The question asks why the discovery of penicillin was considered revolutionary. To answer this, we need to understand the historical context and the impact of penicillin on medicine.
B) It began the antibiotic era. This is the correct answer because penicillin was the first true antibiotic and its discovery revolutionized the treatment of bacterial infections, paving the way for the development of a whole class of drugs known as antibiotics.
The question asks for the definition of the Michaelis-Menten constant (\(K_m\)). This constant is a fundamental parameter in enzyme kinetics, describing the relationship between the substrate concentration and the reaction rate.
where:
Correct Option: A) The substrate concentration at which the reaction rate is half of V max
The problem involves calculating the cost price of an article given its selling price, the percentage by which the marked price is above the cost price, and the discount percentage allowed on the marked price. We will work backward from the selling price to find the marked price, and then use the marked price to find the cost price.
The article is sold for ₹59,860 after a 50% discount on the Marked Price. This means the Selling Price is 50% of the Marked Price.
\[ SP = MP - (\text{Discount Percentage} \times MP) \]\[ SP = MP (1 - \text{Discount Percentage}) \]\[ 59,860 = MP (1 - 0.50) \]\[ 59,860 = MP (0.50) \]\[ MP = \frac{59,860}{0.50} \]\[ MP = 59,860 \times 2 \]\[ MP = \text{₹}119,720 \]The Marked Price is 64% more than the Cost Price. This can be expressed as:
\[ MP = CP + (0.64 \times CP) \]\[ MP = CP (1 + 0.64) \]\[ MP = CP (1.64) \]Now, substitute the value of \(MP\) we found:\[ 119,720 = CP (1.64) \]\[ CP = \frac{119,720}{1.64} \]To simplify the division, we can multiply the numerator and denominator by 100:\[ CP = \frac{119,720 \times 100}{1.64 \times 100} \]\[ CP = \frac{11,972,000}{164} \]Let's perform the division:\[ 11972000 \div 164 \]\[ 11972 \div 164 = 73 \]So, \[ CP = 73 \times 1000 \]\[ CP = \text{₹}73,000 \]D) 73,000
If \( a^{2} + b^{2} = 83 \), a × b = 6, and a > b, find \(\frac{a-b}{a+b}\).
\(\sqrt{\frac{62}{95}}\)
\(\sqrt{\frac{71}{95}}\)
\(\frac{71}{95}\)
\(\frac{62}{95}\)
The problem asks us to find the value of \(\frac{a-b}{a+b}\) given the values of \(a^2 + b^2\) and \(a \times b\), along with the condition \(a > b\). We can use algebraic identities to find the values of \((a-b)^2\) and \((a+b)^2\) first, and then take their square roots to find \(a-b\) and \(a+b\). Finally, we will form the required ratio.
Given information:
Find \((a+b)^2\):
We know the identity \((a+b)^2 = a^2 + b^2 + 2ab\).
Substitute the given values:
Find \((a-b)^2\):
We know the identity \((a-b)^2 = a^2 + b^2 - 2ab\).
Substitute the given values:
Find \(a+b\) and \(a-b\):
From \((a+b)^2 = 95\), we get \(a+b = \pm\sqrt{95}\).
From \((a-b)^2 = 71\), we get \(a-b = \pm\sqrt{71}\).
Since \(a > b\), \(a-b\) must be positive. So, \(a-b = \sqrt{71}\).
To determine the sign of \(a+b\), we can find \(a\) and \(b\). We have \(a+b = \sqrt{95}\) and \(a-b = \sqrt{71}\). Adding these two equations gives \(2a = \sqrt{95} + \sqrt{71}\), so \(a = \frac{\sqrt{95} + \sqrt{71}}{2}\). Subtracting the second from the first gives \(2b = \sqrt{95} - \sqrt{71}\), so \(b = \frac{\sqrt{95} - \sqrt{71}}{2}\). Both \(a\) and \(b\) are positive. Thus, \(a+b\) must be positive. So, \(a+b = \sqrt{95}\).
