The question asks for the island where Indira Point, the southernmost point of India, is located. This requires knowledge of the geography of the Andaman and Nicobar Islands.
Correct Option: D) Great Nicobar island
To find the curved surface area of a right circular cylinder, we need its height and the radius of its base. The problem provides the height directly and the circumference of the base, from which we can calculate the radius. Once we have both, we can use the formula for the curved surface area.
The formula for the circumference of a circle is \(C = 2\pi r\), where \(r\) is the radius. We can rearrange this to find \(r\).
\[ 77 = 2 \times \frac{22}{7} \times r \]\[ r = \frac{77 \times 7}{2 \times 22} \]\[ r = \frac{7 \times 7}{2 \times 2} \]\[ r = \frac{49}{4} \text{ cm} \]The formula for the curved surface area of a cylinder is \(\text{CSA} = 2\pi rh\).
\[ \text{CSA} = 2 \times \frac{22}{7} \times \frac{49}{4} \times 23 \]\[ \text{CSA} = \frac{2 \times 22 \times 49 \times 23}{7 \times 4} \]Simplify the expression:
\[ \text{CSA} = \frac{2 \times 22 \times (7 \times 7) \times 23}{7 \times 4} \]\[ \text{CSA} = \frac{2 \times 22 \times 7 \times 23}{4} \]\[ \text{CSA} = \frac{11 \times 7 \times 23}{1} \]\[ \text{CSA} = 77 \times 23 \]\[ \text{CSA} = 1771 \text{ cm}^2 \]B) The calculated curved surface area is \(1771 \text{ cm}^2\).
This problem involves analyzing statements and conclusions based on the principles of Syllogism. We will use Venn diagrams to represent the relationships given in the statements and then check which conclusions logically follow from these diagrams.
B) Only conclusion II follows.
The question asks to identify the type of electrical circuit commonly used for festival lights in buildings. We need to understand the characteristics of series and parallel circuits and how they apply to such decorative lighting.
Correct Option: A) a series circuit
Festival lights are commonly wired in a series circuit. In a series circuit, all components are connected along a single path, so the same current flows through each component. If one bulb in a series circuit burns out or breaks, the circuit becomes open, and current stops flowing to all the other bulbs, causing them all to go out. This is a common characteristic observed in traditional festival light strings.
This problem involves setting up a system of two linear equations based on the given profit/loss scenarios for two articles, X and Y. We will define variables for the cost prices of X and Y, formulate the equations, and then solve them simultaneously to find the individual cost prices. Finally, we will sum them up to get the total cost price.
Define variables:
Let \(C_X\) be the cost price of article X.
Let \(C_Y\) be the cost price of article Y.
Formulate the first equation:
In the first scenario, article X is sold at a loss of 10%, and article Y at a gain of 15%. The man gains ₹7.
Loss on X: \(10\%\) of \(C_X = 0.10 C_X\)
Gain on Y: \(15\%\) of \(C_Y = 0.15 C_Y\)
The net gain is the gain on Y minus the loss on X:
\[ 0.15 C_Y - 0.10 C_X = 7 \quad \text{(Equation 1)} \]Formulate the second equation:
In the second scenario, article X is sold at a gain of 12%, and article Y at a gain of 5%. The man gains ₹10.
Gain on X: \(12\%\) of \(C_X = 0.12 C_X\)
Gain on Y: \(5\%\) of \(C_Y = 0.05 C_Y\)
The net gain is the sum of gains on X and Y:
\[ 0.12 C_X + 0.05 C_Y = 10 \quad \text{(Equation 2)} \]Solve the system of equations:
We have two equations:
Equation 1: \( -0.10 C_X + 0.15 C_Y = 7 \)
Equation 2: \( 0.12 C_X + 0.05 C_Y = 10 \)
To eliminate \(C_Y\), multiply Equation 2 by 3:
Equation 1: \( -0.10 C_X + 0.15 C_Y = 7 \)
Equation 2 \(\times 3\): \( 0.36 C_X + 0.15 C_Y = 30 \)
Subtract Equation 1 from (Equation 2 \(\times 3\)):
\[ (0.36 C_X + 0.15 C_Y) - (-0.10 C_X + 0.15 C_Y) = 30 - 7 \]\[ 0.36 C_X + 0.10 C_X = 23 \]\[ 0.46 C_X = 23 \]\[ C_X = \frac{23}{0.46} = \frac{2300}{46} = 50 \]Find \(C_Y\):
Substitute \(C_X = 50\) into Equation 2:
Calculate the total original cost price:
Total cost price \( = C_X + C_Y = 50 + 80 = 130 \)
D) The total original cost price of X and Y is ₹130.
