The question asks to identify which of the given diseases is NOT caused by a virus. This requires knowledge of the causative agents (bacteria, viruses, fungi, etc.) for common diseases.
Correct Option: D) Tuberculosis is caused by a bacterium, not a virus.
The question asks to identify the constitutional provision that mandates citizens to uphold and protect the sovereignty, unity, and integrity of India. This requires knowledge of the different parts of the Indian Constitution, specifically Fundamental Rights, Fundamental Duties, and other legal provisions.
B) fundamental duty. Article 51A(c) of the Indian Constitution explicitly states that it shall be the duty of every citizen of India "to uphold and protect the sovereignty, unity and integrity of India."
The question asks for the location of the Chashma-III nuclear power plant. This requires knowledge of major nuclear power facilities and their geographical locations, which is a common topic in general knowledge sections of competitive exams.
Correct Option: B) The Chashma-III nuclear power plant is part of the Chashma Nuclear Power Plant complex, which is located in Pakistan. This plant was developed with Chinese assistance and is a significant part of Pakistan's energy infrastructure.
This problem involves calculating the time spent cycling when a person covers a total distance by cycling and walking, given their respective speeds and the total time taken. We can set up a system of two linear equations based on the total distance and total time, and then solve for the time spent cycling.
Let \(t_c\) be the time spent cycling (in hours) and \(t_w\) be the time spent walking (in hours).
The total time taken is 7 hours. So, we have the equation:
\[ t_c + t_w = 7 \quad \text{(Equation 1)} \]The speed of cycling is 12.5 km/h, and the speed of walking is 3 km/h.
The distance covered by cycling is \( \text{Speed}_c \times t_c = 12.5 t_c \).
The distance covered by walking is \( \text{Speed}_w \times t_w = 3 t_w \).
The total distance covered is 40 km. So, we have the equation:
\[ 12.5 t_c + 3 t_w = 40 \quad \text{(Equation 2)} \]From Equation 1, we can express \(t_w\) in terms of \(t_c\):
\[ t_w = 7 - t_c \]Substitute this expression for \(t_w\) into Equation 2:
\[ 12.5 t_c + 3 (7 - t_c) = 40 \]Now, solve for \(t_c\):
\[ 12.5 t_c + 21 - 3 t_c = 40 \]\[ (12.5 - 3) t_c = 40 - 21 \]\[ 9.5 t_c = 19 \]\[ t_c = \frac{19}{9.5} \]\[ t_c = 2 \]So, Ravikant spent 2 hours cycling.
C) 2 — As calculated, the time spent cycling is 2 hours.
We are given the ratio of incomes and expenditures of two individuals, Barun and Anil, along with their respective savings. We need to find their actual incomes. We can set up equations based on the formula: Income - Expenditure = Savings, and then solve for the unknown income values.
Let the income of Barun be \(12x\) and the income of Anil be \(13x\), where \(x\) is a common multiple for their incomes.
Let the expenditure of Barun be \(10y\) and the expenditure of Anil be \(13y\), where \(y\) is a common multiple for their expenditures.
We know that Income - Expenditure = Savings. We are given their savings:
Set up equations for Barun and Anil:
For Barun:
\[ 12x - 10y = 2100 \quad \text{(Equation 1)} \]For Anil:
\[ 13x - 13y = 1300 \quad \text{(Equation 2)} \]Simplify Equation 2 by dividing by 13:
\[ x - y = 100 \]From this, we can express \(y\) in terms of \(x\):
\[ y = x - 100 \quad \text{(Equation 3)} \]Substitute Equation 3 into Equation 1:
\[ 12x - 10(x - 100) = 2100 \]\[ 12x - 10x + 1000 = 2100 \]\[ 2x + 1000 = 2100 \]\[ 2x = 2100 - 1000 \]\[ 2x = 1100 \]\[ x = \frac{1100}{2} \]\[ x = 550 \]Now that we have the value of \(x\), we can find the incomes of Barun and Anil.
Income of Barun \( = 12x = 12 \times 550 = 6600 \)
Income of Anil \( = 13x = 13 \times 550 = 7150 \)
To verify, let's find their expenditures and check savings:
First, find \(y\):
\[ y = x - 100 = 550 - 100 = 450 \]Expenditure of Barun \( = 10y = 10 \times 450 = 4500 \)
Expenditure of Anil \( = 13y = 13 \times 450 = 5850 \)
Barun's savings \( = \text{Income} - \text{Expenditure} = 6600 - 4500 = 2100 \)
Anil's savings \( = \text{Income} - \text{Expenditure} = 7150 - 5850 = 1300 \)
The calculated savings match the given savings, so our incomes are correct.
Correct Option: D) ₹6,600 and ₹7,150
To evaluate the given expression, we must follow the order of operations, commonly remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
Thus, the value of the expression is 31.
Correct Option: B) 31
What is the simplest form of the ratio of 6 h : 3 days?
\( \frac{1}{9} \)
\( \frac{1}{3} \)
\( \frac{1}{12} \)
\( \frac{1}{6} \)
To find the simplest form of a ratio between two quantities, it is essential that both quantities are expressed in the same unit. In this problem, the given quantities are in hours and days. We need to convert one of the units so that both are consistent, and then simplify the ratio.
