To find the next term in the series, we need to analyze the pattern for each component (first letter, number, second letter) separately.
The first letters are X, T, P, L, H.
Following this pattern, the next letter should be \(8 - 4 = 4\text{th}\) letter, which is D.
The numbers are 90, 135, 180, 225, 270.
The numbers are increasing by 45 each time. So, the next number should be \(270 + 45 = \textbf{315}\).
The second letters are D, H, L, P, T.
Following this pattern, the next letter should be \(20 + 4 = 24\text{th}\) letter, which is X.
Combining the next first letter (D), the next number (315), and the next second letter (X), the next term in the series is D315X.
D) D315X — This option correctly follows all three identified patterns for the letters and the number sequence.
If A is 70% more than B, then B is what percent less than A?
58 \( \frac{14}{17} \)
38 \( \frac{4}{17} \)
41 \( \frac{3}{17} \)
37 \( \frac{1}{17} \)
To solve this problem, we will first assume a value for B to make calculations easier. Then, we will calculate A based on the given percentage increase. Finally, we will find the percentage by which B is less than A using the formula for percentage decrease.
Assume a value for B: Let's assume \(B = 100\).
Calculate A: A is 70% more than B. So, A will be:
\[ A = B + 70\% \text{ of } B \] \[ A = 100 + \frac{70}{100} \times 100 \] \[ A = 100 + 70 \] \[ A = 170 \]Find the difference between A and B: Difference \( = A - B = 170 - 100 = 70\).
Calculate the percentage by which B is less than A: To find out what percent B is less than A, we use A as the base for comparison. The formula for percentage decrease is:
\[ \text{Percentage less} = \frac{\text{Difference}}{\text{Value of A}} \times 100 \] \[ \text{Percentage less} = \frac{70}{170} \times 100 \] \[ \text{Percentage less} = \frac{7}{17} \times 100 \] \[ \text{Percentage less} = \frac{700}{17} \]Convert the fraction to a mixed number: Now, we divide 700 by 17:
\[ 700 \div 17 \] \(700 = 17 \times 41 + 3\) So, the mixed fraction is \(41 \frac{3}{17}\).Therefore, B is \(41 \frac{3}{17}\)% less than A.
Correct Option: C) \(41 \frac{3}{17}\)
The question asks about the Guest of Honour for India's First Republic Day parade. This is a factual question related to Indian history and general knowledge. To answer this, one needs to recall the historical details of India's first Republic Day celebrations.
Correct Option: A) President of Indonesia
The question asks for the full form of the acronym ISP in the context of the Internet. This is a common acronym related to computer networks and internet services.
Correct Option: A) Internet Service Provider
This is the universally accepted full form for ISP in the context of the Internet. An Internet Service Provider is a company that provides individuals and organizations access to the Internet and other related services.