The question asks to identify the term for the ratio of the total increment in equilibrium output to the initial increment in autonomous expenditure. This concept is fundamental to Keynesian macroeconomic theory, explaining how an initial change in spending can lead to a larger change in national income.
Correct Option: C) The investment multiplier is defined as the ratio of the total increment in equilibrium value of final goods output (national income) to the initial increment in autonomous investment (a form of autonomous expenditure). It is a core concept in Keynesian economics, illustrating how a change in investment leads to a magnified change in national income. The formula is typically given by \( \frac{1}{1 - \text{MPC}} \) or \( \frac{1}{\text{MPS}} \), where MPC is the marginal propensity to consume and MPS is the marginal propensity to save.
The question asks for the primary reason why the River Ganga is considered endangered. We need to evaluate each option in the context of environmental threats to a major river system like the Ganga.
Correct Option: B) Aquatic life is diminishing. This is the most direct and comprehensive indicator of a river being ecologically endangered, as it signifies a severe breakdown in the river's ecosystem due to various pressures like pollution, habitat loss, and altered flow.
If in a parallelogram ABCD, E and F are points on the diagonal AC such that \(\overline{AE}\) = \(\overline{FC}\), then quadrilateral BEDF is a:
trapezium, but not a parallelogram
rectangle
square
parallelogram
To determine the type of quadrilateral BEDF, we will use the properties of parallelograms. Specifically, we will show that its diagonals bisect each other, which is a defining property of a parallelogram.
Given Information: We have a parallelogram ABCD. E and F are points on the diagonal AC such that \(\overline{AE} = \overline{FC}\).
Properties of Parallelogram ABCD: In a parallelogram, diagonals bisect each other. Let O be the point of intersection of the diagonals AC and BD. Therefore, \(\overline{AO} = \overline{OC}\) and \(\overline{BO} = \overline{OD}\).
Analyze Diagonal AC: We are given that \(\overline{AE} = \overline{FC}\). We also know that \(\overline{AO} = \overline{OC}\).
Consider Point E: Since \(\overline{AO} = \overline{OC}\), we can write \(\overline{AO} = \overline{AE} + \overline{EO}\) and \(\overline{OC} = \overline{OF} + \overline{FC}\).
Relate Segments on AC: We have \(\overline{AO} = \overline{OC}\). Subtract \(\overline{AE}\) from \(\overline{AO}\) and \(\overline{FC}\) from \(\overline{OC}\).
Since \(\overline{AE} = \overline{FC}\), we can write:
\[ \overline{AO} - \overline{AE} = \overline{OC} - \overline{FC} \]
This simplifies to:
\[ \overline{EO} = \overline{OF} \]
Conclusion for Quadrilateral BEDF: We have established that the diagonals of quadrilateral BEDF are BD and EF. We know from step 2 that \(\overline{BO} = \overline{OD}\) (O is the midpoint of BD). From step 5, we found that \(\overline{EO} = \overline{OF}\) (O is the midpoint of EF). Since the diagonals BD and EF bisect each other at point O, the quadrilateral BEDF must be a parallelogram.
D) parallelogram — As shown in the step-by-step explanation, the diagonals BD and EF of quadrilateral BEDF bisect each other at point O. This is a fundamental property of a parallelogram.
The question asks to identify which of the given elements is a metal. This requires knowledge of the classification of elements in the periodic table into metals, non-metals, and metalloids.
Based on this classification, Iron (Fe) is the only metal among the given options.
Correct Option: D) Fe — Iron (Fe) is a transition metal, characterized by its metallic properties like high electrical and thermal conductivity, malleability, ductility, and luster.
Read the given statement(s) and conclusions carefully and decide which of the conclusions logically follow(s) on basis of the statement(s).
Statements: B < D, C = E, F > D, E < G, K = G, C < F
Conclusions:
1. G > C
2. G < C
Only conclusion 1 follows.
Both conclusions 1 and 2 follow.
Neither conclusion 1 nor 2 follows.
Only conclusion 2 follows.
To solve this problem, we need to combine the given inequalities and equalities to establish a relationship between G and C. We will create a chain of relationships from C to G and then evaluate each conclusion.
We are looking for a connection between C and G. Let's start from C and use the given statements to link it to G.
Combining these two, if \(C = E\) and \(E < G\), then it logically follows that \(C < G\).
As derived in the previous step, \(C < G\). This is equivalent to \(G > C\).
Therefore, Conclusion 1 logically follows from the statements.
From our derivation, we found that \(C < G\), which means \(G\) is greater than \(C\). Therefore, \(G < C\) is false.
Thus, Conclusion 2 does not follow.
A) Only conclusion 1 follows.