The question asks to identify the first Union Territory to achieve full functional literacy under the ULLAS-Nav Bharat Saaksharta Karyakram. This requires knowledge of recent government initiatives and their implementation milestones in various Union Territories.
B) Ladakh — Ladakh became the first Union Territory to achieve full functional literacy under the ULLAS-Nav Bharat Saaksharta Karyakram in September 2023.
This problem requires us to find the median of a dataset given its mode and mean, using the empirical formula relating these three measures of central tendency. The empirical formula states that for a moderately skewed distribution, the relationship is approximately:
\( \text{Mode} \approx 3 \times \text{Median} - 2 \times \text{Mean} \)
We will substitute the given values of mode and mean into this formula and solve for the median.
Correct Option: D) 21.6
We will solve this problem by setting up equations based on the given profit/loss scenarios. We'll assume an initial cost price, calculate the selling price, and then adjust the cost price and selling price according to the second condition to form an equation that can be solved for the assumed cost price.
Assume the initial Cost Price (CP):
Let the original Cost Price (CP) of the article be \(\text{₹}x\).
Calculate the initial Selling Price (SP):
The man sells the article at a profit of 25%. So, the initial Selling Price (SP) is:
Calculate the new Cost Price (CP'):
If he had bought it at 20% less, the new Cost Price (CP') would be:
Calculate the new Selling Price (SP'):
He sold it for ₹10.50 less than the original selling price. So, the new Selling Price (SP') is:
Formulate the equation based on the new profit:
With the new CP' and SP', he would have gained 30%. This means the new SP' is 130% of the new CP'.
Substitute the expressions for SP' and CP' into the equation:
\[ 1.25x - 10.50 = 1.30 \times (0.80x) \]Solve the equation for \(x\):
\[ 1.25x - 10.50 = 1.04x \] \[ 1.25x - 1.04x = 10.50 \] \[ 0.21x = 10.50 \] \[ x = \frac{10.50}{0.21} \] \[ x = \frac{1050}{21} \] \[ x = 50 \]So, the original cost price of the article is ₹50.
Correct Option: C) ₹50
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 37)
(8, 65)
The problem asks us to identify the relationship between the numbers in the given pairs \((6, 37)\) and \((8, 65)\). Once the pattern is identified, we need to apply the same pattern to the given options and find the pair that follows the rule.
D) \((9, 82)\)
The problem presents a series of three-letter combinations and asks us to find the next combination in the series. We need to identify the pattern in how the letters change from one term to the next based on their positions in the English alphabet.
Correct Option: B) QRW
The pattern for each position (first, second, and third letter) is an increment of 2 in the alphabetical order. Applying this rule to the last given term OPU:
Thus, the next term is QRW.
The question asks to identify the phenomenon where a solid substance transforms into a liquid substance. This involves understanding the basic phase changes of matter.
A) Fusion is the process by which a solid changes into a liquid upon heating. It is also commonly known as melting. For example, ice (solid water) turns into liquid water when heated above 0°C.
This problem involves calculating the net displacement and direction from a series of movements. We can solve this by breaking down each movement into its North-South and East-West components and then summing them up to find the final position relative to the starting point. Once the final position is known, we can determine the shortest distance and direction needed to return to the starting point.
At Point Z, Vineet is 0 km North/South of Point Y and 16 km East of Point Y. Therefore, to return to Point Y, he needs to drive 16 km towards the West.
C) 16 km towards the west
As calculated, the final position (Point Z) is 16 km to the East of the starting point (Point Y). To return to Point Y, Vineet must drive 16 km in the opposite direction, which is West.
A fraction becomes \( \frac{1}{2} \) if 2 is added to the numerator and 5 is added to the denominator. It also becomes \( \frac{1}{3} \) if 2 is subtracted from both the numerator and denominator. The positive difference between the denominator and the numerator of the fraction is:
The problem can be solved by setting up a system of two linear equations based on the given conditions. We will define the numerator as \(x\) and the denominator as \(y\), form the equations, solve for \(x\) and \(y\), and then find the positive difference between the denominator and the numerator.
Define the fraction:
Let the fraction be \( \frac{x}{y} \), where \(x\) is the numerator and \(y\) is the denominator.
Formulate the first equation:
"A fraction becomes \( \frac{1}{2} \) if 2 is added to the numerator and 5 is added to the denominator."
This translates to:
Cross-multiply to simplify:
\[ 2(x+2) = 1(y+5) \]\[ 2x + 4 = y + 5 \]\[ 2x - y = 5 - 4 \]\[ 2x - y = 1 \quad \text{(Equation 1)} \]Formulate the second equation:
"It also becomes \( \frac{1}{3} \) if 2 is subtracted from both the numerator and denominator."
This translates to:
Cross-multiply to simplify:
\[ 3(x-2) = 1(y-2) \]\[ 3x - 6 = y - 2 \]\[ 3x - y = -2 + 6 \]\[ 3x - y = 4 \quad \text{(Equation 2)} \]Solve the system of equations:
We have two equations:
Equation 1: \( 2x - y = 1 \)
Equation 2: \( 3x - y = 4 \)
Subtract Equation 1 from Equation 2:
\[ (3x - y) - (2x - y) = 4 - 1 \]\[ 3x - y - 2x + y = 3 \]\[ x = 3 \]Substitute \(x\) back into one of the equations to find \(y\):
Using Equation 1:
Determine the original fraction:
The original fraction is \[\frac{x}{y} = \frac{3}{5}\].
Calculate the positive difference between the denominator and the numerator:
Difference \( = y - x \)
Difference \( = 5 - 3 \)
Difference \( = 2 \)
D) 2 — The positive difference between the denominator (5) and the numerator (3) is \(5 - 3 = 2\).
The problem asks us to identify a triad that follows the same pattern as the two given triads: LG-MH-OP and HC-ID-KL. We need to analyze the letter positions in the English alphabet for each letter in the given triads to find the underlying rule.
Correct Option: C) JE-KF-MN
Since both parts of the triad JE-KF-MN follow the established pattern, this is the correct answer.