The question asks for the first month of the Indian National Calendar, which is based on the Saka Era and was adopted for official purposes in 1957. To answer this, one needs to know the structure and starting month of this specific calendar.
C) Chaitra is the first month of the Indian National Calendar, which was adopted from March 22, 1957, and is based on the Saka Era.
To find the percentage gain, we first need to calculate the actual gain (profit) by subtracting the cost price from the selling price. Then, we divide the gain by the cost price and multiply by 100 to express it as a percentage.
Gain is the difference between the Selling Price and the Cost Price.
\[ \text{Gain} = \text{SP} - \text{CP} \]\[ \text{Gain} = \text{βΉ}350 - \text{βΉ}200 \]\[ \text{Gain} = \text{βΉ}150 \]Percentage Gain is calculated using the formula:
\[ \text{Percentage Gain} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \% \]Substitute the values:
\[ \text{Percentage Gain} = \left( \frac{150}{200} \right) \times 100 \% \]\[ \text{Percentage Gain} = \left( \frac{3}{4} \right) \times 100 \% \]\[ \text{Percentage Gain} = 0.75 \times 100 \% \]\[ \text{Percentage Gain} = 75 \% \]Correct Option: D) 75%
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the third word to find the fourth word.
Correct Option: C) Curing
The question asks to identify the first social media site. This requires knowledge of the history and evolution of social networking platforms.
Correct Option: B) Six Degrees
Six Degrees is widely recognized as the first social media site. Launched in 1997, it allowed users to create profiles, list friends, and send messages to other users. Its name was inspired by the "six degrees of separation" concept, which posits that any two people on Earth are connected by a chain of no more than six acquaintances.
The question asks for the previous name of the Department of AYUSH. This requires knowledge of the historical evolution of government departments related to traditional Indian medicine systems.
Correct Option: D) Department of Indian System of Medicine and Homeopathy
Which of the following options is equal to \(\sqrt{2-\sqrt{3}}\) ?
\(\frac{\sqrt{6}-\sqrt{2}}{2}\)
\(\frac{2-\sqrt{3}}{2}\)
\(\frac{\sqrt{6}-\sqrt{3}}{2}\)
\(\frac{\sqrt{2}-\sqrt{3}}{2}\)
To simplify the expression \(\sqrt{2-\sqrt{3}}\), we aim to transform the term inside the square root into a perfect square of the form \((a-b)^2\) or \((a+b)^2\). A common technique for expressions like \(\sqrt{A \pm \sqrt{B}}\) is to multiply and divide by 2 inside the square root to get \(\frac{\sqrt{4A \pm 2\sqrt{4B}}}{2}\) or similar, which helps in creating a term with \(2ab\).
We have the expression \(\sqrt{2-\sqrt{3}}\). To create a term of the form \(2ab\), we can multiply the term inside the square root by 2 and divide the entire expression by \(\sqrt{2}\) (which is equivalent to multiplying the numerator and denominator by \(\sqrt{2}\) inside the square root).
\[ \sqrt{2-\sqrt{3}} = \sqrt{\frac{2(2-\sqrt{3})}{2}} = \sqrt{\frac{4-2\sqrt{3}}{2}} \]Now, we can write this as:
\[ \frac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}} \]We need to find two numbers whose sum is 4 and whose product is 3. These numbers are 3 and 1. So, we can write \(4-2\sqrt{3}\) as \(3+1-2\sqrt{3}\).
\[ \sqrt{4-2\sqrt{3}} = \sqrt{3+1-2\sqrt{3}} \]This is in the form \((a-b)^2 = a^2+b^2-2ab\), where \(a=\sqrt{3}\) and \(b=1\). So, \(a^2=3\), \(b^2=1\), and \(2ab=2\sqrt{3}\cdot 1 = 2\sqrt{3}\).
