The question asks to identify the oldest university established in modern India among the given options. This requires knowledge of the establishment dates of these prominent Indian universities.
Correct Option: A) The University of Calcutta was established on January 24, 1857, making it one of the first modern universities in India, alongside the Universities of Bombay and Madras, all founded in the same year based on the Wood's Despatch of 1854.
The question presents an analogy where the relationship between the first two pairs of words needs to be identified and then applied to the third pair to find the missing word. The pattern is "Carrier/Source : Disease".
Correct Option: B) Plague — Rats, particularly through the fleas they carry, are primary vectors for the transmission of the bacterium Yersinia pestis, which causes Plague. This fits the "Carrier/Source : Disease" analogy.
The question asks to identify the state with the maximum urban population according to the final data of Census 2011. This requires knowledge of demographic statistics from the Census 2011 report, specifically regarding urban populations of major Indian states.
The urban population figures for the given states as per Census 2011 are approximately:
Comparing the options provided, Maharashtra clearly has the highest urban population.
C) Maharashtra had the maximum urban population among the given options as per the final data of Census 2011, with approximately 50.8 million urban dwellers.
Birds achieve flight through a complex interplay of physical principles. This question asks about the primary mechanism for generating thrust (forward motion) and lift (upward motion).
B) flapping of wings — The dynamic flapping motion of a bird's wings is the fundamental process that generates both the thrust required for forward movement and the lift needed to overcome gravity and stay aloft. This involves pushing air downwards and backwards, creating reactive forces for lift and thrust, respectively.
The problem provides the sum of two numbers and their ratio. We can represent the numbers using a common multiplier based on their ratio and then use the given sum to find the value of this multiplier. Once the multiplier is known, we can find the actual numbers.
Let the two numbers be \(A\) and \(B\).
We are given that the sum of the two numbers is 45:
\[ A + B = 45 \quad \text{(Equation 1)} \]We are also given that their ratio is 7:8. This means:
\[ \frac{A}{B} = \frac{7}{8} \]From the ratio, we can express the numbers in terms of a common variable, say \(x\). Let:
\[ A = 7x \]\[ B = 8x \]Substitute these expressions for \(A\) and \(B\) into Equation 1:
\[ 7x + 8x = 45 \]Combine the terms on the left side:
\[ 15x = 45 \]Solve for \(x\):
\[ x = \frac{45}{15} \]\[ x = 3 \]Now, substitute the value of \(x\) back into the expressions for \(A\) and \(B\) to find the numbers:
\[ A = 7x = 7 \times 3 = 21 \]\[ B = 8x = 8 \times 3 = 24 \]Thus, the two numbers are 21 and 24.
Check the sum: \(21 + 24 = 45\). Check the ratio: \[\frac{21}{24} = \frac{7 \times 3}{8 \times 3} = \frac{7}{8}\]. Both conditions are satisfied.
Correct Option: B) 21, 24
The question asks to identify the India-born physicist credited with the invention of 'Optical Fibre'. This requires knowledge of key figures in physics and their contributions, particularly in the field of optics and communication technology.
Correct Option: D) Narinder Singh Kapany. Narinder Singh Kapany (1926-2020) was an Indian-born American physicist who is widely regarded as the "Father of Fibre Optics." He conducted groundbreaking research in the 1950s at Imperial College London and later in the United States, which led to the development of optical fibres for communication and other applications. He coined the term "fibre optics" in 1960.
The question asks to identify the first Chairman of the Planning Commission of India. This is a factual question related to Indian political history and governance. The Chairman of the Planning Commission was always the Prime Minister of India.
Correct Option: C) Jawaharlal Nehru was the first Prime Minister of India and, by virtue of that office, became the first Chairman of the Planning Commission when it was constituted in 1950.
To find the square of 349, we can either multiply 349 by itself directly or use algebraic identities to simplify the calculation. Using the identity \((a-b)^2 = a^2 - 2ab + b^2\) can be efficient if we choose 'a' and 'b' appropriately.
Both methods yield the same result.
Correct Option: C) 121801
The question asks for the freezing point of water in degrees Fahrenheit. This requires knowledge of standard temperature scales and the phase change properties of water.
D) 32° F is the correct freezing point of water at standard atmospheric pressure.
This problem tests the understanding of decimal multiplication and how it relates to integer multiplication. We are given a base multiplication of two integers and asked to find the product of two decimal numbers that are derived from the original integers by placing decimal points.
Understand the given information: We are given that \(25 \times 32 = 800\).
Analyze the numbers in the question: We need to find the value of \(2.5 \times 3.2\).
Relate the decimal numbers to the integers: Notice that \(2.5\) can be written as \(25 \div 10\) or \(\frac{25}{10}\). Similarly, \(3.2\) can be written as \(32 \div 10\) or \(\frac{32}{10}\).
Perform the multiplication with fractions: Substitute these fractional forms into the expression:
\[ 2.5 \times 3.2 = \frac{25}{10} \times \frac{32}{10} \]Multiply the numerators and denominators:
\[ \frac{25 \times 32}{10 \times 10} \]Use the given product: We know that \(25 \times 32 = 800\). So, substitute this value:
\[ \frac{800}{100} \]Simplify the fraction:
\[ \frac{800}{100} = 8 \]Alternatively, we can count the number of decimal places. In \(2.5\), there is one decimal place. In \(3.2\), there is one decimal place. So, in the product \(2.5 \times 3.2\), there will be a total of \(1 + 1 = 2\) decimal places. Since \(25 \times 32 = 800\), we place the decimal point two places from the right in \(800\), which gives \(8.00\).
Correct Option: B) 8.00