This problem can be solved by setting up a system of two linear equations with two variables, representing the cost of a plate and the cost of a spoon. We can then solve this system using methods like substitution or elimination to find the individual costs and subsequently their difference.
Let the cost of one plate be \(P\) (in Rs) and the cost of one spoon be \(S\) (in Rs).
From the first statement, "The cost of two plates and three spoons is Rs 86", we can form the first equation:
\[ 2P + 3S = 86 \quad \text{(Equation 1)} \]From the second statement, "The cost of four plates and a spoon is Rs 112", we can form the second equation:
\[ 4P + S = 112 \quad \text{(Equation 2)} \]Now, we need to solve this system of equations. Let's use the elimination method. Multiply Equation 2 by 3 to make the coefficient of \(S\) the same as in Equation 1:
\[ 3 \times (4P + S) = 3 \times 112 \]\[ 12P + 3S = 336 \quad \text{(Equation 3)} \]Subtract Equation 1 from Equation 3:
\[ (12P + 3S) - (2P + 3S) = 336 - 86 \]\[ 12P - 2P + 3S - 3S = 250 \]\[ 10P = 250 \]Solve for \(P\):
\[ P = \frac{250}{10} \]\[ P = 25 \]Substitute the value of \(P\) (Rs 25) into Equation 2 to find \(S\):
\[ 4(25) + S = 112 \]\[ 100 + S = 112 \]\[ S = 112 - 100 \]\[ S = 12 \]So, the cost of a plate is Rs 25 and the cost of a spoon is Rs 12.
The question asks for the difference between the cost of a plate and that of a spoon:
\[ \text{Difference} = P - S \]\[ \text{Difference} = 25 - 12 \]\[ \text{Difference} = 13 \]The question asks to identify which of India's Five-Year Plans was based on the Mahalanobis model. This requires knowledge of the historical context and economic planning models adopted during different Five-Year Plans in India.
Correct Option: D) Second Five-Year Plan — The Second Five-Year Plan (1956-1961) was famously based on the Mahalanobis model. This plan prioritized industrialization, particularly the development of heavy industries, to achieve self-reliance and accelerate economic growth. It aimed to shift the economic structure towards a more industrialized base, moving away from primary agriculture.
Naresh deposited a sum of Rs 10,000 at 10% rate of interest per annum, compounded annually. The total amount received by Naresh after 2 years is:
To find the total amount received when interest is compounded annually, we can use the compound interest formula or calculate the interest year by year. The compound interest formula is \(A = P \left(1 + \frac{R}{100}\right)^N\), where \(A\) is the amount, \(P\) is the principal, \(R\) is the rate of interest, and \(N\) is the number of years.
The formula for the amount (\(A\)) when interest is compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]Since the interest is compounded, the amount at the end of the 1st year becomes the principal for the 2nd year.
\[ P_2 = \text{Rs } 11000 \]The total amount received by Naresh after 2 years is Rs 12,100.
C) 12,100
The problem presents a number series, and we need to find the next number in the sequence. We will analyze the differences between consecutive terms to identify a pattern.
A) 99 — The pattern of differences between consecutive terms is a sequence of perfect squares starting from \(2^2\). The next difference is \(6^2 = 36\), so the next term in the series is \(63 + 36 = 99\).
To solve this problem, we need to visualize Akshay's path and determine his final position relative to his starting point (the restaurant). We can use a coordinate system or draw a diagram to represent the movements. The shortest distance will be the straight-line distance between the restaurant and home, and the direction will be determined by the relative positions.
D) The shortest distance is 12 km, and the restaurant's direction with respect to the home is North.
Study the following table and answer the question.
| Name of the Student | Marks | ||
| English | Maths | Computer | |
| Arav | 74 | 82 | 72 |
| Toshita | 71 | 92 | 49 |
| Pranay | 59 | 65 | 66 |
| Vibhor | 81 | 78 | 82 |
By what percentage is the total marks of Arav in the three subjects more than the total marks of Pranay in the three subjects?
To solve this problem, we need to calculate the total marks for Arav and Pranay from the given table. Then, we will find the difference between Arav's total marks and Pranay's total marks. Finally, we will express this difference as a percentage of Pranay's total marks.
B) 20 % is the correct answer. Arav's total marks are 20% more than Pranay's total marks.
This question asks about the product formed when lead nitrate and potassium iodide are mixed. This is a classic example of a double displacement reaction, specifically a precipitation reaction, where two soluble ionic compounds react to form an insoluble product (precipitate) and another soluble compound.
B) Lead iodide — As explained in the step-by-step analysis, lead iodide (\(\text{PbI}_2\)) is formed as a precipitate when lead nitrate and potassium iodide are mixed. It is a bright yellow solid.
The problem asks us to determine which wavelength of light will experience the greatest angle of deviation when passed through a prism. This involves understanding the phenomenon of dispersion of light and how the refractive index of a material varies with the wavelength of light.
Correct Option: A) more in light of 4500 Å
If 5n+2 = 3125, then n = ________.
To solve for \(n\) in the given exponential equation, we need to express both sides of the equation with the same base. Once the bases are the same, we can equate the exponents and solve for \(n\).
\(5^{n+2} = 3125\)
We need to find out how many times 5 must be multiplied by itself to get 3125.
So, \(3125 = 5^5\).
\(5^{n+2} = 5^5\)
Since the bases are the same (both are 5), the exponents must be equal.
\(n+2 = 5\)
Subtract 2 from both sides of the equation.
\(n = 5 - 2\)
\(n = 3\)
Correct Option: C) The value of \(n\) is 3.
To find the average of a set of numbers, we need to sum all the numbers and then divide the sum by the count of the numbers. This is a fundamental concept in statistics and arithmetic mean calculation.
Thus, the average of the given numbers is 24.
Correct Option: D) 24