To find the combined ratio \(a : b : c\) from two given ratios \(a : b\) and \(b : c\), we need to make the common term (in this case, \(b\)) equal in both ratios. Once the common term is equal, we can combine the ratios directly.
Write down the given ratios:
\[ a : b = 7 : 9 \]\[ b : c = 1 : 12 \]Identify the common term, which is \(b\). In the first ratio, \(b\) is \(9\). In the second ratio, \(b\) is \(1\).
To make the value of \(b\) the same in both ratios, find the Least Common Multiple (LCM) of \(9\) and \(1\). The LCM of \(9\) and \(1\) is \(9\).
Adjust the second ratio \(b : c = 1 : 12\) so that the value of \(b\) becomes \(9\). To do this, multiply both parts of the second ratio by \(9\):
\[ b : c = (1 \times 9) : (12 \times 9) \]\[ b : c = 9 : 108 \]Now, both ratios have the common term \(b\) as \(9\):
\[ a : b = 7 : 9 \]\[ b : c = 9 : 108 \]Since the value of \(b\) is now the same in both ratios, we can combine them to get \(a : b : c\):
\[ a : b : c = 7 : 9 : 108 \]Correct Option: A) 7 : 9 : 108
The question asks to identify the personality who predicted the essential role of nuclear technology beyond just power generation, extending to societal uses for betterment of life. This requires knowledge of prominent Indian scientists and their contributions, particularly in the field of nuclear science.
Correct Option: A) Homi J Bhabha is credited with foreseeing the broad applications of nuclear technology for societal benefit, beyond just electricity generation. He was the principal architect of India's nuclear program and emphasized its role in various sectors like medicine, agriculture, and industry for improving the quality of life.
The question asks to identify the largest gland in the human body. To answer this, we need to recall the major glands and their relative sizes.
Correct Option: A) Liver is the largest gland in the human body, weighing approximately 1.4 kg (3 pounds) in an adult and performing over 500 vital functions.
The question asks to identify the ruler who intended to construct the Alai Minar near the Qutub Minar but could not complete it. This requires knowledge of the history of the Delhi Sultanate, specifically the architectural ambitions of its rulers.
Correct Option: A) Ala-ud-Din Khilji was a powerful ruler of the Khilji dynasty who had ambitious architectural plans. He intended to build the Alai Minar, a minaret that would be twice the height of the Qutub Minar, as part of an expansion of the Quwwat-ul-Islam Mosque. However, he died before its completion, and only the first storey (a rubble core) was built, which still stands today near the Qutub Minar complex.
If \( \frac{A}{4} \) = \( \frac{B}{5} \) = \( \frac{C}{6} \), then A : B : C is:
To find the ratio A : B : C from the given equation \[\frac{A}{4} = \frac{B}{5} = \frac{C}{6}\], we can use the property of ratios. When three or more ratios are equal, they can be equated to a common constant, say \(k\).
Given the equation:
\[ \frac{A}{4} = \frac{B}{5} = \frac{C}{6} \]Let's assume that these equal ratios are all equal to a constant, \(k\). So, we can write:
\[ \frac{A}{4} = k \]This implies \( A = 4k \).
Similarly, for the second part:
\[ \frac{B}{5} = k \]This implies \( B = 5k \).
And for the third part:
\[ \frac{C}{6} = k \]This implies \( C = 6k \).
Now, we need to find the ratio A : B : C. Substitute the values of A, B, and C in terms of \(k\):
\[ A : B : C = 4k : 5k : 6k \]Since \(k\) is a common factor in all parts of the ratio, we can cancel it out:
\[ A : B : C = 4 : 5 : 6 \]Correct Option: A) 4 : 5 : 6
This question tests knowledge about various agricultural and industrial revolutions in India, specifically the "Grey Revolution." These revolutions are often named after colors to signify their focus areas and impact on production.
B) Fertilizer production is the correct answer. The Grey Revolution refers to the increased production and use of fertilizers in India, which was crucial for supporting the Green Revolution and boosting agricultural output.
This problem involves calculating the time period required for a given principal amount to yield a specific simple interest at a given annual rate. We will use the formula for simple interest to find the time.
Correct Option: C) 22.5
The question asks to identify the bank that was nationalized in 1955 and subsequently became the State Bank of India, also noting its status as having the largest number of branches globally. This requires knowledge of the history of banking in India, specifically the nationalization process and the origins of the State Bank of India.
Correct Option: C) The Imperial Bank of India was nationalized in 1955 and renamed the State Bank of India. It is one of the largest banks in the world by branch network.
The question asks for the name of a computer program that translates an entire program written in a high-level language into machine language. We need to identify the correct term among the given options by understanding the function of each.
C) Compiler — A compiler is a special program that processes statements written in a particular programming language (the source language) and turns them into machine language or "code" that a computer's processor uses. It translates the entire program before it is executed.
The question asks to identify a navigation satellite among the given options. This requires knowledge of the primary functions of various satellites launched by ISRO.
Correct Option: A) IRNSS-1I
IRNSS-1I is the ninth satellite in the Indian Regional Navigation Satellite System (IRNSS) constellation, which is now officially called NAVIC. NAVIC is an independent regional navigation satellite system developed by India to provide accurate real-time positioning and timing services.