Identify the given quantities and their units:
Convert the units to be consistent:
It's usually easier to convert the larger unit to the smaller unit. We know that \(1 \text{ day} = 24 \text{ hours}\).
So, convert \(3 \text{ days}\) into hours:
\[ 3 \text{ days} = 3 \times 24 \text{ hours} = 72 \text{ hours} \]Form the ratio with consistent units:
The ratio is \(6 \text{ h} : 72 \text{ h}\).
This can be written as a fraction:
\[ \frac{6}{72} \]Simplify the ratio to its simplest form:
Find the greatest common divisor (GCD) of the numerator and the denominator and divide both by it.
Both 6 and 72 are divisible by 6.
\[ \frac{6 \div 6}{72 \div 6} = \frac{1}{12} \]Thus, the simplest form of the ratio \(6 \text{ h} : 3 \text{ days}\) is \( \frac{1}{12} \).
C) \( \frac{1}{12} \) is the correct answer, as derived by converting days to hours and then simplifying the resulting ratio.
This problem involves calculating the total work done by individuals and then finding the combined work rate to determine the time taken to complete the task together. We will first find the total work units for each person, then their individual daily work rates, and finally their combined daily work rate to calculate the total days required.
A works 5 hours a day for 8 days. So, the total hours A works to complete the task is:
\[ \text{Total hours for A} = 5 \text{ h/day} \times 8 \text{ days} = 40 \text{ hours} \]B works 6 hours a day for 10 days. So, the total hours B works to complete the task is:
\[ \text{Total hours for B} = 6 \text{ h/day} \times 10 \text{ days} = 60 \text{ hours} \]Let the total work be 1 unit. Then, A's work rate is \( \frac{1}{40} \) of the task per hour, and B's work rate is \( \frac{1}{60} \) of the task per hour.
When A and B work together, their combined work rate per hour is the sum of their individual rates:
\[ \text{Combined work rate per hour} = \frac{1}{40} + \frac{1}{60} \]\[ \text{Combined work rate per hour} = \frac{3}{120} + \frac{2}{120} = \frac{5}{120} = \frac{1}{24} \text{ of the task per hour} \]If they work together, they complete \( \frac{1}{24} \) of the task per hour. So, to complete the entire task (1 unit), they will need:
\[ \text{Total hours jointly} = \frac{1}{\text{Combined work rate per hour}} = \frac{1}{1/24} = 24 \text{ hours} \]They work 8 hours a day. So, the number of days required is:
\[ \text{Number of days} = \frac{\text{Total hours jointly}}{\text{Hours per day}} = \frac{24 \text{ hours}}{8 \text{ h/day}} = 3 \text{ days} \]C) 3 days
This problem involves work and time. We need to find the individual time taken by B to complete the work. We are given a relationship between the work done and time taken by A and B, and the combined time they take to complete the work.
Let the total work be \(W\). Let the time taken by B to complete the work be \(T_B\) days and by A be \(T_A\) days.
According to the problem statement, A does half as much work as B in three-fourth of the time taken by B. Let's consider a specific amount of work, say \(W_0\).
If B does \(W_0\) work in time \(t_B\), then A does \(\frac{1}{2} W_0\) work in time \(\frac{3}{4} t_B\).
Let's find the ratio of their efficiencies (work done per unit time). Efficiency is Work/Time.
Efficiency of A, \[E_A = \frac{\frac{1}{2} W_0}{\frac{3}{4} t_B} = \frac{1}{2} W_0 \times \frac{4}{3 t_B} = \frac{2}{3} \frac{W_0}{t_B}\].
Efficiency of B, \(E_B = \frac{W_0}{t_B}\).
Therefore, the ratio of efficiencies is:
\[ \frac{E_A}{E_B} = \frac{\frac{2}{3} \frac{W_0}{t_B}}{\frac{W_0}{t_B}} = \frac{2}{3} \]This means \(E_A = \frac{2}{3} E_B\). If B's efficiency is \(3x\), then A's efficiency is \(2x\).
Alternatively, the ratio of efficiencies is inversely proportional to the ratio of times taken to complete the same amount of work. If A and B work together, their combined efficiency is \(E_A + E_B\).
They take 12 days to complete the work together. So, their combined efficiency is \(\frac{1}{12}\) of the total work per day.
\[ E_A + E_B = \frac{1}{12} \]Substitute \(E_A = \frac{2}{3} E_B\) into the equation:
\[ \frac{2}{3} E_B + E_B = \frac{1}{12} \]\[ \left(\frac{2}{3} + 1\right) E_B = \frac{1}{12} \]\[ \frac{5}{3} E_B = \frac{1}{12} \]Solve for \(E_B\):
\[ E_B = \frac{1}{12} \times \frac{3}{5} = \frac{3}{60} = \frac{1}{20} \]Since \(E_B\) is the fraction of work B can do in one day, the time B takes to complete the entire work alone is the reciprocal of \(E_B\).
\[ T_B = \frac{1}{E_B} = \frac{1}{\frac{1}{20}} = 20 \text{ days} \]B) 20 days
The problem presents a series of alphanumeric terms. To find the next term, we need to identify the pattern in the numbers and letters within each term.
Correct Option: A) 1R8 is the correct term as it follows the identified patterns for the first digit, middle letter, and last digit.