The problem asks us to decode a pattern from a given word transformation and then apply that pattern to a new word. We need to analyze the positions of the letters in the original word and their corresponding positions in the coded word to find the rule.
Original word: DEFECT
Coded word: FEDTCE
Let's assign positions to the letters in DEFECT:
Now, let's see their positions in FEDTCE:
The first three letters (DEF) are reversed to become FED.
The last three letters (ECT) are rearranged as TCE. Specifically, the 6th letter (T) moves to the 4th position, the 5th letter (C) stays at the 5th position, and the 4th letter (E) moves to the 6th position.
Let's represent the positions:
Original: 1 2 3 | 4 5 6
Coded: 3 2 1 | 6 5 4
Original word: DEARTH
Letters and their positions:
Apply the pattern (3 2 1 | 6 5 4):
Combining these, the coded word is AEDHTR.
Correct Option: B) AEDHTR
In how many categories did the Industrial Policy Resolution 1956 that formed the basis of 2nd 5 year plan classified the industries?
The question asks about the classification of industries by the Industrial Policy Resolution (IPR) of 1956, which was a cornerstone of India's Second Five Year Plan. Understanding the key features of this policy is crucial.
C) 3 — The Industrial Policy Resolution 1956 classified industries into three distinct categories: Schedule A (exclusively state-owned), Schedule B (progressively state-owned with private sector participation), and Schedule C (primarily private sector, with state intervention possible).
To determine the number of conical bottles needed, we need to calculate the volume of the liquid in the hemispherical bowl and the volume of a single conical bottle. Then, divide the total liquid volume by the volume of one bottle.
Calculate the volume of the hemispherical bowl:
The internal radius of the hemispherical bowl is given as \(R = 12 \text{ cm}\).
The formula for the volume of a hemisphere is:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi R^3 \]Substitute the value of \(R\):
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (12)^3 \]\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (1728) \]\[ V_{\text{hemisphere}} = 2 \pi (576) \]\[ V_{\text{hemisphere}} = 1152 \pi \text{ cm}^3 \]Calculate the volume of one conical bottle:
The base diameter of the conical bottle is \(3 \text{ cm}\), so its radius is \(r = \frac{3}{2} = 1.5 \text{ cm}\).
The height of the conical bottle is \(h = 4 \text{ cm}\).
The formula for the volume of a cone is:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]Substitute the values of \(r\) and \(h\):
\[ V_{\text{cone}} = \frac{1}{3} \pi (1.5)^2 (4) \]\[ V_{\text{cone}} = \frac{1}{3} \pi (2.25) (4) \]\[ V_{\text{cone}} = \frac{1}{3} \pi (9) \]\[ V_{\text{cone}} = 3 \pi \text{ cm}^3 \]Calculate the number of bottles needed:
The number of bottles needed is the total volume of liquid divided by the volume of one bottle:
\[ \text{Number of bottles} = \frac{V_{\text{hemisphere}}}{V_{\text{cone}}} \]\[ \text{Number of bottles} = \frac{1152 \pi}{3 \pi} \]\[ \text{Number of bottles} = \frac{1152}{3} \]\[ \text{Number of bottles} = 384 \]Therefore, 384 conical bottles are needed to empty the bowl.
B) 384 — This is the correct number of bottles calculated by dividing the volume of the hemispherical bowl by the volume of one conical bottle.
To answer this question, we need to understand the definitions of atomic number, mass number, and how they relate to the concept of isotopes. Isotopes are variants of a particular chemical element which have different numbers of neutrons, and therefore different mass numbers, but the same number of protons and thus the same atomic number.
Correct Option: C) elements having same atomic number but different mass number
The question asks to identify the incorrect pair among the given UNESCO World Heritage Sites in India and their year of inclusion. To answer this, we need to recall the correct inclusion years for each site listed.
Based on this verification, the pair for Sanchi Stupa is incorrect.
Correct Option: B) Sanchi Stupa (MP) - 1988
The problem requires us to calculate the difference between the original price of a car and the amount received from an insurance claim after the car was completely damaged. We need to follow a series of steps: first, calculate the insured value of the car; second, calculate the amount paid by the insurance company; and finally, find the difference between the original price and the received amount.
The car was insured to 80% of its price. The original price of the car is ₹6,25,000.
\[ \text{Insured Value} = 80\% \text{ of } \text{Price of Car} \\ \text{Insured Value} = \frac{80}{100} \times 6,25,000 \\ \text{Insured Value} = 0.80 \times 6,25,000 \\ \text{Insured Value} = \text{₹}5,00,000 \]The insurance company paid 90% of the insured value.
\[ \text{Amount Received} = 90\% \text{ of } \text{Insured Value} \\ \text{Amount Received} = \frac{90}{100} \times 5,00,000 \\ \text{Amount Received} = 0.90 \times 5,00,000 \\ \text{Amount Received} = \text{₹}4,50,000 \]This is the difference between the original price and the amount the owner received from the insurance company.
\[ \text{Difference} = \text{Price of Car} - \text{Amount Received} \\ \text{Difference} = 6,25,000 - 4,50,000 \\ \text{Difference} = \text{₹}1,75,000 \]Correct Option: D) ₹1,75,000
The question asks about the president of the first session of the Indian National Congress (INC). This is a factual recall question from modern Indian history. We need to identify the individual who held this significant position.
Correct Option: C) W.C. Bannerjee presided over the first session of the Indian National Congress.
The question asks to identify the river on which the Idukki Hydroelectric Project is built. This is a factual question related to Indian geography and major infrastructure projects. Knowledge of the location of major dams and hydroelectric projects in India is essential for competitive exams.
Correct Option: B) The Idukki Hydroelectric Project is indeed built on the Periyar River in Kerala. It is a significant arch dam and a major source of hydroelectric power for the state.
The question asks about a specific international agreement regarding the construction of the Shahtoot Dam in February 2021. This requires knowledge of India's foreign relations and development projects in neighboring countries.
Correct Option: A) India and Afghanistan signed an agreement to build Shahtoot Dam in Feb 2021. This dam, also known as Lalandar Dam, is a significant project aimed at providing safe drinking water to Kabul city and irrigation for agricultural land.