To find the least number that must be subtracted from a given number to make it a perfect square, we need to find the largest perfect square less than or equal to the given number. This can be achieved by using the long division method to find the square root of the number and identifying the remainder.
\[ \begin{array}{rll} 2\,4\,6 & \\ \sqrt{6\,00\,65} & \\ -4 & \downarrow \downarrow & (2 \times 2 = 4) \\ \hline 2\,00 & & (44 \times 4 = 176) \\ -1\,76 & \downarrow \\ \hline 24\,65 & & (486 \times 6 = 2916) \\ -29\,16 & & \text{This is incorrect. Let's re-do the last step.} \end{array} \]
Let's correct the long division method for finding the square root of 60065:
\[ \begin{array}{rll} 2\,4\,5 & \\ \sqrt{6\,00\,65} & \\ -4 & \downarrow \downarrow & (2 \times 2 = 4) \\ \hline 2\,00 & & \text{Bring down 00} \\ -1\,76 & \downarrow & (44 \times 4 = 176) \\ \hline 24\,65 & & \text{Bring down 65} \\ -24\,25 & & (485 \times 5 = 2425) \\ \hline 40 & & \text{Remainder} \end{array} \]
\[ 245^2 = 245 \times 245 = 60025 \]
Number to be subtracted \( = 60065 - 60025 = 40 \)
Alternatively, the remainder obtained from the long division method is the least number that must be subtracted from the original number to make it a perfect square.
A) 40 is the remainder when 60065 is divided by 245 in the context of finding the square root, meaning that subtracting 40 from 60065 results in the perfect square \(245^2 = 60025\).
The question asks about the year when the Bharat Ratna award, India's highest civilian honor, was instituted. This is a factual question related to Indian history and awards.
Correct Option: B) 1954 is the correct year when the provision of Bharat Ratna was introduced.
The question asks to identify which sector of an economy the service sector belongs to. Understanding the classification of economic activities into primary, secondary, and tertiary sectors is crucial to answer this question.
Correct Option: B) tertiary sector — The service sector, which includes activities like banking, transportation, education, and healthcare, is fundamentally categorized as the tertiary sector of an economy. It provides services rather than producing physical goods.
The question asks about the number of member states in SAARC (South Asian Association for Regional Cooperation). To answer this, one needs to recall the current composition of SAARC.
Correct Option: C) 8
The question asks about the number of wars fought between the British and the Kingdom of Mysore. This requires knowledge of the Anglo-Mysore Wars, which were a series of conflicts in the late 18th century.
D) 4 — There were four Anglo-Mysore Wars fought between the British and the Kingdom of Mysore.
Simplify:
\(\frac{25+3\times8-4}{27-3\times(8-4)}\)
To simplify the given expression, 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 simplify the numerator and the denominator separately before performing the final division.
The numerator is \(25 + 3 \times 8 - 4\).
First, perform the multiplication:
\[ 3 \times 8 = 24 \]Now, substitute this back into the numerator:
\[ 25 + 24 - 4 \]Perform addition and subtraction from left to right:
\[ 25 + 24 = 49 \]\[ 49 - 4 = 45 \]So, the simplified numerator is \(45\).
The denominator is \(27 - 3 \times (8 - 4)\).
First, perform the operation inside the parentheses:
\[ 8 - 4 = 4 \]Now, substitute this back into the denominator:
\[ 27 - 3 \times 4 \]Next, perform the multiplication:
\[ 3 \times 4 = 12 \]Now, substitute this back into the denominator:
\[ 27 - 12 \]Perform the subtraction:
\[ 27 - 12 = 15 \]So, the simplified denominator is \(15\).
Now, divide the simplified numerator by the simplified denominator:
\[ \frac{\text{Numerator}}{\text{Denominator}} = \frac{45}{15} \]Perform the division:
\[ \frac{45}{15} = 3 \]Thus, the simplified value of the expression is \(3\).
C) 3 — The step-by-step simplification following the order of operations correctly yields 3.
The question asks for the Indian state where Kolleru Lake is located. This is a factual question about Indian geography. To answer this, one needs to recall the location of major geographical features in India.
Correct Option: D) Andhra Pradesh. Kolleru Lake is a large freshwater lake located in the state of Andhra Pradesh, India. It is a significant wetland and a Ramsar site, known for its rich biodiversity, especially migratory birds.
The question asks about the number of cities selected in the first batch of the Smart Cities Mission in 2016. To answer this, one needs to recall the initial selections made under this flagship urban development program of the Indian government.
A) 20 — On January 28, 2016, the Ministry of Urban Development announced the first list of 20 cities selected under the Smart Cities Mission.
The question asks for the approximate year when the construction of the Taj Mahal Complex began. This requires knowledge of historical facts related to Mughal architecture and the reign of Shah Jahan.
Correct Option: C) 1632 AD
This problem involves simple interest where the number of years is equal to the rate of interest. We will use the formula for simple interest to set up an equation and solve for the rate of interest.
The problem states that Anil Kumar took a loan for as many years as the rate of interest. Let the rate of interest be \(R\) percent per annum. Then, the time period (T) in years will also be \(R\).
\[ T = R \]The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]Substitute \(P = 24000\), \(SI = 19440\), and \(T = R\) into the formula:
\[ 19440 = \frac{24000 \times R \times R}{100} \]First, simplify the right side of the equation:
\[ 19440 = \frac{24000 \times R^2}{100} \]\[ 19440 = 240 \times R^2 \]Divide both sides by 240:
\[ R^2 = \frac{19440}{240} \]\[ R^2 = 81 \]Take the square root of both sides:
\[ R = \sqrt{81} \]\[ R = 9 \]The rate of interest is 9%.
Correct Option: B) 9%