Select the option that is related to the fifth letter-cluster in the same way as the second letter-cluster is related to the first letter-cluster and the fourth letter-cluster is related to the third letter-cluster.
NALAYAK : KAYALAN :: BEAUTY : YTUAEB :: POWERTY :?
The problem presents a series of letter-cluster analogies. We need to identify the pattern or rule that transforms the first letter-cluster into the second, and the third into the fourth. Once this rule is established, we apply it to the fifth letter-cluster to find the missing sixth letter-cluster.
This question involves analyzing a given statement of inequalities and determining the truthfulness of two conclusions based on that statement. We need to combine the inequalities and check each conclusion individually.
The statement is: \(L > M \geq N > P \leq Q < R\)
From the given statement, we have the direct inequality \(Q < R\). This part of the statement is explicitly given and is therefore true.
To check this conclusion, we need to find a relationship between \(M\) and \(Q\) from the given statement. Let's trace the path from \(M\) to \(Q\):
\[ M \geq N > P \leq Q \]Here, we have \(M \geq N\), \(N > P\), and \(P \leq Q\). The relationship between \(P\) and \(Q\) is \(P \leq Q\). This means \(P\) can be less than or equal to \(Q\). There is no definite relationship established between \(M\) and \(Q\). For example, if \(M=5, N=4, P=3\), then \(Q\) could be \(3\) (in which case \(M > Q\)) or \(Q\) could be \(6\) (in which case \(M < Q\)). Since we cannot establish a definite greater than or less than relationship between \(M\) and \(Q\), this conclusion is not definitely true.
Conclusion I is true.
Conclusion II is false (not definitely true).
Correct Option: B) Only conclusion I is true
The question asks about the first state to receive rainfall from the southwest monsoon. This requires knowledge of the typical onset and progression of the southwest monsoon in India.
Correct Option: D) Kerala
The question asks to identify which option is NOT a key feature of the Indian Constitution. We need to evaluate each option based on the established characteristics of the Indian Constitution.
Correct Option: D) Promotion of uniformity is NOT a key feature of the Indian Constitution in the sense of enforcing absolute sameness. While it strives for national integration and provides for certain uniform laws, it equally protects and promotes diversity (e.g., cultural, linguistic, religious diversity), making it a diverse and inclusive document rather than one solely focused on uniformity.
G, H, I, J, K and L are six friends sitting around a circular table facing the centre of the table discussing the outcome of a cricket match. I is an immediate neighbour of both L and J. K is not the immediate neighbour of J. H is seated second to the left of L. Which of the following options represents I’s position from G?
Third to the left
Second to the right
Second to the left
Immediate right
This is a circular seating arrangement puzzle. We need to deduce the positions of six friends (G, H, I, J, K, L) sitting around a circular table facing the center based on the given clues. We will place the friends one by one using the clues and then determine I's position relative to G.
C) Second to the left. As determined in step 6, I is second to the left of G.
The question asks to identify the correct statement regarding the relationship between the sides of a triangle ABC. This relates to the fundamental property of triangles known as the Triangle Inequality Theorem.
A) Side AB + Side BC > Side AC
This statement directly reflects one of the conditions of the Triangle Inequality Theorem. For any triangle, the sum of the lengths of two sides must always be greater than the length of the third side. If this condition is not met, the three segments cannot form a triangle.
The value of \(\frac{(0.68)^{2}+(0.32)^{2}+16\times0.0136}{\left[(0.68)^{3}-(0.32)^{3}\right]\div(0.3)^{2}}\) is:
\( \frac{1}{4} \)
\( \frac{3}{5} \)
\( \frac{3}{8} \)
\( \frac{1}{2} \)
The problem involves simplifying a complex fraction using algebraic identities. We will identify common patterns like \((a+b)^2\), \((a-b)^2\), and \((a^3-b^3)\) and substitute the given decimal values to simplify the expression.
Let's denote \(a = 0.68\) and \(b = 0.32\).
First, simplify the numerator:
The numerator is \((0.68)^2 + (0.32)^2 + 16 \times 0.0136\).
Notice that \(0.68 \times 0.32 = 0.2176\). Also, \(2ab = 2 \times 0.68 \times 0.32 = 2 \times 0.2176 = 0.4352\).
We have \(16 \times 0.0136 = 0.2176\). This is exactly \(ab\). So, the term \(16 \times 0.0136\) can be written as \(0.68 \times 0.32\).
Thus, the numerator becomes \(a^2 + b^2 + ab\).
