The question asks about a specific creation of the Charter Act of 1833. We need to recall the key provisions of this Act, particularly those related to legal and administrative reforms in British India.
C) Law Commission in India — The Charter Act of 1833 explicitly provided for the appointment of a Law Commission in India to codify Indian laws. Lord Macaulay was the first Law Member appointed under this Act.
Which of the following cities hosted the 20th edition of the IISS Regional Security Summit, a major Middle East security dialogue, in December 2024?
Doha, Qatar
Manama, Bahrain
Riyadh, Saudi Arabia
Abu Dhabi, UAE
The question asks for the host city of the 20th edition of the IISS Regional Security Summit (Manama Dialogue) in December 2024. This is a factual question requiring knowledge of international events and their locations.
Correct Option: B) Manama, Bahrain
The question asks to identify the region associated with the Singphos' Rebellion. This requires knowledge of historical tribal uprisings in British India, specifically their geographical locations.
B) Assam is the correct answer. The Singphos' Rebellion, which took place in the 19th century, was centered in the Upper Assam region against British colonial rule. The Singphos are an indigenous community predominantly found in this area.
The question asks about the seasonal change that marks the withdrawal of the monsoon in India. Understanding the dynamics of the Indian monsoon, particularly the role of the Inter-Tropical Convergence Zone (ITCZ), is crucial to answering this question.
B) Southward shift of ITCZ — The southward shift of the ITCZ is directly linked to the sun's apparent southward movement, which causes the low-pressure trough over the Indian subcontinent to weaken and move south. This change in pressure patterns leads to the reversal of winds and the withdrawal of the monsoon.
To determine the type of quadrilateral, we need to find the actual measures of its angles. The sum of the interior angles of any quadrilateral is \(360^\circ\). Given the ratio of the angles, we can set up an equation to find the value of one part of the ratio and then calculate each angle. After finding the angles, we will check the properties of different quadrilaterals.
Define the angles using the given ratio:
Let the angles of the quadrilateral PQRS be \(2x\), \(8x\), \(3x\), and \(7x\) respectively, where \(x\) is a constant.
Use the sum of angles property of a quadrilateral:
The sum of the interior angles of any quadrilateral is \(360^\circ\).
So, \( \angle P + \angle Q + \angle R + \angle S = 360^\circ \)
\( 2x + 8x + 3x + 7x = 360^\circ \)
Solve for \(x\):
\( 20x = 360^\circ \)
\[ x = \frac{360^\circ}{20} = 18^\circ \]
Calculate the measure of each angle:
\( \angle P = 2x = 2 \times 18^\circ = 36^\circ \)
\( \angle Q = 8x = 8 \times 18^\circ = 144^\circ \)
\( \angle R = 3x = 3 \times 18^\circ = 54^\circ \)
\( \angle S = 7x = 7 \times 18^\circ = 126^\circ \)
Check for parallel sides:
A quadrilateral is a trapezium if at least one pair of opposite sides is parallel. This happens if the sum of consecutive interior angles between the parallel sides is \(180^\circ\).
Let's check consecutive angles:
Since \( \angle P + \angle Q = 180^\circ \), this implies that side PS is parallel to side QR (if P and Q are consecutive angles along one of the parallel sides, or if PQ is a transversal intersecting PS and QR). However, the angles are taken in order, so PQ, QR, RS, SP are the sides. If \( \angle P + \angle Q = 180^\circ \), then PS and QR are parallel. If \( \angle R + \angle S = 180^\circ \), then PQ and RS are parallel.
In our case, \( \angle P + \angle Q = 180^\circ \). This means that the sum of consecutive angles between sides PS and QR is \(180^\circ\), implying that PS is parallel to QR. Also, \( \angle R + \angle S = 180^\circ \). This means that the sum of consecutive angles between sides PQ and RS is \(180^\circ\), implying that PQ is parallel to RS.
Wait, let's re-evaluate the condition for parallel lines. If a transversal intersects two lines such that the sum of consecutive interior angles is \(180^\circ\), then the lines are parallel.
Given angles in order P, Q, R, S:
However, if we consider sides PQ and RS as parallel, then \( \angle P + \angle S \) and \( \angle Q + \angle R \) would be the sums of consecutive interior angles. This is not the case.
Let's consider the standard definition of a trapezium: a quadrilateral with at least one pair of parallel sides. If PQ is parallel to RS, then \( \angle P + \angle S = 180^\circ \) and \( \angle Q + \angle R = 180^\circ \). This is not true here.
If PS is parallel to QR, then \( \angle P + \angle Q = 180^\circ \) and \( \angle S + \angle R = 180^\circ \).
We found:
\( \angle P + \angle Q = 36^\circ + 144^\circ = 180^\circ \)
\( \angle R + \angle S = 54^\circ + 126^\circ = 180^\circ \)
The fact that \( \angle P + \angle Q = 180^\circ \) means that if PQ is a transversal intersecting PS and QR, then PS is parallel to QR. The fact that \( \angle R + \angle S = 180^\circ \) means that if RS is a transversal intersecting PS and QR, then PS is parallel to QR.
Both conditions indicate that PS is parallel to QR. Since one pair of opposite sides (PS and QR) is parallel, the quadrilateral PQRS is a trapezium.
Correct Option: A) Trapezium
The problem asks us to identify numbers in a given series that are immediately preceded by another number and immediately followed by a symbol. We need to scan the series from left to right and apply this condition to each element.
The problem asks us to find the total monthly salary of a man given his expenses and savings. We are given the percentage of salary spent on house rent and the fixed amounts spent on conveyance, grocery, and savings. We can calculate the total amount spent on conveyance, grocery, and savings, which represents the remaining percentage of his salary after house rent. From this, we can determine the total monthly salary.
