The question asks to identify the major contributor to photochemical smog among the given options. Photochemical smog is a type of air pollution resulting from reactions between sunlight and pollutants like nitrogen oxides and volatile organic compounds. We need to understand the role of each option in the formation and composition of photochemical smog.
B) Ozone — Ozone (\(\text{O}_3\)) is a secondary pollutant formed during photochemical smog. It is the primary component responsible for the detrimental effects of smog, such as respiratory issues, eye irritation, and damage to plants. Its concentration is often used as an indicator of smog severity.
What is the maturity value of Rs.25,000 at the end of 2 years at 9.25% Simple Interest?
To find the maturity value, we first need to calculate the simple interest earned over the given period. The simple interest formula is \(I = \frac{P \times R \times T}{100}\), where \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(T\) is the time in years. Once the interest is calculated, the maturity value is the sum of the principal and the simple interest.
Using the formula \(I = \frac{P \times R \times T}{100}\):
\[ I = \frac{25000 \times 9.25 \times 2}{100} \]\[ I = \frac{25000 \times 18.5}{100} \]\[ I = 250 \times 18.5 \]\[ I = 4625 \]Maturity Value = Principal + Simple Interest
\[ \text{Maturity Value} = P + I \]\[ \text{Maturity Value} = 25000 + 4625 \]\[ \text{Maturity Value} = 29625 \]Thus, the maturity value is Rs. 29,625.
A) Rs.29,625 is the correct maturity value calculated by adding the principal amount and the simple interest earned over 2 years.
This is a work and time problem. We need to calculate the individual work rates of P, Q, and R, find their combined work rate for different scenarios (P working alone, P with Q and R), and then determine the total time taken for the work to be completed under the given alternate day assistance condition.
Calculate individual daily work rates:
If P can do a work in 11 days, P's 1-day work is \(\frac{1}{11}\).
If Q can do a work in 20 days, Q's 1-day work is \(\frac{1}{20}\).
If R can do a work in 55 days, R's 1-day work is \(\frac{1}{55}\).
Determine the work cycle:
P works every day. Q and R assist P on alternate days. This means:
And so on. The cycle repeats every two days.
Calculate work done in each part of the cycle:
Work done on Day 1 (P alone):
\[ W_1 = \frac{1}{11} \]Work done on Day 2 (P + Q + R):
\[ W_2 = \frac{1}{11} + \frac{1}{20} + \frac{1}{55} \]To add these fractions, find the Least Common Multiple (LCM) of 11, 20, and 55.
LCM(11, 20, 55) = LCM(11, 4 \(\times\) 5, 5 \(\times\) 11) = 4 \(\times\) 5 \(\times\) 11 = 220.
\[ W_2 = \frac{20}{220} + \frac{11}{220} + \frac{4}{220} = \frac{20 + 11 + 4}{220} = \frac{35}{220} = \frac{7}{44} \]Calculate work done in one complete 2-day cycle:
Work in 2 days = Work on Day 1 + Work on Day 2
\[ W_{\text{cycle}} = \frac{1}{11} + \frac{7}{44} = \frac{4}{44} + \frac{7}{44} = \frac{11}{44} = \frac{1}{4} \]So, in every 2 days, \(\frac{1}{4}\) of the total work is completed.
Determine the total number of days:
If \(\frac{1}{4}\) of the work is done in 2 days, then the full work (1 unit) will be done in:
\[ \text{Total Days} = \frac{1}{\frac{1}{4}} \times 2 \text{ days} = 4 \times 2 \text{ days} = 8 \text{ days} \]C) 8
The question asks for the chemical name of quick lime. This requires knowledge of common chemical names and their corresponding chemical formulas or systematic names.
Quick lime is the common name for calcium oxide, which has the chemical formula \(\text{CaO}\). It is a widely used chemical compound.
C) Calcium oxide is the correct chemical name for quick lime.
The question asks to identify the diagnostic tool used for heart problems from the given options. We need to understand the full forms and applications of each acronym.
Correct Option: C) ECG
The question asks to identify the antibiotic discovered by Alexander Fleming in 1928. This is a direct factual recall question related to the history of medicine and scientific discoveries.
Correct Option: C) Penicillin — Alexander Fleming discovered penicillin in 1928, marking a pivotal moment in the history of medicine and the development of antibiotics.
The question asks to identify an oil-yielding plant from the given options. This requires knowledge of common agricultural crops and their primary uses.
Correct Option: A) Groundnut is a major oilseed crop. Its seeds are pressed to extract groundnut oil, which is widely used for cooking and in various food products.
The question asks to identify the metal that is essential for forming an amalgam. An amalgam is a specific type of alloy where mercury is one of the constituent metals. Therefore, we need to find the option that represents mercury.
B) Mercury is the correct answer because an amalgam is specifically defined as an alloy of mercury with another metal. Mercury is unique in its ability to dissolve many metals to form these alloys, which are often used in dentistry and other applications.
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then find x² + y² + z².
The problem asks us to find the value of \(x^2 + y^2 + z^2\) given the expressions for \(x\), \(y\), and \(z\) in terms of \(r\), \(A\), and \(B\). We will substitute the given expressions into the required sum of squares and use trigonometric identities to simplify the result.
C) \(r^2\) is the correct answer. This result is significant as \(x, y, z\) represent the Cartesian coordinates of a point, and \(r, A, B\) are its spherical coordinates. The expression \(x^2 + y^2 + z^2\) represents the square of the distance from the origin to the point, which is \(r^2\) in spherical coordinates.
The problem can be solved by translating the given word statement into a quadratic equation. We will then solve this quadratic equation to find the possible values for the integer. Since the problem specifies a "positive integer", we will select the positive integer solution.
"Five times a positive integer" can be written as \(5x\).
"Twice its square" can be written as \(2x^2\).
"Five times a positive integer is 3 less than twice its square" means:
\[ 5x = 2x^2 - 3 \]We need two numbers that multiply to \((2)(-3) = -6\) and add up to \(-5\). These numbers are \(-6\) and \(1\).
Rewrite the middle term \(-5x\) as \(-6x + x\):
\[ 2x^2 - 6x + x - 3 = 0 \]Case 1:
\[ 2x + 1 = 0 \]\[ 2x = -1 \]\[ x = -\frac{1}{2} \]Case 2:
\[ x - 3 = 0 \]\[ x = 3 \]Therefore, the integer is 3.
C) 3 is the positive integer that satisfies the given condition. When \(x=3\), five times the integer is \(5 \times 3 = 15\). Twice its square is \(2 \times 3^2 = 2 \times 9 = 18\). Indeed, \(15\) is \(3\) less than \(18\).