In a row of 48 students facing North, Tinu is 15th from the left end. If Dinesh is 9th to the right of Tinu, what is Dinesh's position from the right end of the line?
To solve this problem, we need to first find Tinu's position from the left end, then use that to find Dinesh's position from the left end. Once Dinesh's position from the left end is known, we can calculate his position from the right end using the total number of students in the row.
Identify Tinu's position from the left end:
The problem states that Tinu is 15th from the left end.
Calculate Dinesh's position from the left end:
Dinesh is 9th to the right of Tinu. This means we add 9 to Tinu's position from the left.
So, Dinesh is 24th from the left end of the row.
Calculate Dinesh's position from the right end:
The total number of students in the row is 48. The formula to find the position from the other end is:
Substitute the values:
\[\text{Dinesh's position from right} = (48 - 24) + 1\] \[\text{Dinesh's position from right} = 24 + 1\] \[\text{Dinesh's position from right} = 25\]Correct Option: A) 25 th
The problem presents a number-pair analogy where the relationship between the first number and the second number on the left side of '::' must be the same as the relationship on the right side. We need to find a mathematical operation or pattern that transforms the first number into the second. Once this pattern is identified, we apply it to find the missing numbers X and Y.
Analyze the given analogy: \(X : 112 :: 15 : Y\).
We need to find a relationship between the first number and the second number. Let's test common arithmetic operations (addition, subtraction, multiplication, division, squares, cubes, etc.).
Consider the options to find a possible pattern. Let's assume the pattern involves squaring the first number and then adding or subtracting a multiple of the first number or a constant.
Let's try a pattern of the form \(n^2 + k \cdot n\) or \(n^2 + k\).
Let's examine Option B, which suggests \(X = 12\) and \(Y = 184\).
If \(X = 12\), then the first pair is \(12 : 112\).
Let's see if \(12^2\) is close to \(112\). \(12^2 = 144\). This is too high.
Let's try \(n^2 - k \cdot n\). For \(X=12\), \(12^2 - k \cdot 12 = 112\).
\[ 144 - 12k = 112 \] \[ 12k = 144 - 112 \] \[ 12k = 32 \] \[ k = \frac{32}{12} = \frac{8}{3} \]This is not an integer, so this pattern might not be correct.
Let's try a pattern of the form \(n^2 - (\text{some multiple of n})\).
Consider \(n^2 - 3n\). For \(n=12\):
\[ 12^2 - 3 \times 12 = 144 - 36 = 108 \]This is close to \(112\). What if it's \(n^2 - 3n + 4\)?
\[ 108 + 4 = 112 \]So, the pattern could be \(n^2 - 3n + 4\).
Let's verify this pattern with the second pair \(15 : Y\), using \(n=15\).
\[ Y = 15^2 - 3 \times 15 + 4 \] \[ Y = 225 - 45 + 4 \] \[ Y = 180 + 4 \] \[ Y = 184 \]This matches the value of \(Y\) in Option B.
Therefore, the pattern is \(n^2 - 3n + 4\).
The pattern identified is \(n^2 - 3n + 4\).
For the first pair \(X : 112\): If \(X = 12\), then \(12^2 - 3 \times 12 + 4 = 144 - 36 + 4 = 108 + 4 = 112\). This matches the given second number.
For the second pair \(15 : Y\): If \(n = 15\), then \(Y = 15^2 - 3 \times 15 + 4 = 225 - 45 + 4 = 180 + 4 = 184\). This matches the value of \(Y\) in Option B.
A) X = 14, Y = 166: If \(X = 14\), then \(14^2 - 3 \times 14 + 4 = 196 - 42 + 4 = 154 + 4 = 158\). This is not \(112\). So, this option is incorrect.
C) X = 10, Y = 148: If \(X = 10\), then \(10^2 - 3 \times 10 + 4 = 100 - 30 + 4 = 70 + 4 = 74\). This is not \(112\). So, this option is incorrect.
D) X = 16, Y = 192: If \(X = 16\), then \(16^2 - 3 \times 16 + 4 = 256 - 48 + 4 = 208 + 4 = 212\). This is not \(112\). So, this option is incorrect.
When a solid object is melted and recast into smaller objects, the total volume of the material remains constant. Therefore, we can find the number of small spheres by dividing the volume of the large sphere by the volume of one small sphere.
The volume of a sphere with radius \(x\) is given by:
\[ V = \frac{4}{3} \pi x^3 \]Using the formula with \(R = 12 \text{ cm}\):
\[ V_{\text{large}} = \frac{4}{3} \pi (12)^3 \]\[ V_{\text{large}} = \frac{4}{3} \pi (1728) \text{ cm}^3 \]Using the formula with \(r = 2 \text{ cm}\):
\[ V_{\text{small}} = \frac{4}{3} \pi (2)^3 \]\[ V_{\text{small}} = \frac{4}{3} \pi (8) \text{ cm}^3 \]Let \(N\) be the number of small spheres formed. Since the total volume remains constant:
\[ N \times V_{\text{small}} = V_{\text{large}} \]\[ N = \frac{V_{\text{large}}}{V_{\text{small}}} \]\[ N = \frac{\frac{4}{3} \pi (1728)}{\frac{4}{3} \pi (8)} \]The terms \(\frac{4}{3} \pi\) cancel out:
\[ N = \frac{1728}{8} \]\[ N = 216 \]Thus, 216 small spheres are formed.
Correct Option: B) 216
The question asks to identify the team that the Indian women's chess team defeated to win the Chess Olympiad 2024 title. This requires knowledge of recent major chess tournament results.
A) Azerbaijan — The Indian women's chess team won the Chess Olympiad 2024 title by defeating Azerbaijan in a crucial match, securing the gold medal.
To find the missing number in the series, we need to identify the pattern or rule governing the sequence of numbers. This typically involves looking at the differences between consecutive terms.
Thus, the next number in the series is 189.
C) 189 — The pattern of differences between consecutive terms is an arithmetic progression (24, 48, 72, 96, ...), where each term is a multiple of 24. The next difference in this sequence would be 120. Subtracting 120 from 309 gives 189.
The question asks for the venue of the Khelo India Para Games (2023). This is a factual question related to current affairs and sports events in India. Knowledge of major national sporting events and their locations is essential for competitive exams.
Correct Option: D) New Delhi
This is a blood relation problem where symbols represent relationships. We need to decode the given expression step-by-step to determine the relationship between K and Q.
Correct Option: D) Daughter's husband
To solve this problem, we need to track Rohit's movements on a 2D plane. We can consider East as the positive x-axis and North as the positive y-axis. We will calculate his final position relative to his starting point (Point A) and then determine the shortest distance and direction needed to return to Point A.
D) 6 km towards the North — Rohit's final position is 6 km South of Point A. To return to Point A, he must drive 6 km towards the North.
The question asks about the phenomenon responsible for the bending of light rays as they travel through Earth's atmosphere. This involves understanding how light interacts with a medium whose properties change with altitude.
Correct Option: A) Atmospheric refraction is the phenomenon that causes the bending of light rays when they move through the Earth's atmosphere due to the varying refractive index of different atmospheric layers.
To find the duration in which a sum of money doubles itself at a given simple interest rate, we can use the formula for simple interest. When the sum doubles, the simple interest earned will be equal to the principal amount.
Thus, it will take 10 years for the sum of money to double itself at a 10% per annum simple interest rate.
A) 10 years — As calculated, the time required for the principal to double is 10 years.