If the mass of a body is 'm' on the surface of the earth, its mass on the surface of the moon will be:
The question asks about the mass of a body on the Moon's surface given its mass on Earth. It's crucial to understand the fundamental difference between mass and weight in physics.
C) m — Mass is a fundamental property of matter and remains constant irrespective of the gravitational field or location. Therefore, if the mass of a body is 'm' on Earth, it will still be 'm' on the Moon.
This question tests basic knowledge of magnetism and the properties of common substances. Magnets attract ferromagnetic materials. We need to identify which of the given options is a ferromagnetic material or contains one.
Correct Option: B) Iron Filings are small pieces of iron, which is a ferromagnetic material and thus strongly attracted by a magnet.
To find the smallest number by which 3600 must be divided to make it a perfect cube, we need to perform prime factorization of 3600. A number is a perfect cube if, in its prime factorization, the exponent of every prime factor is a multiple of 3. We will identify the prime factors whose exponents are not multiples of 3 and determine what factors need to be removed (by division) to make all exponents multiples of 3.
First, we find the prime factors of 3600.
\[ 3600 = 36 \times 100 \]\[ 36 = 2^2 \times 3^2 \]\[ 100 = 10^2 = (2 \times 5)^2 = 2^2 \times 5^2 \]\[ 3600 = (2^2 \times 3^2) \times (2^2 \times 5^2) \]\[ 3600 = 2^{2+2} \times 3^2 \times 5^2 \]\[ 3600 = 2^4 \times 3^2 \times 5^2 \]For a number to be a perfect cube, the power of each prime factor in its prime factorization must be a multiple of 3. Let's look at the powers of the prime factors of 3600:
The smallest number by which 3600 must be divided to make it a perfect cube is the product of the factors identified in the previous step:
\[ \text{Divisor} = 2^1 \times 3^2 \times 5^2 \]\[ \text{Divisor} = 2 \times 9 \times 25 \]\[ \text{Divisor} = 18 \times 25 \]\[ \text{Divisor} = 450 \]If we divide 3600 by 450:
\[ \frac{3600}{450} = \frac{360}{45} = 8 \]\[ 8 = 2^3 \]This is a perfect cube.Correct Option: D) 450
The question asks to identify the organ affected by Leukoderma. Leukoderma is a medical condition characterized by the loss of pigment in certain areas of the body. We need to determine which of the given options is the primary organ where this condition manifests.
Correct Option: D) Skin
The problem asks us to determine how many times a rope can go around a cylinder of a different radius, given its length and the number of rounds it makes on a cylinder of a known radius. The key idea is that the length of the rope remains constant. We will first calculate the total length of the rope using the information from the first cylinder, and then use this length to find out how many rounds it can make on the second cylinder.
B) 98 is the correct answer, as calculated.
The question asks about the regulatory body responsible for issuing norms for Initial Public Offerings (IPOs) specifically for life insurance companies. To answer this, one needs to identify the primary regulator for the insurance sector in India.
D) IRDA (Insurance Regulatory and Development Authority of India) is the statutory body formed under an Act of Parliament, i.e., the Insurance Regulatory and Development Authority Act, 1999. It is tasked with regulating and promoting the insurance and re-insurance industries in India. This includes setting norms for various operations of insurance companies, including their Initial Public Offerings (IPOs).
The question asks to identify a fighter plane manufactured in France from the given options. This requires knowledge of the origin countries of prominent fighter aircraft.
Correct Option: A) Dassault Rafale is a multirole fighter aircraft designed and manufactured by the French company Dassault Aviation. India has also procured these fighter jets.
This problem involves calculating the total distance of a journey given the total time taken and different speeds for two equal halves of the distance. We will use the fundamental formula relating distance, speed, and time: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\). We will set up an equation based on the total time and solve for the total distance.
Let the total length of the journey be \(D\) km.
The man covers half the distance at 40 km/hr. So, the first half of the distance is \(\frac{D}{2}\) km.
The time taken for the first half of the journey (\(T_1\)) is:
\[ T_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{D/2}{40} = \frac{D}{80} \text{ hours} \]The man covers the rest (the other half) of the distance at 60 km/hr. So, the second half of the distance is also \(\frac{D}{2}\) km.
The time taken for the second half of the journey (\(T_2\)) is:
\[ T_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{D/2}{60} = \frac{D}{120} \text{ hours} \]The total time taken for the journey is given as 8 hours. So, \(T_1 + T_2 = 8\).
Substitute the expressions for \(T_1\) and \(T_2\) into the total time equation:
\[ \frac{D}{80} + \frac{D}{120} = 8 \]Find a common denominator for 80 and 120. The least common multiple (LCM) of 80 and 120 is 240.
Rewrite the equation with the common denominator:
\[ \frac{3D}{240} + \frac{2D}{240} = 8 \]Combine the terms on the left side:
\[ \frac{3D + 2D}{240} = 8 \]\[ \frac{5D}{240} = 8 \]Simplify the fraction on the left side:
\[ \frac{D}{48} = 8 \]Solve for \(D\):
\[ D = 8 \times 48 \]\[ D = 384 \text{ km} \]C) 384 km is the correct length of the journey.
The question asks to identify the Chairperson of the National Commission for Women (NCW) in India as of 2013. This requires knowledge of the historical appointments to this statutory body.
Correct Option: B) Mamta Sharma was the Chairperson of the National Commission for Women from 29th September 2011 to 28th September 2014. Hence, she was the Chairperson in 2013.
The question asks to identify the incorrect match between an author and the language they primarily wrote in. This requires knowledge of prominent Indian authors and their literary contributions in specific languages.
Correct Option: A) S.K. Pottekkat - Telugu. This option is incorrect because S.K. Pottekkat was a famous Malayalam writer, not a Telugu writer. He was a recipient of the Jnanpith Award, India's highest literary honour, for his contributions to Malayalam literature.