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.
LETTER : RETTEL :: OPTION : NOITPO :: SELECT :?
The problem asks us to find the relationship between letter-clusters. We need to identify the pattern in the first two pairs (LETTER : RETTEL and OPTION : NOITPO) and apply the same pattern to the third pair (SELECT : ?).
Therefore, the missing letter-cluster is TCELES.
D) TCELES is the correct answer because it is the reverse of the word SELECT.
This problem can be solved by setting up a system of two linear equations with two variables. We will define variables for the cost of one pencil and one eraser, form equations based on the given information, and then solve the system to find the individual costs. Finally, we will sum these individual costs to find the combined cost.
Let \(P\) be the cost of one pencil in Rupees.
Let \(E\) be the cost of one eraser in Rupees.
From the first statement, "The cost of 2 pencils and 3 erasers is Rs 7", we can form the first equation:
\[ 2P + 3E = 7 \quad \text{(Equation 1)} \]From the second statement, "the cost of 5 pencils and 6 erasers is Rs 16", we can form the second equation:
\[ 5P + 6E = 16 \quad \text{(Equation 2)} \]We need to solve this system of linear equations. One common method is elimination. We can multiply Equation 1 by 2 to make the coefficient of \(E\) the same as in Equation 2:
\[ 2 \times (2P + 3E) = 2 \times 7 \]\[ 4P + 6E = 14 \quad \text{(Equation 3)} \]Now, subtract Equation 3 from Equation 2:
\[ (5P + 6E) - (4P + 6E) = 16 - 14 \]\[ 5P - 4P + 6E - 6E = 2 \]\[ P = 2 \]So, the cost of one pencil is Rs 2.
Substitute the value of \(P = 2\) into Equation 1 to find the cost of one eraser:
\[ 2(2) + 3E = 7 \]\[ 4 + 3E = 7 \]\[ 3E = 7 - 4 \]\[ 3E = 3 \]\[ E = 1 \]So, the cost of one eraser is Rs 1.
The question asks for the combined cost of one pencil and one eraser, which is \(P + E\).
\[ P + E = 2 + 1 = 3 \]The combined cost of one pencil and one eraser is Rs 3.
B) 3 is the correct answer. The cost of one pencil is Rs 2 and the cost of one eraser is Rs 1, making their combined cost Rs 3.
To find the shortest distance between the starting and end positions, we need to determine the net displacement in the North-South direction and the East-West direction. Once we have these net displacements, we can use the Pythagorean theorem to calculate the shortest distance, as the path forms a right-angled triangle.
Since the net displacement in the North-South direction is 0 km, Aman's final position is directly East of his starting position. The shortest distance is simply the net displacement in the East-West direction.
Alternatively, using the Pythagorean theorem, if \(\Delta N\) is the net North-South displacement and \(\Delta E\) is the net East-West displacement, the shortest distance \(D\) is given by:
\[ D = \sqrt{(\Delta N)^2 + (\Delta E)^2} \]\[ D = \sqrt{(0 \text{ km})^2 + (9 \text{ km})^2} \]\[ D = \sqrt{0 + 81 \text{ km}^2} \]\[ D = \sqrt{81 \text{ km}^2} \]\[ D = 9 \text{ km} \]B) The shortest distance between his starting and end positions is 9 km, as the net displacement in the North-South direction is zero, and the net displacement in the East-West direction is 9 km.
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). We will evaluate the innermost parentheses first and work our way outwards.
A) The final calculated value is 3.
The question asks about India's bronze medal win at the World Games 2022 in the USA in a specific event. To answer this, one needs to recall the key achievements of Indian athletes at that particular event.
Correct Option: C) Archery — India's Jyothi Surekha Vennam won a bronze medal in the women's compound individual event at the World Games 2022.
The question asks about the number of testaments in the Bible. This is a fundamental piece of knowledge regarding the structure of the Christian Bible.
Correct Option: D) two
The question asks about the installation location of the PARAM Ganga supercomputer. This requires knowledge of current affairs related to India's National Supercomputing Mission (NSM).
Correct Option: D) IIT Roorkee
To find the perimeter of a square field, we first need to determine the length of its side. We are given the area of the square, and we know that the area of a square is calculated by squaring the length of its side. Once the side length is found, the perimeter can be calculated by multiplying the side length by 4.
The perimeter of the square field is \(52 \text{ m}\).
Correct Option: B) 52
The question asks for the headquarters of Bandhan Financial Services Ltd., a prominent microfinance institution that later transformed into a universal bank. This is a factual question requiring knowledge of financial institutions and their locations in India.
Correct Option: D) Kolkata is the correct answer as Bandhan Financial Services Ltd. (now Bandhan Bank Ltd.) has its headquarters in Kolkata, West Bengal.
From a book containing 264 pages, the teacher taught \( \frac{2}{3} \) of the total number of pages and the children studied \( \frac{1}{8} \) of the remaining pages at home. How many pages were yet to be either taught by the teacher or studied on their own by the students?
To find the number of pages yet to be covered, we need to calculate the pages taught by the teacher and the pages studied by the students. Then, subtract these from the total number of pages in the book.
D) 77 is the correct answer. This represents the number of pages that have not yet been taught by the teacher or studied by the students.