The question asks about the specific Charter Act that reduced the number of directors of the East India Company. To answer this, we need to recall the key provisions of each Charter Act mentioned in the options, particularly those related to the Company's administration and governance.
D) The Charter Act of 1853 reduced the number of directors of the East India Company from 24 to 18. This Act also provided that 6 of the 18 directors were to be appointed by the Crown, further increasing the British government's control over the Company's affairs.
The question asks to identify a state that is both landlocked (does not have a coastline) and does not share a border with any other country (international boundary). We need to examine each option based on its geographical location and borders.
C) Chhattisgarh is a landlocked state within India and does not share any international boundary. It is bordered by Madhya Pradesh, Maharashtra, Telangana, Andhra Pradesh, Odisha, Jharkhand, and Uttar Pradesh.
This problem involves analyzing statements and conclusions based on logical reasoning, often using Venn diagrams to visualize the relationships between categories. We need to determine which conclusions logically follow from the given statements, assuming the statements are true.
Let's represent the given statements using Venn diagrams:
Now let's evaluate the conclusions:
Conclusion (I): Some rats are cats.
Conclusion (II): Some bats can be cats.
C) Only conclusion (II) follows
We need to find the length of the longer side of a rectangle given two conditions: the relationship between its sides and the relationship between its area and perimeter. We will set up equations based on these conditions and solve for the dimensions of the rectangle.
Let the length of the longer side of the rectangle be \(L\) cm and the shorter side be \(W\) cm.
According to the first condition, "The shorter side of a rectangle is 15 cm less than the longer side."
\[ W = L - 15 \quad \text{(Equation 1)} \]The area of a rectangle is given by \(A = L \times W\).
The perimeter of a rectangle is given by \(P = 2(L + W)\).
According to the second condition, "The numerical value of its area is equal to 5 times the numerical value of its perimeter."
\[ A = 5P \]\[ L \times W = 5 \times 2(L + W) \]\[ LW = 10(L + W) \quad \text{(Equation 2)} \]Now, substitute Equation 1 into Equation 2:
\[ L(L - 15) = 10(L + (L - 15)) \]\[ L^2 - 15L = 10(2L - 15) \]\[ L^2 - 15L = 20L - 150 \]Rearrange the terms to form a quadratic equation:
\[ L^2 - 15L - 20L + 150 = 0 \]\[ L^2 - 35L + 150 = 0 \]Solve the quadratic equation for \(L\). We can factorize it:
We need two numbers that multiply to 150 and add up to -35. These numbers are -5 and -30.
\[ (L - 5)(L - 30) = 0 \]This gives two possible values for \(L\):
\[ L = 5 \quad \text{or} \quad L = 30 \]If \(L = 5\), then from Equation 1, \(W = 5 - 15 = -10\). A side length cannot be negative, so \(L = 5\) is not a valid solution.
If \(L = 30\), then from Equation 1, \(W = 30 - 15 = 15\). Both \(L = 30\) cm and \(W = 15\) cm are positive, so this is a valid solution. Also, \(L > W\) (30 > 15), which satisfies the condition that \(L\) is the longer side.
The length of the longer side is 30 cm.
A) 30
The question asks about the Supreme Court's stance on 'child witnesses' based on the 'The State of Madhya Pradesh vs Balveer Singh' case. This requires knowledge of legal principles concerning the admissibility and evidentiary value of a child's testimony in India.
A) A child's evidence is admissible if found voluntary, reliable and untutored. This statement accurately reflects the legal position in India. The Supreme Court has consistently held that there is no rule of law that a child's testimony cannot be relied upon unless corroborated. The crucial test is whether the child understands the questions and gives rational answers, and whether the testimony is voluntary, reliable, and free from tutoring.
To find the median of a set of observations, we first need to arrange the observations in ascending or descending order. Then, we identify the middle value. If the number of observations is odd, the median is the single middle value. If the number of observations is even, the median is the average of the two middle values.
31, 40, 74, 47, 14, 44, 46, 29, 36, 97, 87
There are 11 observations. So, \(n = 11\).
14, 29, 31, 36, 40, 44, 46, 47, 74, 87, 97
Since \(n\) is odd, the median is the \((\frac{n+1}{2})^{\text{th}}\) observation.
\[ \text{Median position} = \frac{11+1}{2} = \frac{12}{2} = 6^{\text{th}} \]The 6th observation in the sorted list is 44.
Sorted list: 14, 29, 31, 36, 40, 44, 46, 47, 74, 87, 97
Therefore, the median is 44.
Correct Option: C) 44
The question asks for the theme of the 54th National Safety Week, observed in March 2025. This requires specific knowledge of current events and national campaigns related to safety.
Correct Option: C) Safety & Well-being Crucial for Viksit Bharat
The problem asks us to find the missing letter-clusters, # and %, such that the relationship between the letter-cluster pair on the left side of '::' is the same as that on the right side. We need to identify the pattern or rule applied to transform one letter-cluster into another.
C) # = CQG, % = VUP
The problem presents a series of letter groups, and we need to find the next group in the sequence. We will analyze the pattern for each letter's position (first, second, and third) across the groups based on their positions in the English alphabetical order.
The first letters are U, S, Q, O.
Following this pattern, the next first letter should be O - 2. O is the 15th letter, so \(15 - 2 = 13\). The 13th letter is M.
The second letters are N, L, J, H.
Following this pattern, the next second letter should be H - 2. H is the 8th letter, so \(8 - 2 = 6\). The 6th letter is F.
The third letters are P, N, L, J.
Following this pattern, the next third letter should be J - 2. J is the 10th letter, so \(10 - 2 = 8\). The 8th letter is H.
The next group in the series is formed by combining the letters found in steps 1, 2, and 3: MFH.
Correct Option: B) MFH
This question tests knowledge about the classical dance forms of India and their associated musical traditions. Indian classical music is broadly divided into two main systems: Hindustani (North Indian) and Carnatic (South Indian). We need to identify which of the given dance forms uses Carnatic music.
Based on this analysis, Kuchipudi is the dance form whose music belongs to the Carnatic system.
Correct Option: B) Kuchipudi