To find the number of sides of a regular polygon when the measure of each exterior angle is given, we use the fundamental property that the sum of the measures of all exterior angles of any convex polygon is 360 degrees. For a regular polygon, all exterior angles are equal.
Thus, the number of sides of the regular polygon is 12.
C) 12 — As calculated, a regular polygon with each exterior angle measuring \(30^\circ\) has 12 sides.
The question asks to identify the British Act that established the subordination of the Madras and Bombay Presidencies to the Bengal Presidency in specific matters. This requires knowledge of the key provisions of various British parliamentary acts related to the administration of British India.
Correct Option: A) Pitt's India Act, 1784. This Act clearly established the subordination of the Presidencies of Madras and Bombay to the Presidency of Bengal in matters of war, diplomatic relations, and revenue, thereby strengthening the central authority of the Governor-General of Bengal.
This problem involves calculating a person's total income given the percentage of income spent and the amount saved. We will determine the percentage of income saved and then use this percentage along with the saved amount to find the total income.
If David spends 55% of his income, the remaining percentage is saved. Total income is always considered 100%.
\[ \text{Percentage of income saved} = 100\% - \text{Percentage of income spent} \]\[ \text{Percentage of income saved} = 100\% - 55\% = 45\% \]We know that 45% of David's income is equal to ₹36,000.
\[ 45\% \text{ of Income} = \text{₹}36,000 \]Let David's total income be \( I \). We can set up the equation:
\[ 0.45 \times I = 36,000 \]\[ I = \frac{36,000}{0.45} \]\[ I = \frac{36,000}{\frac{45}{100}} \]\[ I = \frac{36,000 \times 100}{45} \]\[ I = \frac{3,600,000}{45} \]\[ I = 80,000 \]So, David's income is ₹80,000.
Correct Option: A) 80,000
The question asks about the constitutional provision regarding the oath of office for State Ministers in India. We need to identify the authority responsible for administering this oath as per Article 164(3) of the Indian Constitution.
C) Governor of the State
As per Article 164(3) of the Constitution of India, the Governor of the State administers the oaths of office and secrecy to the State Ministers before they enter upon their office. This is a clear constitutional mandate.
To find the breadth of the rectangular pitch, we will set up an equation based on the given information. We are told that the length is 30 m more than its breadth and its area is 18,271 m². We will use the formula for the area of a rectangle, which is \(\text{Area} = \text{Length} \times \text{Breadth}\), to form a quadratic equation and solve for the breadth.
Let the breadth of the rectangular pitch be \(b\) meters.
According to the problem statement, the length \(l\) is 30 m more than its breadth. So, we can write the length as:
\[ l = b + 30 \]
The area of the rectangular pitch is given as 18,271 m². The formula for the area of a rectangle is \(\text{Area} = \text{Length} \times \text{Breadth}\).
Substitute the expressions for length and breadth into the area formula:
\[ (b + 30) \times b = 18271 \]
Expand the equation:
\[ b^2 + 30b = 18271 \]
Rearrange the equation into a standard quadratic form \(ax^2 + bx + c = 0\):
\[ b^2 + 30b - 18271 = 0 \]
We need to solve this quadratic equation for \(b\). We can use the quadratic formula or factorization. Let's try to factorize it by finding two numbers that multiply to -18271 and add up to 30.
Consider the options given. If we test option B, \(b = 121\):
Since \(121 \times 151 = 18271\), this matches the given area. Therefore, the breadth is 121 m.
Alternatively, using the quadratic formula \(b = \frac{-B \pm \sqrt{B^2 - 4AC}}{2A}\) for \(b^2 + 30b - 18271 = 0\):
\[ b = \frac{-30 \pm \sqrt{30^2 - 4(1)(-18271)}}{2(1)} \] \[ b = \frac{-30 \pm \sqrt{900 + 73084}}{2} \] \[ b = \frac{-30 \pm \sqrt{73984}}{2} \] To find \(\sqrt{73984}\): We know \(200^2 = 40000\) and \(300^2 = 90000\). The last digit is 4, so the square root must end in 2 or 8. Let's try \(272^2\) or \(278^2\). \(270^2 = 72900\). Let's try \(272^2\): \(272 \times 272 = 73984\).
\[ b = \frac{-30 \pm 272}{2} \] Since breadth cannot be negative, we take the positive root:
\[ b = \frac{-30 + 272}{2} \] \[ b = \frac{242}{2} \] \[ b = 121 \]
Correct Option: B) 121
The question asks to identify a commercial crop promoted by the British during colonial rule. This requires knowledge of British economic policies in India, specifically their focus on cash crops for export to fuel their industries.
D) Indigo — Indigo was a crucial commercial crop for the British. It was used as a dye for textiles, and its cultivation was aggressively promoted, often through coercive means, leading to significant exploitation of Indian farmers. The "Indigo Revolt" (or "Blue Rebellion") of 1859-60 in Bengal is a testament to the oppressive nature of indigo cultivation under British rule.
The question asks us to identify the FALSE statement among the given options regarding a rectangle PQRS. We need to recall the fundamental properties of a rectangle to evaluate each statement.
Correct Option: A) The diagonals of rectangle PQRS do not bisect each other
This problem involves applying a set of given symbol transformations to a mathematical expression and then evaluating the resulting expression using the standard order of operations (BODMAS/PEMDAS).
First, perform division and multiplication from left to right.
Next, perform addition and subtraction from left to right.
Correct Option: D) 199
The question asks to identify the name of Ramagupta's widow whom Chandragupta II married after defeating the Saka king. This is a direct historical fact related to the Gupta dynasty.
D) Dhruvadevi — Historical accounts and literary works such as Vishakhadatta's 'Devichandraguptam' mention that Dhruvadevi was the wife of Ramagupta, who was later married by Chandragupta II after Ramagupta's defeat and death at the hands of the Sakas, or after Chandragupta II himself overthrew Ramagupta.
In March 2025, where was the main event of the 56th Central Industrial Security Force (CISF) Raising Day celebrated?
Gurugram, Haryana
Pune, Maharashtra
Mumbai, Maharashtra
Thakkolam, Tamil Nadu
This question tests knowledge of current affairs, specifically the location of significant national events. The Central Industrial Security Force (CISF) Raising Day is an annual event, and its location often varies. Candidates need to recall the specific venue for the 56th CISF Raising Day in March 2025.
Correct Option: D) Thakkolam, Tamil Nadu