The question asks to identify the primary source of energy in India. This requires knowledge of India's energy mix and the dominant fuel used for power generation and other energy needs.
Correct Option: C) Coal is the primary source of energy in India, especially for electricity generation, accounting for a significant majority of the country's power production.
The question asks for the full form of the acronym DRDL. This is a factual recall question related to organizations involved in defence research in India. Knowing the full forms of key defence and scientific organizations is important for competitive exams.
DRDL stands for Defence Research and Development Laboratory. It is a premier laboratory of the Defence Research and Development Organisation (DRDO) in India, primarily involved in the development of missile systems.
A) Defence Research and Development Laboratory is the correct full form of DRDL. It is a well-known laboratory under DRDO, focusing on missile technology.
We are looking for a three-digit number that satisfies two conditions: it is 2 more than a perfect square and 2 less than a perfect cube. We can represent this mathematically and then test the given options or systematically search for such a number.
Let the three-digit number be \(N\). According to the problem statement:
From these two equations, we can write:
\[ k^2 + 2 = m^3 - 2 \] \[ k^2 = m^3 - 4 \]We need to find a three-digit number. This means \(100 \le N \le 999\).
Let's list perfect squares and perfect cubes around the range of three-digit numbers:
Now, let's test values for \(m\) such that \(m^3 - 2\) is a three-digit number and also \(k^2 + 2\) for some \(k\).
Check if 123 is 2 more than a perfect square: \(123 - 2 = 121\). Since \(121 = 11^2\), this condition is met.
So, \(N = 123\) satisfies both conditions.
Check: \(214 - 2 = 212\). 212 is not a perfect square.
Check: \(341 - 2 = 339\). 339 is not a perfect square (\(18^2 = 324\), \(19^2 = 361\)).
Check: \(510 - 2 = 508\). 508 is not a perfect square (\(22^2 = 484\), \(23^2 = 529\)).
Check: \(727 - 2 = 725\). 725 is not a perfect square (\(26^2 = 676\), \(27^2 = 729\)).
The number 123 is the only one that satisfies both conditions.
Correct Option: C) 123
The pH scale measures the acidity or alkalinity of a solution. It ranges from 0 to 14. Pure water is considered a neutral substance, meaning it is neither acidic nor basic. We need to identify the pH value that corresponds to neutrality on this scale.
Correct Option: C) Equal to 7. Pure water is a neutral substance, and by definition, a neutral solution has a pH of 7 at \(25^\circ\text{C}\).
The question asks to identify the element to which Protium, Deuterium, and Tritium belong. These terms refer to different isotopes of a specific element. Understanding the concept of isotopes is key to answering this question.
Correct Option: A) Hydrogen
The problem involves decoding a word based on a given coding pattern. We need to identify the rule applied to transform "BEFORE" into "FEBERO" and then apply the same rule to "JUNGLE".
A) NUJELG is the correct code for JUNGLE based on the identified pattern.
The question asks to identify the Mughal emperor who was a contemporary of the renowned poet-saint Tulsidas. This requires knowledge of the historical timelines of both Tulsidas and the Mughal emperors listed in the options.
A) Akbar — Tulsidas (1532-1623 CE) lived and wrote during the reign of Emperor Akbar (1556-1605 CE). Their timelines significantly overlap, making Akbar the correct contemporary.
The International Day for Biological Diversity was observed on :
The question asks for the date on which the International Day for Biological Diversity is observed. This is a factual question related to environmental awareness and international observances.
Correct Option: B) 22 nd May is the correct date for observing the International Day for Biological Diversity.
The question asks to identify the first Indian to achieve a solo, non-stop circumnavigation of the globe on a sailboat. This is a factual question related to Indian maritime achievements.
Correct Option: B) Lt. Cdr. Abhilash Tomy
To determine which number is not a perfect cube, we need to find the cube root of each given number. A number is a perfect cube if its prime factorization consists of groups of three identical prime factors. Alternatively, we can find the cube root of each number; if the cube root is an integer, the number is a perfect cube.
We find the prime factorization of 64:
\[ 64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^6 \]\[ 64 = (2^2)^3 = 4^3 \]So, 64 is a perfect cube of 4.We find the prime factorization of 216:
\[ 216 = 2 \times 108 \]\[ 216 = 2 \times 2 \times 54 \]\[ 216 = 2 \times 2 \times 2 \times 27 \]\[ 216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \]\[ 216 = 2^3 \times 3^3 = (2 \times 3)^3 = 6^3 \]So, 216 is a perfect cube of 6.We find the prime factorization of 243:
\[ 243 = 3 \times 81 \]\[ 243 = 3 \times 3 \times 27 \]\[ 243 = 3 \times 3 \times 3 \times 9 \]\[ 243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5 \]Since the prime factors (all 3s) do not form groups of three completely (we have \(3^3 \times 3^2\)), 243 is not a perfect cube.We find the prime factorization of 1728:
\[ 1728 = 2 \times 864 \]\[ 1728 = 2 \times 2 \times 432 \]\[ 1728 = 2 \times 2 \times 2 \times 216 \]We already know from Option B that \(216 = 6^3 = 2^3 \times 3^3\).So,
\[ 1728 = 2^3 \times (2^3 \times 3^3) = 2^6 \times 3^3 \]\[ 1728 = (2^2)^3 \times 3^3 = (4)^3 \times 3^3 = (4 \times 3)^3 = 12^3 \]So, 1728 is a perfect cube of 12.Correct Option: C) 243 is not a perfect cube because its prime factorization \(3^5\) does not result in an integer cube root.