To find the Least Common Multiple (LCM) of a set of numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then taking the highest power of each prime factor that appears in any of the numbers.
Correct Option: A) 210 is the Least Common Multiple of 14, 21, and 35.
The problem asks us to identify the fifth term from the right after a specific transformation is applied to a given series. The transformation involves dropping every alternate letter, number, or symbol starting from the first term.
Correct Option: B) #
This question asks us to evaluate the strength of arguments for or against the abolition of income tax in India. We need to determine which argument provides a logical and significant reason related to the statement.
B) Only argument 2 is strong.
Argument 2 highlights the primary purpose of income tax from the government's perspective: revenue generation. This revenue is vital for the functioning of the state and the provision of public goods and services. Therefore, it is a strong argument against abolishing income tax.
This problem involves work and time, specifically comparing the work rates of men and women. We will first establish a relationship between the work done by men and women, then calculate the total work units, and finally determine the time taken by the combined group.
Establish the relationship between men and women's work:
Given that 5 men or 10 women can complete a job in 20 days, this means their total work capacity is equal.
Convert the combined group into an equivalent number of women:
The new group consists of 3 men and 4 women. We convert the men into an equivalent number of women using the relationship found in step 1.
Calculate the total work units:
We know that 10 women can complete the job in 20 days. Let's assume the total work is \(W\). The work rate of 10 women is \(R_{10W}\).
Determine the time taken by the combined group:
The combined group is equivalent to 10 women. Since 10 women can complete the job in 20 days, the group of 3 men and 4 women (which is equivalent to 10 women) will also complete the job in the same number of days.
Correct Option: B) 20
The question asks for the venue where R. Ashwin achieved the milestone of becoming the quickest bowler to reach 300 Test wickets in 54 matches. This requires knowledge of significant cricketing records and their associated locations.
C) Nagpur — R. Ashwin achieved his 300th Test wicket in his 54th Test match at the Vidarbha Cricket Association Stadium in Nagpur against Sri Lanka in November 2017.
To find the other number, we can set up an equation where the product of the two numbers is equal to 20. We are given one number, so we can divide the product by the given number to find the unknown number.
Correct Option: D) 16
The question asks about the area for which the Shanti Swarup Bhatnagar Prize is awarded. This is a factual question related to awards and honors in India, specifically in the field of science.
Correct Option: C) Science and Technology
The question asks to identify which classification system for elements is based on atomic numbers. We need to recall the fundamental principles behind the various periodic table developments and laws mentioned in the options.
Correct Option: A) The Modern Periodic Table is based on the Modern Periodic Law, which states that the properties of elements are a periodic function of their atomic numbers. This was proposed by Henry Moseley after his work on X-ray spectra, which showed that atomic number is a more fundamental property than atomic mass.
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Thus, the final answer is \(6\).
Correct Option: C) 6
To find the acceleration of the car, we need to use the definition of acceleration, which is the rate of change of velocity over time. We are given the initial velocity, final velocity, and the time taken for this change.
Identify the given values:
Recall the formula for acceleration (\(a\)):
Acceleration is defined as the change in velocity divided by the time taken for that change.
\[ a = \frac{\text{Change in velocity}}{\text{Time taken}} = \frac{v - u}{t} \]Substitute the given values into the formula:
\[ a = \frac{10 \text{ m/s} - 5 \text{ m/s}}{5 \text{ s}} \]Calculate the change in velocity:
\[ \text{Change in velocity} = 10 \text{ m/s} - 5 \text{ m/s} = 5 \text{ m/s} \]Calculate the acceleration:
\[ a = \frac{5 \text{ m/s}}{5 \text{ s}} = 1 \text{ m/s}^2 \]B) The calculated acceleration is 1 m/s², which matches option B.