\[ \sqrt{3+1-2\sqrt{3}} = \sqrt{(\sqrt{3})^2 + (1)^2 - 2(\sqrt{3})(1)} = \sqrt{(\sqrt{3}-1)^2} \]Since \(\sqrt{3} \approx 1.732 > 1\), \(\sqrt{3}-1\) is positive. Therefore,
\[ \sqrt{(\sqrt{3}-1)^2} = \sqrt{3}-1 \]Now, substitute this back into the expression from Step 2:
\[ \frac{\sqrt{3}-1}{\sqrt{2}} \]Multiply the numerator and denominator by \(\sqrt{2}\) to rationalize the denominator:
\[ \frac{(\sqrt{3}-1) \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{3}\cdot\sqrt{2} - 1\cdot\sqrt{2}}{2} = \frac{\sqrt{6}-\sqrt{2}}{2} \]Correct Option: A) \(\frac{\sqrt{6}-\sqrt{2}}{2}\)
This is a blood relations question. We need to break down the statement made by the man into smaller parts and then combine them to find the relationship between the woman and the man. We will work backward from the end of the statement to deduce the relationship.
D) Cousin β As deduced, the woman is the daughter of the man's paternal aunt, which means she is his cousin.
The problem presents a sequence of numbers and asks to find the missing value 'x' by identifying the underlying pattern. The numbers provided are: 36, 25, 16, 9, 4, 361, x, 289, 256, 225. A common approach for such problems is to check if the numbers are squares, cubes, or follow an arithmetic or geometric progression, or some combination of these.
The question asks to identify the scientists who received the Nobel Prize for their discovery of Helicobacter pylori and its role in peptic ulcers. This requires knowledge of specific Nobel laureates and their contributions to medicine.
B) Robin Warren and Barry Marshall
In 2005, the Nobel Prize in Physiology or Medicine was awarded to Barry J. Marshall and J. Robin Warren for their discovery of the bacterium Helicobacter pylori and its role in gastritis and peptic ulcer disease. Their groundbreaking work challenged the long-held belief that stress and lifestyle factors were the primary causes of ulcers, demonstrating instead that a bacterial infection was often responsible. This discovery led to effective antibiotic treatments for peptic ulcers.
What is the positive difference between \( \frac{5}{16} \) and its reciprocal?
2 \( \frac{73}{80} \)
2 \( \frac{61}{80} \)
2 \( \frac{71}{80} \)
2 \( \frac{69}{80} \)
To find the positive difference between a fraction and its reciprocal, we first need to determine the reciprocal of the given fraction. Then, we subtract the smaller value from the larger value to ensure a positive difference. Finally, we simplify the result to a mixed number.
Identify the given fraction:
The given fraction is \( \frac{5}{16} \).
Find the reciprocal of the fraction:
The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \). Therefore, the reciprocal of \( \frac{5}{16} \) is \( \frac{16}{5} \).
Determine which value is larger:
To find the positive difference, we need to subtract the smaller fraction from the larger one. We can compare \( \frac{5}{16} \) and \( \frac{16}{5} \). Since \( \frac{16}{5} = 3.2 \) and \( \frac{5}{16} = 0.3125 \), it is clear that \( \frac{16}{5} \) is larger than \( \frac{5}{16} \).
Calculate the difference:
The positive difference is \[\frac{16}{5} - \frac{5}{16}\].
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 16 is \( 5 \times 16 = 80 \).
\[ \frac{16}{5} - \frac{5}{16} = \frac{16 \times 16}{5 \times 16} - \frac{5 \times 5}{16 \times 5} \]\[ = \frac{256}{80} - \frac{25}{80} \]\[ = \frac{256 - 25}{80} \]\[ = \frac{231}{80} \]Convert the improper fraction to a mixed number:
To convert \( \frac{231}{80} \) to a mixed number, divide 231 by 80:
\( 231 \div 80 = 2 \) with a remainder of \( 231 - (2 \times 80) = 231 - 160 = 71 \).
So, \[\frac{231}{80} = 2 \frac{71}{80}\].
Correct Option: C) 2 \( \frac{71}{80} \)