Alternatively, since \(ab=6\) is positive, \(a\) and \(b\) must have the same sign. Since \(a>b\), if \(a\) and \(b\) were both negative, say \(a=-2, b=-3\), then \(a>b\) would be false. So, both \(a\) and \(b\) must be positive. Therefore, \(a+b\) must be positive.
Calculate the required ratio:
\[ \frac{a-b}{a+b} = \frac{\sqrt{71}}{\sqrt{95}} \]\[ \frac{a-b}{a+b} = \sqrt{\frac{71}{95}} \]B) \(\sqrt{\frac{71}{95}}\) is the correct answer, as derived from our calculations.
The problem presents a series of numbers, and we need to find the next number in the sequence. To solve this, we will analyze the differences between consecutive terms to identify a pattern.
Therefore, the next number in the series is 942.
A) 942 — This is the correct number derived from the identified pattern of subtracting consecutive even numbers (2, 4, 6, 8, 10).
To find the average of the remaining three numbers, we first need to calculate the sum of all eight numbers and the sum of the five numbers. Then, we subtract the sum of the five numbers from the sum of all eight numbers to get the sum of the remaining three numbers. Finally, we divide this sum by 3 to find their average.
Calculate the sum of all eight numbers:
Given that the average of eight numbers is 15.
The formula for average is:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \]So, the sum of eight numbers is:
\[ \text{Sum}_8 = \text{Average}_8 \times \text{Count}_8 = 15 \times 8 = 120 \]Calculate the sum of five of these numbers:
Given that the average of five of these numbers is 18.
The sum of these five numbers is:
\[ \text{Sum}_5 = \text{Average}_5 \times \text{Count}_5 = 18 \times 5 = 90 \]Calculate the sum of the remaining three numbers:
The remaining numbers are \(8 - 5 = 3\) numbers.
The sum of the remaining three numbers is the total sum minus the sum of the five numbers:
\[ \text{Sum}_3 = \text{Sum}_8 - \text{Sum}_5 = 120 - 90 = 30 \]Calculate the average of the remaining three numbers:
The average of the remaining three numbers is their sum divided by their count (which is 3):
\[ \text{Average}_3 = \frac{\text{Sum}_3}{\text{Count}_3} = \frac{30}{3} = 10 \]The average of the remaining three numbers is 10.
Correct Option: D) 10
This is a logical reasoning problem involving arrangement on floors. We need to deduce the floor on which each person lives based on the given clues and then answer the question about the number of people living below D.
Correct Option: A) 3
To find the volume of a cube, we first need to determine the length of its side. We can do this by using the given total surface area of the cube and the formula for the total surface area of a cube. Once the side length is found, we can calculate the volume using the volume formula for a cube.
Recall the formula for the total surface area of a cube:
If \(a\) is the side length of the cube, the total surface area (\(TSA\)) is given by:
\[ TSA = 6a^2 \]Use the given total surface area to find the side length (\(a\)):
We are given \(TSA = 216 \text{ cm}^2\). So,
\[ 216 = 6a^2 \]Solve for \(a^2\):
\[ a^2 = \frac{216}{6} \] \[ a^2 = 36 \]Solve for \(a\):
\[ a = \sqrt{36} \] \[ a = 6 \text{ cm} \]Recall the formula for the volume of a cube:
The volume (\(V\)) of a cube with side length \(a\) is given by:
\[ V = a^3 \]Calculate the volume using the side length found:
Substitute \(a = 6 \text{ cm}\) into the volume formula:
\[ V = (6 \text{ cm})^3 \] \[ V = 6 \times 6 \times 6 \text{ cm}^3 \] \[ V = 216 \text{ cm}^3 \]Correct Option: C) 216 cm³
The question asks for the location of the World Sustainable Development Summit (WSDS) in March 2025. This is a factual question requiring knowledge of current affairs and international conference venues.
Correct Option: B) New Delhi, India
The World Sustainable Development Summit (WSDS) is an annual flagship event of The Energy and Resources Institute (TERI). It consistently takes place in New Delhi, India. The summit brings together global leaders and thinkers to discuss issues related to sustainable development, climate change, and energy transition. Therefore, New Delhi is the correct venue for the WSDS in March 2025.