Which of the following Constitution Amendments empowers Parliament to establish a common High Court for two or more than two States?
9th Constitutional Amendment Act
7th Constitutional Amendment Act
6th Constitutional Amendment Act
8th Constitutional Amendment Act
The question asks to identify the Constitutional Amendment Act that empowers Parliament to establish a common High Court for two or more states. We need to recall the major amendments related to the judiciary and state reorganization.
B) 7th Constitutional Amendment Act. This amendment, passed in 1956, made it possible for the Parliament to establish a common High Court for two or more states or for two or more states and a Union Territory. This was a crucial change in the judicial structure following the States Reorganisation Act, 1956.
This question asks about the fundamental energy conversion that occurs in an electric motor. Understanding the basic principle of how an electric motor operates will lead to the correct answer.
Correct Option: D) mechanical energy
The problem involves setting up algebraic equations based on the given ratios and conditions. We will represent the two numbers using a common multiple, form an equation from the new ratio, solve for the multiple, and then find the sum of the original numbers.
Represent the original numbers:
Let the two numbers be \(7x\) and \(5x\), since their ratio is \(7:5\).
Apply the given changes:
The first number is increased by 14, so it becomes \(7x + 14\).
The second number is decreased by 5, so it becomes \(5x - 5\).
Formulate the new ratio:
After the changes, the ratio becomes \(4:2\), which simplifies to \(2:1\). So, we can write the equation:
Solve the equation for \(x\):
Cross-multiply:
Isolate \(x\):
Subtract \(7x\) from both sides:
Add 10 to both sides:
\[ 14 + 10 = 3x \]\[ 24 = 3x \]Divide by 3:
\[ x = \frac{24}{3} \]\[ x = 8 \]Find the original numbers:
First number \(= 7x = 7 \times 8 = 56\)
Second number \(= 5x = 5 \times 8 = 40\)
Calculate the sum of the original numbers:
Sum \(= 56 + 40 = 96\)
A) 96 β The sum of the original numbers is 96, as calculated by solving the algebraic equation derived from the given ratios and conditions.
To solve this problem, we will first assume a base cost for the TV. Then, we will calculate the initial cost of the washing machine based on the given percentage. Next, we will determine the initial total cost of 5 washing machines and 7 TVs. After that, we will calculate the new costs of the washing machine and TV after their respective percentage changes. Finally, we will find the new total cost and compare it with the initial total cost to determine the percentage change.
Correct Option: C) Increase by 5.2%
\(\frac{a^{10}\times b^3\times c^9}{a^9\times b^6\times c^9}\) in simplified form is:
(aβ»¹) × (bβ»³) × (cβ»¹β°)
(a¹) × (bβ»³) × (cβ°)
(a¹) × (bβ»βΉ) × (cβ»β·)
(aβ»¹) × (bβ»βΉ) × (cβ»βΈ)
To simplify the given algebraic expression, we will use the laws of exponents, specifically the rule for division of powers with the same base: \( \frac{x^m}{x^n} = x^{m-n} \). We will apply this rule to each variable (a, b, and c) separately.
The given expression is:
\[ \frac{a^{10} \times b^3 \times c^9}{a^9 \times b^6 \times c^9} \]We can rewrite the expression as a product of terms for each base:
\[ \left( \frac{a^{10}}{a^9} \right) \times \left( \frac{b^3}{b^6} \right) \times \left( \frac{c^9}{c^9} \right) \]Multiply the simplified terms together:
\[ a^1 \times b^{-3} \times c^0 \]This can also be written as \( (a^1) \times (b^{-3}) \times (c^0) \).
Correct Option: B) \( (a^1) \times (b^{-3}) \times (c^0) \)
The question asks why a garden is considered an ecosystem. To answer this, we need to understand the definition of an ecosystem and identify which option best aligns with that definition.
A) the living organisms in it interact with each other and are affected by abiotic components
This option perfectly describes an ecosystem. It highlights the interaction among living organisms (biotic components) and their dependence on and influence by non-living environmental factors (abiotic components). A garden, with its plants, animals, and microorganisms interacting with each other and with elements like soil, water, and sunlight, fits this definition.
