Which of the following Venn diagrams correctly represents the following classes:
Men, Fathers, Doctors
To determine the correct Venn diagram, we need to understand the relationships between the classes: Men, Fathers, and Doctors. Some men are fathers, some men are doctors, and some fathers can also be doctors. Therefore, the diagram should reflect these overlapping relationships.
Correct Option: C) The diagram accurately reflects that all fathers are men and some men and fathers are doctors.
When two individuals work together and earn a total amount, their earnings are distributed in proportion to the amount of work they do, or equivalently, in proportion to their individual efficiencies (rate of work). The efficiency is inversely proportional to the time taken to complete the job.
Determine the efficiency (rate of work) of Arjun:
Arjun completes the job in 6 days. So, Arjun's 1-day work (efficiency) is:
Determine the efficiency (rate of work) of Anurag:
Anurag completes the job in 7 days. So, Anurag's 1-day work (efficiency) is:
Find the ratio of their efficiencies:
The ratio of their efficiencies (or 1-day work) is directly proportional to their share of earnings.
To simplify the ratio, multiply both sides by the least common multiple of 6 and 7, which is 42.
\[ \text{Ratio} = \left(\frac{1}{6} \times 42\right) : \left(\frac{1}{7} \times 42\right) \]\[ \text{Ratio} = 7 : 6 \]Calculate Arjun's share:
The total amount earned is Rs. 780. The total parts in the ratio are \(7 + 6 = 13\).
Arjun's share will be 7 parts out of 13 total parts.
D) Arjun's share is Rs. 420.
To answer this question, we need to recall the structure of the modern periodic table, specifically the number of elements in each period. The number of elements in a period is determined by the electron shells being filled.
Correct Option: A) 2 and 3
To find the selling price, we need to calculate the profit amount based on the given percentage gain and add it to the cost price. The profit is 16% of the cost price.
The item was purchased for Rs. 1,500.
\[ \text{CP} = \text{Rs. } 1,500 \]Qamar gained 16% on the resale.
\[ \text{Gain Percentage} = 16\% \]Profit is 16% of the Cost Price.
\[ \text{Profit} = \frac{16}{100} \times \text{CP} \] \[ \text{Profit} = \frac{16}{100} \times 1,500 \] \[ \text{Profit} = 16 \times 15 \] \[ \text{Profit} = \text{Rs. } 240 \]The Selling Price is the Cost Price plus the Profit.
\[ \text{SP} = \text{CP} + \text{Profit} \] \[ \text{SP} = 1,500 + 240 \] \[ \text{SP} = \text{Rs. } 1,740 \]Alternatively, the selling price can be calculated directly:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Gain Percentage}}{100}\right) \] \[ \text{SP} = 1,500 \times \left(1 + \frac{16}{100}\right) \] \[ \text{SP} = 1,500 \times \left(1 + 0.16\right) \] \[ \text{SP} = 1,500 \times 1.16 \] \[ \text{SP} = \text{Rs. } 1,740 \]C) Rs. 1,740
The unit of momentum is:
To determine the unit of momentum, we need to recall its definition and the standard SI units for mass and velocity. Momentum is defined as the product of an object's mass and its velocity.
Correct Option: D) kg m s -1
This unit correctly represents the product of mass (kg) and velocity (m s-1).
Select the Answer Figure that is the correct water image of the given Problem Figure.
Problem Figure:
Answer Figures:
To find the water image of a given figure, we need to reflect the figure vertically, as if there is a mirror placed horizontally below the figure. This means that the top and bottom parts of the figure will be inverted.
Correct Option: A) …
The question asks to identify the first Malayalam movie released in 2016 that crossed the 100-crore revenue mark. This requires knowledge of Malayalam cinema box office records, specifically for the year 2016.
Correct Option: B) Pulimurugan was released in 2016 and became the first Malayalam film to cross the ₹100 crore mark at the box office, setting a new benchmark for the industry.
The problem presents a sequence of characters and symbols, followed by an analogy. We need to identify the pattern in the first part of the analogy (ADG : +=2) by mapping the characters to their positions in the given sequence and then apply the same pattern to the second part (CEI : ______) to find the missing term.
B) D?@ is the correct answer as derived from the pattern.
This problem involves setting up a system of two linear equations based on the given age relationships between Roshan and Usha at two different points in time (present and 12 years ago). We will define variables for their current ages and then translate the given statements into algebraic equations. Finally, we will solve the system of equations to find Roshan's present age.
Define variables for present ages:
Let Roshan's current age be \(R\) years.
Let Usha's current age be \(U\) years.
Formulate the first equation (present age relationship):
The first statement says, "Roshan's current age is three years less than 1.5 times that of Usha's."
This can be written as:
Formulate the second equation (age relationship 12 years ago):
12 years ago, Roshan's age was \(R - 12\).
12 years ago, Usha's age was \(U - 12\).
The second statement says, "12 years ago Usha's age was three years more than half of Roshan's age."
This can be written as:
Simplify Equation 2:
\[ U - 12 = \frac{R}{2} - \frac{12}{2} + 3 \]\[ U - 12 = \frac{R}{2} - 6 + 3 \]\[ U - 12 = \frac{R}{2} - 3 \]\[ U = \frac{R}{2} - 3 + 12 \]\[ U = \frac{R}{2} + 9 \quad \text{(Equation 2)} \]Solve the system of equations:
Substitute Equation 2 into Equation 1 to eliminate \(U\):
Find Usha's age (optional, but good for verification):
Substitute \(R = 42\) into Equation 2:
Verify the conditions:
Present: Roshan \(R=42\), Usha \(U=30\). Is \(42 = 1.5 \times 30 - 3\)? \(42 = 45 - 3\), which is true.
12 years ago: Roshan \(42-12=30\), Usha \(30-12=18\). Is \(18 = \frac{1}{2}(30) + 3\)? \(18 = 15 + 3\), which is true.
Both conditions are satisfied.
Correct Option: D) 42
