This is a logical reasoning question where we need to evaluate conclusions based solely on the given statement, without introducing outside knowledge or personal opinions. The key is to determine what can be logically inferred from the statement: "Restaurant X sold more pizzas than burgers in the last month."
C) Only conclusion II follows. The sales data directly supports the idea of higher popularity for pizzas at Restaurant X, but it does not provide any basis to judge the inherent quality of pizzas versus burgers.
We need to find three distinct prime numbers whose sum is 40. Once we identify these numbers, we will calculate their product. A key property to remember is that 2 is the only even prime number. All other prime numbers are odd.
Let the three distinct prime numbers be \(p_1\), \(p_2\), and \(p_3\).
We are given that their sum is 40:
\[ p_1 + p_2 + p_3 = 40 \]Since 40 is an even number, and the sum of three numbers is even, there are two possibilities for the parity of the numbers:
Therefore, one of the prime numbers must be 2 (the only even prime number). Let \(p_1 = 2\).
Now the equation becomes:
\[ 2 + p_2 + p_3 = 40 \]\[ p_2 + p_3 = 38 \]We need to find two distinct odd prime numbers \(p_2\) and \(p_3\) that sum to 38. Let's list odd prime numbers and try combinations:
So, the three distinct prime numbers are 2, 7, and 31.
Let's verify their sum: \(2 + 7 + 31 = 9 + 31 = 40\). This is correct.
Now, we need to find the product of these prime numbers:
\[ \text{Product} = 2 \times 7 \times 31 \]\[ \text{Product} = 14 \times 31 \]\[ \text{Product} = 434 \]Correct Option: D) 434
The question asks for the establishment year of the Industrial Finance Corporation of India (IFCI) as a statutory corporation. This requires knowledge of the history of financial institutions in India.
D) 1948 — The Industrial Finance Corporation of India (IFCI) was established on July 1, 1948, under the IFCI Act, 1948. It was the first development financial institution in India, created to cater to the medium and long-term financial needs of the industrial sector.
The question asks for the phenotypic ratio observed in the F2 generation of a dihybrid cross in Mendel's experiments. This is a fundamental concept in Mendelian genetics, specifically dealing with the inheritance of two different traits simultaneously.
B) 9 : 3 : 3 : 1 is the classic phenotypic ratio observed in the F2 generation of a dihybrid cross, as established by Mendel's experiments and the Law of Independent Assortment.
This question tests knowledge about coal production statistics in India for a specific financial year. To answer this, one needs to recall or know the leading coal-producing states in India and their relative production volumes during the Financial Year 2020–21.
Correct Option: D) Chhattisgarh was the leading state in terms of coal production in India during the Financial Year 2020–21. It produced approximately 158.49 million tonnes of coal in that period, making it the highest among all states.
The problem asks us to calculate the speed of light in a diamond, given its refractive index. We can use the definition of the refractive index, which relates the speed of light in a vacuum to the speed of light in the medium.
The refractive index (\(n\)) of a medium is defined as the ratio of the speed of light in a vacuum (\(c\)) to the speed of light in that medium (\(v\)).
\[ n = \frac{c}{v} \]Rounding to two decimal places, we get:
\[ v \approx 1.24 \times 10^8 \text{ m/s} \]Correct Option: B) \(1.24 \times 10^8 \text{ m/s}\)
The question asks to identify the correct properties of magnetic field lines from the given statements. We need to evaluate each statement based on the established laws and characteristics of magnetism.
A) (a), (b), (d) are the correct properties. Statements (a), (b), and (d) are true based on the evaluation.
Find the value of 3 × 6 + 5 − 6 ÷ 2 − 9 + 72 ÷ (3 × 4) + 42
To solve this problem, we need to follow the order of operations, commonly known as BODMAS/PEMDAS. This acronym stands for Brackets (Parentheses), Orders (Exponents), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
Brackets: First, evaluate the expression inside the brackets.
\[ 3 \times 4 = 12 \] So the expression becomes: \[ 3 \times 6 + 5 - 6 \div 2 - 9 + 72 \div 12 + 42 \]
Division and Multiplication (from left to right): Next, perform all division and multiplication operations in the order they appear.
Substituting these values, the expression is now: \[ 18 + 5 - 3 - 9 + 6 + 42 \]
Addition and Subtraction (from left to right): Finally, perform all addition and subtraction operations in the order they appear.
Thus, the final value of the expression is 59.
C) 59 is the correct answer, obtained by strictly following the BODMAS/PEMDAS order of operations.
This problem involves the relationship between speed, distance, and time. When distance is constant, speed and time are inversely proportional. We can set up equations based on the given information about the change in speed and the resulting delay to find the normal travel time.
Let the normal speed of Ravi be \(S\) and the normal time taken to travel from City A to City B be \(T\). Let the distance between City A and City B be \(D\).
The relationship between speed, distance, and time is given by:
\[ D = S \times T \]According to the problem, Ravi drives at two-fifths of his normal speed. So, the new speed \(S'\) is:
\[ S' = \frac{2}{5} S \]At this new speed, he reaches City B 30 minutes late. This means the new time taken \(T'\) is \(T + 30\) minutes. Since the normal time \(T\) will be calculated in minutes, we keep the delay in minutes.
The distance \(D\) remains the same. So, we can write the equation for the new speed and time:
\[ D = S' \times T' \]\[ D = \left(\frac{2}{5} S\right) \times (T + 30) \]Now we have two expressions for \(D\). We can equate them:
\[ S \times T = \left(\frac{2}{5} S\right) \times (T + 30) \]We can cancel \(S\) from both sides (assuming \(S \neq 0\)):
\[ T = \frac{2}{5} (T + 30) \]Now, solve for \(T\):
\[ 5T = 2(T + 30) \]\[ 5T = 2T + 60 \]\[ 5T - 2T = 60 \]\[ 3T = 60 \]\[ T = \frac{60}{3} \]\[ T = 20 \text{ minutes} \]Thus, the time Ravi would have taken to travel from City A to City B at his normal speed is 20 minutes.
D) 20 is the correct answer. The calculation shows that Ravi's normal travel time is 20 minutes.
The problem presents a series of number pairs and asks us to find the missing number in the last pair based on the relationship observed in the previous pairs. We need to identify the pattern that connects the first number to the second number in each given pair.
Therefore, the missing number is 65.
C) 65 — The pattern observed is that the second number is obtained by multiplying the first number by 6 and then subtracting 1. Applying this to 11 gives \((11 \times 6) - 1 = 66 - 1 = 65\).