This question asks us to identify which assumptions are implicit in the given statement. An implicit assumption is something that is not directly stated but must be true for the statement to make sense or be logically valid. We need to evaluate each assumption based solely on the information provided in the statement.
B) Neither assumption I nor II is implicit. Both assumptions go beyond what is directly stated or logically implied by the statement. The statement focuses on building a new, high-speed road, not on the condition or existence of current roads.
The question asks to identify the city that is NOT located on the banks of the River Ganga. This requires knowledge of the geographical locations of major Indian cities relative to the Ganga river.
Correct Option: B) Lucknow is situated on the banks of the Gomti River, which is a tributary of the Ganga, but not directly on the main stem of the Ganga River.
The problem presents a proportion in the form of a continued proportion. We need to convert this proportion into an algebraic equation and then solve for the unknown variable \(y\), given that \(y > 0\).
Understand the proportion: The given expression \(144 : y :: y : 225\) means that the ratio of 144 to \(y\) is equal to the ratio of \(y\) to 225. This can be written as a fraction:
\[ \frac{144}{y} = \frac{y}{225} \]Cross-multiply: To solve this equation, we cross-multiply the terms:
\[ 144 \times 225 = y \times y \]\[ 144 \times 225 = y^2 \]Calculate the product:
\[ 144 \times 225 = 32400 \]Form the equation for \(y^2\):
\[ y^2 = 32400 \]Find the square root of both sides: To find \(y\), we take the square root of 32400:
\[ y = \sqrt{32400} \]Simplify the square root: We can simplify \(\sqrt{32400}\) by recognizing that \(32400 = 324 \times 100\).
\[ y = \sqrt{324 \times 100} \]\[ y = \sqrt{324} \times \sqrt{100} \]Calculate individual square roots:
Calculate \(y\):
\[ y = 18 \times 10 \]\[ y = 180 \]Check the condition: The problem states that \(y > 0\). Our calculated value \(y = 180\) satisfies this condition.
B) 180 is the correct value for \(y\).
The question asks for the specific term used to describe the process of decomposing water into its constituent elements (hydrogen and oxygen gas) using electricity. We need to identify the correct scientific term among the given options.
Correct Option: D) electrolysis of water. This term accurately describes the process of using electricity to break down water into hydrogen and oxygen gases.
To find the approximate value, we should first round off each number to its nearest whole number. Then, we apply the order of operations (BODMAS/PEMDAS) to solve the equation. BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction.
The original equation is:
\[ 8.99 + 17.99 - 3.99 \times 2.99 = ? \]After rounding, it becomes:
\[ 9 + 18 - 4 \times 3 = ? \]First, perform multiplication:
\[ 4 \times 3 = 12 \]Now, substitute this back into the equation:
\[ 9 + 18 - 12 = ? \]First, perform addition:
\[ 9 + 18 = 27 \]Now, perform subtraction:
\[ 27 - 12 = 15 \]Therefore, the approximate value is 15.
B) 15 is the correct approximate value.
The problem states that Ujwal has a total amount of Rs 5,250 in currency notes of denominations Rs 50, Rs 100, and Rs 200. It also specifies that the number of notes of each denomination is equal. We need to find the total number of notes Ujwal has.
Correct Option: C) 45
The question asks to identify the founder of the Indian Statistical Institute and the person considered the Father of Modern Statistics in India. This requires knowledge of prominent figures in Indian statistics and their contributions.
Prasanta Chandra Mahalanobis is renowned for his significant contributions to statistics in India. He founded the Indian Statistical Institute (ISI) in Kolkata in 1931. His work on large-scale sample surveys and the development of the Mahalanobis distance are fundamental to statistical science. He also played a crucial role in India's Second Five-Year Plan, emphasizing industrialization based on his statistical models. These contributions firmly establish him as the Father of Modern Statistics in India.
B) Prasanta Chandra Mahalanobis — He founded the Indian Statistical Institute (ISI) in 1931 and is widely regarded as the Father of Modern Statistics in India due to his pioneering work in statistical theory and application, including the Mahalanobis distance and his role in national planning.
This question asks about the relationship between the real wage rate and the marginal productivity of labor. In a perfectly competitive labor market, firms hire labor up to the point where the additional revenue generated by the last worker (marginal revenue product of labor) equals the additional cost of hiring that worker (wage rate).
A) Real wage rate is equal to the Marginal Productivity of Labour. As derived in the step-by-step explanation, in a perfectly competitive market, a firm hires labor until the real wage rate equals the marginal productivity of labor. This ensures profit maximization for the firm.
The question asks for the term that describes the effective diameter of the circular outline of a spherical lens. This is a fundamental definition in optics.
A) aperture — The aperture of a spherical lens is defined as the effective diameter of its circular outline. It determines the amount of light that can pass through the lens and also influences the resolution of the image formed.
The given series consists of numbers that appear to be perfect cubes. We need to identify the pattern by finding the cube root of each number in the series and then determine the next number based on this pattern.
Therefore, the number that replaces the question mark is 27.
Correct Option: B) 27