The question asks to identify the year in which the Atomic Energy Act was enacted, specifically the act that prohibits private control of nuclear power generation in India. This requires knowledge of Indian legislation related to atomic energy.
Correct Option: B) 1962
The Atomic Energy Act of 1962 is the legislation in India that vests the control and development of atomic energy, including nuclear power generation, exclusively with the Central Government. This act prohibits private entities from owning or operating nuclear power plants.
The question asks to identify the nation that contributed the maximum Foreign Direct Investment (FDI) equity inflows to India during the fiscal year 2019-20. This requires knowledge of economic data and trends related to FDI in India.
D) Singapore was the largest source of FDI equity inflows into India in the fiscal year 2019-20, contributing a substantial amount to India's economy.
The question asks to identify the software associated with the '.PSD' file extension. This requires knowledge of common file extensions and the applications that use them.
Correct Option: B) Adobe PhotoShop is the correct answer because '.PSD' is the native file format for Adobe Photoshop, preserving all layers and editing capabilities of an image project.
The numerator of a fraction is less than its denominator by 2. If we subtract 2 from the numerator and add 2 to the denominator, then the new fraction is \( \frac{1}{3} \). What is the original fraction?
\( \frac{1}{3} \)
\( \frac{3}{7} \)
\( \frac{5}{9} \)
\( \frac{5}{7} \)
We need to find an original fraction based on two given conditions. We can set up algebraic equations based on these conditions and solve for the numerator and denominator, or we can test the given options against the conditions.
Define the fraction: Let the numerator of the fraction be \(x\) and the denominator be \(y\). The original fraction is \( \frac{x}{y} \).
Apply the first condition: "The numerator of a fraction is less than its denominator by 2."
\[ x = y - 2 \quad \text{(Equation 1)} \]Apply the second condition: "If we subtract 2 from the numerator and add 2 to the denominator, then the new fraction is \( \frac{1}{3} \)."
\[ \frac{x - 2}{y + 2} = \frac{1}{3} \quad \text{(Equation 2)} \]Substitute Equation 1 into Equation 2: Replace \(x\) with \(y - 2\) in Equation 2.
\[ \frac{(y - 2) - 2}{y + 2} = \frac{1}{3} \]Simplify the equation:
\[ \frac{y - 4}{y + 2} = \frac{1}{3} \]Cross-multiply to solve for \(y\):
\[ 3(y - 4) = 1(y + 2) \] \[ 3y - 12 = y + 2 \] \[ 3y - y = 2 + 12 \] \[ 2y = 14 \] \[ y = 7 \]Find \(x\) using Equation 1:
\[ x = y - 2 \] \[ x = 7 - 2 \] \[ x = 5 \]Form the original fraction: The original fraction is \[\frac{x}{y} = \frac{5}{7}\].
D) \( \frac{5}{7} \)
Let's verify this fraction with the given conditions:
Numerator is less than denominator by 2: \(5 = 7 - 2\). This is true.
Subtract 2 from numerator and add 2 to denominator: \[\frac{5 - 2}{7 + 2} = \frac{3}{9} = \frac{1}{3}\]. This is also true.
If a ⊕ b = a - b + \(\frac{1}{\sqrt{ab}}\)+ \(\sqrt{\frac{a}{b}}\), then 0.9 ⊕ 0.1 = ?
\( \frac{30}{212} \)
\( \frac{214}{30} \)
\( \frac{212}{30} \)
\( \frac{30}{214} \)
The problem defines a new binary operation \(⊕\) and asks us to evaluate an expression using this operation. We need to substitute the given values into the definition of the operation and simplify the resulting expression.
