The question asks to identify the Director General of the Archaeological Survey of India (ASI) who took office in 1944 and subsequently undertook excavations at Harappa. This requires knowledge of key figures in Indian archaeology and their timelines.
Correct Option: A) R.E.M. Wheeler (commonly known as Sir Mortimer Wheeler) took over as the Director General of the Archaeological Survey of India in 1944. He introduced modern archaeological techniques and undertook extensive excavations at Harappa, among other sites, which significantly contributed to the understanding of the Indus Valley Civilization.
The question asks to identify the canal that connects the Mediterranean Sea and the Red Sea. This requires knowledge of major artificial waterways and their geographical locations.
Correct Option: B) Suez Canal is the artificial sea-level waterway in Egypt, connecting the Mediterranean Sea and the Red Sea. It is one of the world's most heavily used shipping lanes.
The question asks to identify the statement that is NOT true about Plaster of Paris (PoP). We need to evaluate each option based on the known properties and uses of Plaster of Paris.
B) Plaster of Paris doesn't change on wetting with water. This statement is incorrect because Plaster of Paris reacts with water to form gypsum, which is a hard solid, undergoing a significant change.
Find the total surface area of a cone, if its radius and slant height are 2r and \( \frac{1}{2} \) respectively.
π\( (4r^{2} + 1) \)
\(\frac{4r^2+1}{2}\)
πr(4r + 1)
πr(2r + 1)
To find the total surface area of a cone, we use the formula that combines the area of its circular base and its curved surface area. We are given the radius and slant height in terms of 'r' and a constant, so we will substitute these values into the standard formula.
The total surface area (\( \text{TSA} \)) of a cone is given by the sum of the area of its circular base and its curved surface area.
\[ \text{TSA} = \pi r_{c}^{2} + \pi r_{c} l_{c} \]where \( r_{c} \) is the radius of the cone and \( l_{c} \) is its slant height.From the problem statement:
Substitute \( r_{c} = 2r \) and \( l_{c} = \frac{1}{2} \) into the TSA formula:
\[ \text{TSA} = \pi (2r)^{2} + \pi (2r) \left(\frac{1}{2}\right) \]First, calculate \( (2r)^2 \):
\[ (2r)^{2} = 4r^{2} \]Then, calculate \( \pi (2r) \left(\frac{1}{2}\right) \):The \( 2 \) in \( 2r \) and the \( \frac{1}{2} \) cancel each other out:
\[ \pi (2r) \left(\frac{1}{2}\right) = \pi r \]Now, substitute these simplified terms back into the TSA equation:\[ \text{TSA} = \pi (4r^{2}) + \pi r \]\[ \text{TSA} = 4\pi r^{2} + \pi r \]Both terms have \( \pi r \) in common. Factor out \( \pi r \):
\[ \text{TSA} = \pi r (4r + 1) \]C) \( \pi r (4r + 1) \) is the correct expression for the total surface area of the cone after substituting the given radius and slant height and simplifying.
The question asks to identify the first woman Speaker of the Lok Sabha. This requires knowledge of prominent political figures and their historical roles in the Indian Parliament.
Meira Kumar served as the Speaker of the 15th Lok Sabha from 2009 to 2014. She was the first woman to be elected to this prestigious position in the history of the Indian Parliament.
Correct Option: B) Meira Kumar
If r sin θ = \( \frac{7}{2} \) and r cos θ = 7\(\frac{\sqrt{3}}{2}\), then what will be the value of r?
We are given two equations involving \(r\), \(\sin \theta\), and \(\cos \theta\). We need to find the value of \(r\). A common method to eliminate \(\theta\) and solve for \(r\) in such problems is to square both equations and add them, using the identity \(\sin^2 \theta + \cos^2 \theta = 1\).
Write down the given equations:
\[ r \sin \theta = \frac{7}{2} \quad \text{(Equation 1)} \]\[ r \cos \theta = 7\frac{\sqrt{3}}{2} \quad \text{(Equation 2)} \]Square both sides of Equation 1:
\[ (r \sin \theta)^2 = \left(\frac{7}{2}\right)^2 \]\[ r^2 \sin^2 \theta = \frac{49}{4} \quad \text{(Equation 3)} \]Square both sides of Equation 2:
\[ (r \cos \theta)^2 = \left(7\frac{\sqrt{3}}{2}\right)^2 \]\[ r^2 \cos^2 \theta = 49 \times \frac{3}{4} \]\[ r^2 \cos^2 \theta = \frac{147}{4} \quad \text{(Equation 4)} \]Add Equation 3 and Equation 4:
\[ r^2 \sin^2 \theta + r^2 \cos^2 \theta = \frac{49}{4} + \frac{147}{4} \]Factor out \(r^2\) on the left side:
\[ r^2 (\sin^2 \theta + \cos^2 \theta) = \frac{49 + 147}{4} \]Apply the trigonometric identity \(\sin^2 \theta + \cos^2 \theta = 1\):
\[ r^2 (1) = \frac{196}{4} \]\[ r^2 = 49 \]Solve for \(r\):
\[ r = \pm \sqrt{49} \]\[ r = \pm 7 \]In polar coordinates, \(r\) typically represents the distance from the origin and is considered non-negative. However, if \(r\) can be negative, it implies a direction. Given the options, we look for a positive value. If \(r\) were negative, say \(-7\), then \(-7 \sin \theta = 7/2\) implies \(\sin \theta = -1/2\), and \(-7 \cos \theta = 7\sqrt{3}/2\) implies \(\cos \theta = -\sqrt{3}/2\). This is consistent for \(\theta\) in the third quadrant. However, usually \(r\) is taken as the magnitude, which is positive. Since \(7\) is an option and \(-7\) is not, we choose \(7\).
Correct Option: D) 7
The problem asks us to identify the odd word out of four given words. This is a classification type of verbal reasoning question where we need to find a common characteristic among three words and identify the one that does not share that characteristic.
Correct Option: B) Reduce — This word means to make something smaller or less, which is the opposite of increasing or improving.
The question asks to identify the specific Article of the Indian Constitution that grants the President the power to pardon, reprieve, respite, remit, suspend, or commute sentences, especially in cases involving the death penalty. This requires knowledge of the constitutional provisions related to the President's pardoning power.
Correct Option: D) Article 72
Article 72 of the Constitution of India empowers the President to grant pardons, reprieves, respites or remissions of punishment or to suspend, remit or commute the sentence of any person convicted of any offence. This power extends to cases where the punishment or sentence is for an offence against any law relating to a matter to which the executive power of the Union extends, in all cases where the sentence is a sentence of death, and in all cases where the sentence is a sentence of death.
The problem asks us to identify the odd one out from a given set of words. This is a classification type of question where we need to find a common characteristic among three words and identify the one that does not share that characteristic.
Correct Option: B) Storm — Autumn, Winter, and Spring are all names of seasons. Storm is a weather phenomenon, not a season.
The question asks to identify the common industrial sector associated with the given places: Rourkela, Bhilai, Bokaro, and Visakhapatnam. This requires knowledge of major industrial centers in India.
Correct Option: B) iron and steel industry