To simplify the given expression, we need to follow the order of operations, commonly known as BODMAS/PEMDAS. This acronym stands for Brackets (Parentheses), Orders (Exponents), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
B) The step-by-step application of the BODMAS/PEMDAS rule leads to the result of \(20\).
The question asks to identify which of the given options is NOT considered a social evil, particularly from the perspective of a social reformer like Mahatma Gandhi. We need to evaluate each option based on its nature and whether it represents a societal problem that reformers typically address.
D) Inflation — Inflation is an economic phenomenon characterized by a general increase in prices and fall in the purchasing value of money. While it can have social consequences, it is fundamentally an economic issue addressed through monetary and fiscal policies, rather than a social evil in the sense of a harmful social practice or custom that social reformers typically target.
The problem asks us to identify the number that is different from the others among a given set of four numbers. This type of question usually involves finding a common property or pattern shared by three of the numbers, while the fourth number does not share that property.
Let's check for primality:
D) 10 — Numbers 2, 5, and 7 are all prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 10, however, is a composite number because it has divisors other than 1 and 10 (namely, 2 and 5). Therefore, 10 is the different number.
This is a coding-decoding question where letters are assigned numerical values, and these values are then manipulated (e.g., summed, multiplied) to get the coded number. We need to find the pattern used to code 'RAHUL' as '60' and then apply the same pattern to 'ARUN'.
Assign positional values to letters: The standard approach for such problems is to assign each letter its position in the English alphabet (A=1, B=2, ..., Z=26).
Decode 'RAHUL':
Sum of positional values: \(18 + 1 + 8 + 21 + 12 = 60\).
The sum of the positional values of the letters in 'RAHUL' directly gives the coded value '60'.
Apply the same logic to 'ARUN':
Sum of positional values: \(1 + 18 + 21 + 14 = 54\).
Therefore, 'ARUN' will be written as '54' in that language.
B) 54 — The sum of the positional values of the letters in 'RAHUL' is 60. Applying the same rule to 'ARUN', the sum of its positional values is \(1 + 18 + 21 + 14 = 54\).
Simplify: \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\cdots\left(1-\frac{1}{9}\right)\left(1-\frac{1}{10}\right)\)
-\( \frac{1}{10} \)
\( \frac{5}{6} \)
0
\( \frac{1}{10} \)
The problem asks us to simplify a product of terms, each of the form \( \left(1 - \frac{1}{n}\right) \). We will simplify each term individually and then look for a pattern that allows for cancellation across the product.
Each term in the product is of the form \( \left(1 - \frac{1}{n}\right) \). We can rewrite this by finding a common denominator:
\[ 1 - \frac{1}{n} = \frac{n}{n} - \frac{1}{n} = \frac{n-1}{n} \]The given expression is:
\[ \left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\cdots\left(1-\frac{1}{9}\right)\left(1-\frac{1}{10}\right) \]Substitute the simplified form for each term:
\[ \left(\frac{2-1}{2}\right)\left(\frac{3-1}{3}\right)\cdots\left(\frac{9-1}{9}\right)\left(\frac{10-1}{10}\right) \] \[ = \left(\frac{1}{2}\right)\left(\frac{2}{3}\right)\left(\frac{3}{4}\right)\cdots\left(\frac{8}{9}\right)\left(\frac{9}{10}\right) \]This is a telescoping product. Notice that the numerator of each term cancels with the denominator of the preceding term:
\[ \frac{1}{\cancel{2}} \times \frac{\cancel{2}}{\cancel{3}} \times \frac{\cancel{3}}{\cancel{4}} \times \cdots \times \frac{\cancel{8}}{\cancel{9}} \times \frac{\cancel{9}}{10} \]After all the intermediate terms cancel out, we are left with the numerator of the first term and the denominator of the last term.
D) \( \frac{1}{10} \) is the correct answer, as derived from the step-by-step simplification.
The question asks to identify the government organ primarily responsible for implementation and administration. This requires understanding the distinct roles of the three main branches of government: the Legislature, the Executive, and the Judiciary.
Correct Option: D) Executive is the organ of the government that mainly deals with implementation and administration related tasks. It is responsible for carrying out the laws and policies formulated by the legislature.
We need to find a two-digit number based on two conditions: the sum of its digits is 12, and a relationship between the original number and the number formed by reversing its digits. We can solve this by setting up a system of linear equations or by testing the given options.
D) 84 — The number is 84. The sum of its digits is \(8+4=12\). If digits are reversed, the new number is 48. Seven times the new number is \(7 \times 48 = 336\). Four times the original number is \(4 \times 84 = 336\). Since \(336 = 336\), the conditions are satisfied.
The question asks for the specific term describing the practice of farmers growing trees on their land for both commercial and non-commercial purposes. We need to identify the agricultural practice that integrates trees with crop cultivation and/or livestock rearing.
Correct Option: C) Agroforestry is the practice of integrating trees and shrubs on farms and in agricultural landscapes. This system combines agricultural and forestry practices to produce food, fodder, fuel, timber, and other products, serving both commercial and non-commercial needs of farmers.
The question asks to identify Shah Jahan's daughter who was significantly involved in the architectural projects of Shahjahanabad. This requires knowledge of prominent Mughal princesses and their contributions to architecture during Shah Jahan's reign.
Correct Option: A) Jahanara. She was Shah Jahan's eldest daughter and played a significant role in the architectural development of Shahjahanabad, including designing Chandni Chowk.
The question asks to identify which of the given IITs was declared an "Eat Right Campus" by the Food Safety and Standards Authority of India (FSSAI). This requires knowledge of specific FSSAI initiatives and their beneficiaries.
Correct Option: D) IIT Gandhinagar