The question asks for the location of the headquarters of the Indira Gandhi National Centre for Arts (IGNCA). This is a factual question related to Indian cultural institutions and their geographical locations. To answer this, one needs to recall the established headquarters of IGNCA.
C) New Delhi is the correct answer. The Indira Gandhi National Centre for Arts (IGNCA) has its headquarters located in New Delhi, the capital of India.
The question asks to identify the scientist who formulated the laws of planetary motion. This is a direct knowledge-based question related to the history of astronomy and physics.
Correct Option: D) Johannes Kepler proposed the three laws of planetary motion.
To determine which equation is NOT a quadratic equation, we need to simplify each given equation and check if it can be written in the standard form of a quadratic equation, which is \(ax^2 + bx + c = 0\), where \(a \neq 0\).
\(x(x + 1) + 8 = (x + 2)(x - 2)\)
Expand both sides:
\[ x^2 + x + 8 = x^2 - 4 \]Move all terms to one side:
\[ x^2 - x^2 + x + 8 + 4 = 0 \]\[ x + 12 = 0 \]This is a linear equation, not a quadratic equation, because the highest power of \(x\) is 1.
\(m(2m + 3) = m^2 + 1\)
Expand the left side:
\[ 2m^2 + 3m = m^2 + 1 \]Move all terms to one side:
\[ 2m^2 - m^2 + 3m - 1 = 0 \]\[ m^2 + 3m - 1 = 0 \]This is a quadratic equation because the highest power of \(m\) is 2 (and the coefficient of \(m^2\) is 1, which is not zero).
\((y - 2)^2 + 1 = 2y - 3\)
Expand \((y - 2)^2\) using the identity \((a - b)^2 = a^2 - 2ab + b^2\):
\[ y^2 - 4y + 4 + 1 = 2y - 3 \]\[ y^2 - 4y + 5 = 2y - 3 \]Move all terms to one side:
\[ y^2 - 4y - 2y + 5 + 3 = 0 \]\[ y^2 - 6y + 8 = 0 \]This is a quadratic equation because the highest power of \(y\) is 2 (and the coefficient of \(y^2\) is 1, which is not zero).
\((m - 2)^3 = m^3 - 4\)
Expand \((m - 2)^3\) using the identity \((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\):
\[ m^3 - 3(m^2)(2) + 3(m)(2^2) - 2^3 = m^3 - 4 \]\[ m^3 - 6m^2 + 12m - 8 = m^3 - 4 \]Move all terms to one side:
\[ m^3 - m^3 - 6m^2 + 12m - 8 + 4 = 0 \]\[ -6m^2 + 12m - 4 = 0 \]This is a quadratic equation because the highest power of \(m\) is 2 (and the coefficient of \(m^2\) is -6, which is not zero).
Correct Option: A) \(x(x + 1) + 8 = (x + 2)(x - 2)\) is not a quadratic equation because, upon simplification, the \(x^2\) terms cancel out, resulting in a linear equation \(x + 12 = 0\).
The question asks to identify which term is referred to as a "super-network" or "meta-network." This requires understanding the definitions and scope of various network types.
C) Internet — The Internet is a global network of interconnected computer networks. It connects millions of smaller private, public, academic, business, and government networks, making it the quintessential "super-network" or "meta-network."
This is a coding-decoding problem where we need to find the code for each word by comparing the given statements and their codes. Once the individual codes are identified, we can form the code for the target statement.
The target statement is "Blue Cat is Cloud".
Arranging these codes in the order of the words in the statement, we get ZTMS.
D) ZTMS is the correct code for "Blue Cat is Cloud".
The problem requires calculating the actual distance between two cities given their distance on a map and the map's scale. The scale represents the ratio of a distance on the map to the corresponding actual distance. We will use this ratio to find the actual distance and then convert the units to kilometers.
Correct Option: C) 9 km
Four options have been given, out of which three are alike in some manner and one is different. Select the option that is different from the rest.
\(\sqrt{3}\)
0.120120012000........
π
0.\(\overline{45}\)
The problem asks us to identify the odd one out from the given options. This usually involves classifying the numbers into different categories like rational, irrational, terminating, non-terminating, repeating, or non-repeating decimals.
The square root of 3 is an irrational number. This means its decimal representation is non-terminating and non-repeating.
This number has a decimal representation that is non-terminating and non-repeating (the pattern of zeros between 12 increases: one zero, then two zeros, then three zeros, and so on). Therefore, it is an irrational number.
Pi (\(\pi\)) is a well-known mathematical constant that is an irrational number. Its decimal representation is non-terminating and non-repeating.
This notation represents a repeating decimal, \(0.454545...\). A repeating decimal can always be expressed as a fraction of two integers (a rational number). For example, \[0.\overline{45} = \frac{45}{99} = \frac{5}{11}\].
Thus, option D is different from the rest.
Correct Option: D) \(0.\overline{45}\)
To find the third proportional to two numbers, say \(a\) and \(b\), we assume the third proportional is \(x\). The relationship for a third proportional is that \(a\), \(b\), and \(x\) are in continuous proportion. This means the ratio of the first to the second is equal to the ratio of the second to the third.
Correct Option: D) 100
To find the mean of the first eight odd natural numbers, we first need to identify these numbers. Then, we will use the formula for the mean, which is the sum of all observations divided by the number of observations.
C) 8 is the correct answer. The mean of the first eight odd natural numbers is 8.
The question asks to identify the Indian wildlife sanctuary that is the natural habitat for Asiatic Lions. This requires knowledge of the specific wildlife species associated with prominent national parks and sanctuaries in India.
The Asiatic Lion (Panthera leo leo) is a critically endangered subspecies of lion found only in India. Its last remaining natural habitat is the Gir Forest National Park and Wildlife Sanctuary.
D) Gir — The Gir Forest National Park and Wildlife Sanctuary in Gujarat is the only place in the world where Asiatic Lions are found in their natural habitat. It was established to protect these magnificent big cats.