Let the total monthly salary be \(S\).
The man spends 40% of his monthly salary on house rent. So, the amount spent on house rent is \(0.40 \times S\).
The remaining percentage of his salary after spending on house rent is \(100\% - 40\% = 60\%\). This 60% of his salary is used for conveyance, grocery, and savings.
Calculate the total amount spent on conveyance, grocery, and savings:
\[ \text{Total remaining amount} = \text{Conveyance} + \text{Grocery} + \text{Savings} \]\[ \text{Total remaining amount} = \text{₹}442 + \text{₹}9,115 + \text{₹}946 \]\[ \text{Total remaining amount} = \text{₹}10,503 \]This total remaining amount of ₹10,503 represents 60% of his monthly salary. So, we can set up the equation:
\[ 0.60 \times S = \text{₹}10,503 \]Now, solve for \(S\):
\[ S = \frac{\text{₹}10,503}{0.60} \]\[ S = \text{₹}17,505 \]Therefore, his monthly salary is ₹17,505.
C) ₹17,505 is the correct monthly salary calculated by summing the fixed expenses and savings, and then determining the total salary based on the remaining percentage after rent.
This problem requires us to substitute the given operators with their interchanged counterparts and then evaluate the expression following the order of operations (BODMAS/PEMDAS).
Thus, the value of the expression after interchanging the operators is 577.
Correct Option: A) 577 — After interchanging the operators and performing the calculations according to the order of operations, the result is 577.
The volume of a right circular cone is 1078 cm³. Find the total surface area of the cone if its height is 21 cm. (Use π = \( \frac{22}{7} \))
154 cm²
154\(\sqrt{10}\) cm²
154(1 + \(\sqrt{10}\)) cm²
22(7 + \(\sqrt{10}\)) cm²
To find the total surface area of a right circular cone, we need its radius (\(r\)) and slant height (\(l\)). We are given the volume and height (\(h\)). We will first use the volume formula to find the radius, then use the Pythagorean theorem to find the slant height, and finally calculate the total surface area.
The volume of a right circular cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]Given \(V = 1078 \text{ cm}^3\), \(h = 21 \text{ cm}\), and \(\pi = \frac{22}{7}\).
Substitute the given values into the formula:
\[ 1078 = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 21 \]Simplify the equation:
\[ 1078 = \frac{1}{3} \times \frac{22}{7} \times r^2 \times (3 \times 7) \]\[ 1078 = 22 \times r^2 \]Now, solve for \(r^2\):
\[ r^2 = \frac{1078}{22} \]\[ r^2 = 49 \]Take the square root to find \(r\):
\[ r = \sqrt{49} \]\[ r = 7 \text{ cm} \]For a right circular cone, the radius, height, and slant height form a right-angled triangle. So, we can use the Pythagorean theorem:
\[ l^2 = r^2 + h^2 \]Substitute \(r = 7 \text{ cm}\) and \(h = 21 \text{ cm}\):
\[ l^2 = 7^2 + 21^2 \]\[ l^2 = 49 + 441 \]\[ l^2 = 490 \]Take the square root to find \(l\):
\[ l = \sqrt{490} \]\[ l = \sqrt{49 \times 10} \]\[ l = 7\sqrt{10} \text{ cm} \]The total surface area of a cone is given by the formula:
\[ \text{TSA} = \pi r (r + l) \]Substitute \(\pi = \frac{22}{7}\), \(r = 7 \text{ cm}\), and \(l = 7\sqrt{10} \text{ cm}\):
\[ \text{TSA} = \frac{22}{7} \times 7 \times (7 + 7\sqrt{10}) \]\[ \text{TSA} = 22 \times 7 (1 + \sqrt{10}) \]\[ \text{TSA} = 154 (1 + \sqrt{10}) \text{ cm}^2 \]C) 154(1 + \(\sqrt{10}\)) cm² is the correct total surface area calculated.
This problem involves calculating work done and remaining work. We will determine the daily work rate of each person, calculate the work done by B, and then find out how much work is left for A to complete.
Calculate the daily work rate of A:
A can finish the work in 2 days. So, A's one day's work is:
\[ \text{A's 1 day work} = \frac{1}{2} \text{ of the total work} \]Calculate the daily work rate of B:
B can finish the work in 52 days. So, B's one day's work is:
\[ \text{B's 1 day work} = \frac{1}{52} \text{ of the total work} \]Calculate the work done by B in 26 days:
B worked alone for 26 days. The work done by B in 26 days is:
\[ \text{Work done by B} = \text{B's 1 day work} \times \text{Number of days B worked} \] \[ \text{Work done by B} = \frac{1}{52} \times 26 = \frac{26}{52} = \frac{1}{2} \text{ of the total work} \]Calculate the remaining work:
The total work is considered as 1 unit. Work remaining after B left is:
\[ \text{Remaining work} = \text{Total work} - \text{Work done by B} \] \[ \text{Remaining work} = 1 - \frac{1}{2} = \frac{1}{2} \text{ of the total work} \]Calculate the number of days A will take to finish the remaining work:
A's 1 day work is \(\frac{1}{2}\) of the total work. The remaining work is also \(\frac{1}{2}\) of the total work.
Number of days A will take = \[\frac{\text{Remaining work}}{\text{A's 1 day work}}\]
\[ \text{Days A will take} = \frac{\frac{1}{2}}{\frac{1}{2}} = 1 \text{ day} \]Therefore, A alone can finish the remaining work in 1 day.
C) 1