The question asks about the founder of the Natal Indian Congress, an organization established to combat racial discrimination. This is a direct factual question related to the history of the Indian independence movement and the early life of its prominent leaders.
A) Mahatma Gandhi — Mahatma Gandhi founded the Natal Indian Congress in 1894 in South Africa to fight against the racial discrimination faced by Indians.
To find the volume of a cylinder, we use the formula \(V = \pi r^2 h\), where \(r\) is the radius and \(h\) is the height. We are given the radius and height, so we can directly substitute these values into the formula and calculate the volume.
The volume \(V\) of a cylinder is given by:
\[ V = \pi r^2 h \]We will use the approximation \(\pi = \frac{22}{7}\).
\[ V = \frac{22}{7} \times (28 \text{ cm})^2 \times 40 \text{ cm} \]Divide 784 by 7:
\[ \frac{784}{7} = 112 \]Now, multiply the remaining terms:
\[ V = 22 \times 112 \text{ cm}^2 \times 40 \text{ cm} \]First, multiply 22 by 112:
\[ 22 \times 112 = 2464 \]Finally, multiply 2464 by 40:
\[ V = 2464 \times 40 \text{ cm}^3 \]To calculate \(2464 \times 40\):
\[ 2464 \times 4 = 9856 \]So, \(2464 \times 40 = 98560\).
\[ V = 98560 \text{ cm}^3 \]Correct Option: D) 98560 cm³
The question asks about the most common isotopes used in nuclear weapons. This refers to the fissile materials essential for creating a nuclear chain reaction in atomic bombs (fission weapons) or as triggers for thermonuclear bombs (fusion weapons).
Therefore, Uranium and Plutonium are the most common and fundamental isotopes used in nuclear weapons, either as the main explosive material or as the trigger.
A) Uranium and plutonium — Uranium-235 and Plutonium-239 are the two primary fissile materials used in the core of all nuclear weapons, whether they are pure fission devices or the fission triggers for thermonuclear (fusion) devices.
The question asks for the specific term used when Public Sector Undertakings (PSUs) are privatized by selling a portion of their equity to the public. We need to identify the economic term that precisely describes this action.
Correct Option: B) Disinvestment is the process by which the government sells its shares in Public Sector Undertakings (PSUs) to the public or private entities. This reduces the government's stake and transfers ownership, partially or fully, to the private sector. The act of selling off part of the equity of PSUs to the public perfectly fits this definition.
The question asks to identify which of the given Public Sector Undertakings (PSUs) is NOT a Maharatna company. To answer this, one needs to recall the list of Maharatna PSUs in India.
Correct Option: B) BSNL is not a Maharatna PSU. It is a public sector telecommunications company that has not been granted Maharatna status.
The question asks to identify the supercomputer developed by the Tata Group in 2007. This requires knowledge of specific supercomputers and their developers/years of development.
Correct Option: C) EKA — EKA was a supercomputer developed by Tata Computational Research Laboratories (Tata CRL), a part of the Tata Group, and was unveiled in 2007. It achieved a peak performance of 117.9 teraflops and was ranked as the fourth fastest supercomputer in the world in November 2007.
The question asks to identify the Indian state with which the Chholiya dance form is associated. This requires knowledge of traditional Indian folk dances and their regional origins.
Chholiya is a traditional folk dance form originating from the Kumaon region of Uttarakhand. It is a sword dance performed during weddings and other auspicious occasions, often by Rajput men. The dancers wear traditional Kumaoni attire and carry swords and shields, enacting mock battles. This dance form is deeply rooted in the cultural heritage of Uttarakhand.
B) Uttarakhand — Chholiya dance is a well-known martial folk dance of the Kumaon region of Uttarakhand.
If ₹825 is divided into three parts in a proportion of \( \frac{1}{3} \) : \( \frac{4}{9} \) : \( \frac{3}{4} \), then the first part will be:
To divide a sum of money into parts according to a given ratio with fractions, we first need to convert the fractional ratio into a simple whole number ratio. This is done by finding the Least Common Multiple (LCM) of the denominators and multiplying each term of the ratio by the LCM. Once we have a simple ratio, we can find the sum of the ratio terms and then calculate each part by multiplying the total sum by the respective ratio fraction.
\[ \text{First part} : \text{Second part} : \text{Third part} = \left( \frac{1}{3} \times 36 \right) : \left( \frac{4}{9} \times 36 \right) : \left( \frac{3}{4} \times 36 \right) \]
\[ = 12 : 16 : 27 \]
\[ \text{Sum of ratio terms} = 12 + 16 + 27 = 55 \]
\[ \text{First part} = \frac{\text{First ratio term}}{\text{Sum of ratio terms}} \times \text{Total amount} \]
\[ \text{First part} = \frac{12}{55} \times 825 \]
To simplify, we can divide 825 by 55:
\[ 825 \div 55 = 15 \]
So, the first part is:
\[ \text{First part} = 12 \times 15 = 180 \]
C) ₹180 — As calculated, the first part is ₹180.
To find the length of each side of a rhombus, we can use the property that the diagonals of a rhombus bisect each other at right angles. This creates four congruent right-angled triangles within the rhombus. We can then apply the Pythagorean theorem to one of these triangles to find the length of the side, which is the hypotenuse of the right-angled triangle.
Correct Option: B) 20 cm
This problem involves calculating the principal amount (sum) given the simple interest, rate, and time. We will use the standard formula for simple interest to find the unknown principal.
The formula for simple interest is:
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]Where:
First, multiply the rate and time in the numerator:
\[ 4500 = \frac{\text{P} \times 45}{100} \]Now, to isolate \(\text{P}\), multiply both sides by 100 and divide by 45:
\[ \text{P} = \frac{4500 \times 100}{45} \]Simplify the expression:
\[ \text{P} = \frac{450000}{45} \]\[ \text{P} = 10000 \]So, the sum (principal amount) was ₹10,000.
A) ₹10,000 is the correct answer. This matches our calculated principal amount.