The operation is defined as:
\[ a \oplus b = a - b + \frac{1}{\sqrt{ab}} + \sqrt{\frac{a}{b}} \]We need to calculate \(0.9 \oplus 0.1\). Here, \(a = 0.9\) and \(b = 0.1\).
\[ 0.9 \oplus 0.1 = 0.9 - 0.1 + \frac{1}{\sqrt{0.9 \times 0.1}} + \sqrt{\frac{0.9}{0.1}} \]Let's recheck the calculation for \(\frac{107}{15}\). If we multiply numerator and denominator by 2, we get \(\frac{214}{30}\).
\[ \frac{107}{15} = \frac{107 \times 2}{15 \times 2} = \frac{214}{30} \]Correct Option: B) \( \frac{214}{30} \)
The question asks about a pre-independence Indian movement that boosted cotton production. We need to identify which of the given movements directly or indirectly led to an increased demand for and production of cotton within India.
Correct Option: C) The Swadeshi Movement directly promoted the use of Indian-made goods, particularly textiles, leading to a significant increase in the demand for and production of cotton within India as people boycotted foreign cloth.
Angles A, B and C of a triangle are in arithmetic progression. M is a point on BC such that AM is perpendicular to BC. What is\( \frac{BM}{AB} \)?
\( \frac{1}{2} \)
\( \frac{3}{4} \)
\( \frac{1}{3} \)
\( \frac{1}{4} \)
The problem involves a triangle where angles are in arithmetic progression and a perpendicular is drawn from one vertex to the opposite side. We need to find the ratio of a segment on that side to another side of the triangle. We will use properties of arithmetic progression for angles, the sum of angles in a triangle, and trigonometric ratios in right-angled triangles.
Angles in Arithmetic Progression:
Let the angles of the triangle be \(A\), \(B\), and \(C\). Since they are in arithmetic progression, we can write them as \(A = B - d\), \(B\), and \(C = B + d\) for some common difference \(d\).
Sum of Angles in a Triangle:
The sum of angles in a triangle is \(180^\circ\). So,
\[ A + B + C = 180^\circ \]\[ (B - d) + B + (B + d) = 180^\circ \]\[ 3B = 180^\circ \]\[ B = 60^\circ \]Thus, one of the angles of the triangle is \(60^\circ\).
Consider the Right-Angled Triangle:
Given that \(AM \perp BC\), triangle \(AMB\) is a right-angled triangle with \(\angle AMB = 90^\circ\).
Using Trigonometry in \(\triangle AMB\):
In \(\triangle AMB\), we can write the cosine of angle \(B\) as:
\[ \cos B = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{BM}{AB} \]Substitute the Value of Angle B:
We found that \(B = 60^\circ\). Substitute this value into the cosine equation:
\[ \frac{BM}{AB} = \cos 60^\circ \]Calculate the Value:
The value of \(\cos 60^\circ\) is \( \frac{1}{2} \).
\[ \frac{BM}{AB} = \frac{1}{2} \]A) \( \frac{1}{2} \)
The calculation shows that \( \frac{BM}{AB} = \cos B \). Since angle \(B\) is \(60^\circ\), \[\frac{BM}{AB} = \cos 60^\circ = \frac{1}{2}\].
The question asks to identify the chairperson of the drafting committee for the Universal Declaration of Human Rights (UDHR). This is a factual question related to international history and human rights.
Correct Option: B) Eleanor Roosevelt was the chairperson of the drafting committee of the Universal Declaration of Human Rights (UDHR). Her leadership was instrumental in the creation and adoption of this landmark document.
The question asks about the location where Tundra vegetation is found. Tundra vegetation is characterized by cold, treeless biomes, typically found in high latitudes or high altitudes. We need to identify which of the given Indian geographical regions matches these conditions.
Correct Option: C) Himalayan region
The question asks for the full form of the acronym NRDWP. This requires knowledge of common government programs and their abbreviations, which is a typical static general knowledge question in competitive exams.
Correct Option: A) National Rural Drinking Water Programme
The National Rural Drinking Water Programme (NRDWP) was launched by the Government of India to assist states in providing safe and adequate drinking water to the rural population. It was later restructured and subsumed under the Jal Jeevan Mission in 2019.