Next, simplify the denominator:
The denominator is \(\left[(0.68)^3 - (0.32)^3\right] \div (0.3)^2\).
Using the identity \(a^3 - b^3 = (a-b)(a^2 + ab + b^2)\), we have:
\[ (0.68)^3 - (0.32)^3 = (0.68 - 0.32)((0.68)^2 + (0.68)(0.32) + (0.32)^2) \]\[ = (0.36)(a^2 + ab + b^2) \]Now, substitute these simplified forms back into the original expression:
\[ \frac{a^2 + b^2 + ab}{(0.36)(a^2 + ab + b^2) \div (0.3)^2} \]Cancel out the common term \((a^2 + ab + b^2)\) from the numerator and the denominator's first part:
\[ \frac{1}{(0.36) \div (0.3)^2} \]Calculate \((0.3)^2\):
\[ (0.3)^2 = 0.09 \]Substitute this value back:
\[ \frac{1}{0.36 \div 0.09} \]Perform the division in the denominator:
\[ 0.36 \div 0.09 = \frac{36}{100} \div \frac{9}{100} = \frac{36}{100} \times \frac{100}{9} = \frac{36}{9} = 4 \]So, the final value of the expression is:
\[ \frac{1}{4} \]Five boxes numbered 36, 74, 27, 51 and 92 are kept one above the other, not necessarily in the same order. Box 51 is in the topmost position. Only box 92 is between box 74 and box 36. Only one box is above box 27. Box 36 is not at the bottommost position. Which box is kept in the exact middle position?
We need to determine the exact middle position of five boxes based on the given clues. We will deduce the arrangement of the boxes step-by-step, starting with the most definitive clues and then using the relative positions to fill in the remaining boxes.
Clue 1: Box 51 is in the topmost position.
This fixes the position of Box 51.
Clue 2: Only one box is above box 27.
Since Box 51 is at the top, and only one box is above Box 27, Box 27 must be in the second position from the top.
Clue 3: Only box 92 is between box 74 and box 36.
This means Box 74, Box 92, and Box 36 must be in consecutive positions in that order (74-92-36) or (36-92-74). There are three remaining positions (3rd, 4th, 5th from top).
Clue 4: Box 36 is not at the bottommost position.
If the sequence were 74-92-36, then Box 36 would be at the bottommost position (5th position). This contradicts Clue 4. Therefore, the sequence must be 36-92-74.
Now, let's place the sequence 36-92-74 into the remaining slots (3rd, 4th, 5th from top).
The complete arrangement from top to bottom is:
\[ \begin{array}{|c|} \ \hline 51 \ \hline 27 \ \hline 36 \ \hline 92 \ \hline 74 \ \hline \end{array} \]There are five boxes. The exact middle position is the 3rd position from the top (or bottom).
From our arrangement, Box 36 is in the 3rd position.
Correct Option: D) Box 36
The problem requires us to evaluate a given mathematical expression after interchanging certain operators. We need to replace '+' with '–', '–' with '+', '×' with '÷', and '÷' with '×'. After performing these substitutions, we will evaluate the new expression following the order of operations (BODMAS/PEMDAS).
\(15 \div 3 - 10 \times 2 + 18 \times 6 - 17 = ?\)
According to the problem statement, we need to interchange the operators as follows:
Applying these changes to the original equation:
\(15 \times 3 + 10 \div 2 - 18 \div 6 + 17 = ?\)
First, perform multiplication and division from left to right.
Substitute these values back into the expression:
\(45 + 5 - 3 + 17 = ?\)
So, the value of the expression is \(64\).
B) 64 is the correct answer, as derived from the step-by-step evaluation of the modified expression.
This problem involves compound interest. We are given the principal amount, the final amount, and the time period. We need to find the annual rate of interest. The formula for compound interest will be used to solve this problem.
The formula for the amount (\(A\)) after \(n\) years when interest is compounded annually is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]Divide both sides by 10000:
\[ \frac{11025}{10000} = \left(1 + \frac{R}{100}\right)^2 \]\[ 1.1025 = \left(1 + \frac{R}{100}\right)^2 \]To remove the square, take the square root of both sides:
\[ \sqrt{1.1025} = 1 + \frac{R}{100} \]\[ 1.05 = 1 + \frac{R}{100} \]Subtract 1 from both sides:
\[ 1.05 - 1 = \frac{R}{100} \]\[ 0.05 = \frac{R}{100} \]C) 5 % is the correct rate of interest per annum.