The 74th Constitutional Amendment Act provides for _______ for a transitional area between a rural and urban area.
Nagar Panchayat
Municipal Council
Gram Panchayat
Municipal Corporation
The question asks about the specific type of urban local body established by the 74th Constitutional Amendment Act for a transitional area. Understanding the structure of urban local self-government as defined by this amendment is key.
A) Nagar Panchayat is the correct answer. The 74th Constitutional Amendment Act explicitly provides for the constitution of a Nagar Panchayat for a transitional area, which is an area in the process of changing from rural to urban.
To determine the nature and relative size of the image formed by a convex lens, we need to use the lens formula and magnification formula. We are given the object distance and focal length. The sign conventions for spherical lenses are crucial for correct calculations.
Identify the given values and sign conventions:
Apply the lens formula to find the image distance (\(v\)):
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]Substitute the values into the lens formula:
\[ \frac{1}{v} = \frac{1}{20} + \frac{1}{-40} \]\[ \frac{1}{v} = \frac{1}{20} - \frac{1}{40} \]\[ \frac{1}{v} = \frac{2 - 1}{40} \]\[ \frac{1}{v} = \frac{1}{40} \]\[ v = +40 \text{ cm} \]Interpret the image distance (\(v\)):
Since \(v\) is positive, the image is formed on the right side of the lens, which means it is a real image. Real images are always inverted.
Calculate the magnification (\(m\)) to determine the relative size:
The magnification formula for a lens is:
\[ m = \frac{h_i}{h_o} = \frac{v}{u} \]Substitute the values of \(v\) and \(u\) into the magnification formula:
\[ m = \frac{+40 \text{ cm}}{-40 \text{ cm}} \]\[ m = -1 \]Interpret the magnification (\(m\)):
Combine the findings:
The image is real, inverted, and same sized.
D) Real, inverted and same sized. This matches our calculations: \(v = +40 \text{ cm}\) (real, inverted) and \(m = -1\) (same sized).
This question tests knowledge of the thermal decomposition of baking soda (sodium bicarbonate). When heated, baking soda undergoes a chemical reaction, breaking down into simpler substances. Understanding this reaction is key to identifying the correct product.
Correct Option: D) Sodium carbonate
The question describes an element X that forms a compound XCl and is located on the left side of the periodic table. We need to determine the properties of element X based on this information. The formation of XCl suggests that X has a valency of +1, meaning it loses one electron. Elements on the left side of the periodic table are typically metals.
C) Only (i) and (ii) are correct because an element X forming XCl implies X has a valency of +1, meaning it has one valence electron. Being on the left side of the periodic table and having one valence electron strongly indicates it is an alkali metal, which is a metal and solid at room temperature.
This is a syllogism problem. We need to draw Venn diagrams or use logical deduction to determine which conclusions logically follow from the given statements. We must assume the statements are true, even if they contradict common knowledge.
B) Only conclusion II follows
If \(\frac{15x-9}{x}+\frac{15y-9}{y}+\frac{15z-9}{z}\) = 0, then the value of \( \frac{1}{x} \) + \( \frac{1}{y} \) + \( \frac{1}{z} \) is:
The problem provides an equation involving three terms, each of which can be simplified by dividing the numerator by the denominator. By simplifying each term and then combining like terms, we can solve for the required expression \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\].
Given the equation:
\[ \frac{15x-9}{x} + \frac{15y-9}{y} + \frac{15z-9}{z} = 0 \]Simplify each term by dividing the numerator by the denominator:
Substitute these simplified terms back into the original equation:
\[ \left(15 - \frac{9}{x}\right) + \left(15 - \frac{9}{y}\right) + \left(15 - \frac{9}{z}\right) = 0 \]Combine the constant terms and the terms with \[\frac{1}{x}, \frac{1}{y}, \frac{1}{z}\]:
\[ (15 + 15 + 15) - \left(\frac{9}{x} + \frac{9}{y} + \frac{9}{z}\right) = 0 \]\[ 45 - 9\left(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\right) = 0 \]Rearrange the equation to solve for \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\]:
\[ 45 = 9\left(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\right) \]\[ \frac{45}{9} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \]\[ 5 = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \]Thus, the value of \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\] is 5.
Correct Option: B) 5
The question asks to identify the part of the northern plains of India that consists of older alluvium. This requires knowledge of the different regional divisions of the northern plains based on their geomorphological characteristics and the age of their alluvial deposits.
A) Bhangar is the correct answer because it refers to the older alluvial plains, which are found above the flood level of rivers and are characterized by calcareous deposits known as 'kankar'.
The question asks to identify the instrument used for detecting heartbeats. We need to recall the primary function of each medical instrument listed in the options.
Based on these analyses, the stethoscope is the correct instrument for detecting heartbeats.
Correct Option: A) Stethoscope is an instrument used by medical professionals to listen to the internal sounds of the body, most commonly the heart and lungs, thereby aiding in the detection of the heartbeat.
The value of \(\sqrt{74529}\) is:
To find the square root of \(74529\), we can use the long division method or estimation by looking at the last digit and the range of squares. The long division method is precise, while estimation helps in quickly eliminating options.
C) \(273\) is the correct answer because \(273^2 = 74529\).