A man sold an article for βΉ390 by first giving a d% discount on its marked price, and then another discount having the same nominal value (in βΉ). If the marked price of the article is βΉ3,900, then what is the value of d?
The problem involves calculating a discount percentage given the marked price, selling price, and a two-stage discount process. The first discount is a percentage 'd' of the marked price, and the second discount has the same nominal value (in rupees) as the first discount. We need to find the value of 'd'.
Identify the given values:
Calculate the first discount amount:
Let the first discount be \(D_1\). Since it is d% of the Marked Price:
\[ D_1 = \frac{d}{100} \times \text{MP} = \frac{d}{100} \times 3900 = 39d \]Determine the price after the first discount:
Price after first discount (\(P_1\)) = MP - \(D_1\)
\[ P_1 = 3900 - 39d \]Calculate the second discount amount:
The problem states that the second discount (\(D_2\)) has the same nominal value as the first discount.
\[ D_2 = D_1 = 39d \]Formulate the equation for the Selling Price:
The Selling Price (SP) is the price after the first discount minus the second discount.
\[ \text{SP} = P_1 - D_2 \]\[ 390 = (3900 - 39d) - 39d \]Solve the equation for 'd':
\[ 390 = 3900 - 78d \]\[ 78d = 3900 - 390 \]\[ 78d = 3510 \]\[ d = \frac{3510}{78} \]\[ d = 45 \]A) The value of d is 45.
If 214 apples were distributed among Ajay, Amit, and Amar in the ratio \( \frac{1}{5} \) : \( \frac{1}{7} \) : \( \frac{1}{6} \), how many apples did Amar get?
To find the number of apples Amar received, we first need to convert the given fractional ratio into a simple whole number ratio. Then, we can find the total number of ratio parts and distribute the total apples accordingly.
Convert the fractional ratio to a whole number ratio:
The given ratio for Ajay, Amit, and Amar is \[\frac{1}{5} : \frac{1}{7} : \frac{1}{6}\].
To convert this to a whole number ratio, find the Least Common Multiple (LCM) of the denominators (5, 7, 6).
LCM \( = 5 \times 7 \times 2 \times 3 = 210 \).
Multiply each fraction in the ratio by the LCM:
\[ \text{Ajay} : \text{Amit} : \text{Amar} = \left( \frac{1}{5} \times 210 \right) : \left( \frac{1}{7} \times 210 \right) : \left( \frac{1}{6} \times 210 \right) \]\[ \text{Ajay} : \text{Amit} : \text{Amar} = 42 : 30 : 35 \]Calculate the total number of ratio parts:
Total parts \( = 42 + 30 + 35 = 107 \).
Determine the number of apples Amar received:
Amar's share is 35 parts out of the total 107 parts.
Total apples \( = 214 \).
Number of apples Amar received \[= \frac{\text{Amar's ratio part}}{\text{Total ratio parts}} \times \text{Total apples}\]
\[ \text{Amar's apples} = \frac{35}{107} \times 214 \]\[ \text{Amar's apples} = 35 \times 2 \]\[ \text{Amar's apples} = 70 \]B) 70 is the correct number of apples Amar received.
Match the Following:
| Column A | Column B |
| 1. Marginal Efficiency of Capital | A. Spending on consumer goods |
| 2. Autonomous Investment | B. Tendency for employment to fluctuate |
| 3. Consumption Function | C. Expected rate of return on investment |
| 4. Paradox of Thrift | D. Investment independent of income |
| 5. Cyclical Unemployment | E. Increased saving reduces total demand |
1-C, 2-D, 3-A, 4-E, 5-B
1-E, 2-D, 3-A, 4-C, 5-B
1-B, 2-D, 3-A, 4-E, 5-C
1-A, 2-D, 3-C, 4-E, 5-B
This question requires matching economic concepts from Column A with their correct definitions or descriptions in Column B. We need to recall the standard definitions of each term.
A) 1-C, 2-D, 3-A, 4-E, 5-B. This option correctly matches all the economic terms with their respective definitions as derived above.
The question asks about the primary function of 'viharas' in Buddhist architecture. To answer this, one needs to recall the different types of Buddhist architectural structures and their specific purposes.
Correct Option: B) To serve as residential places for Buddhist priests
Viharas were monasteries in Buddhist architecture. They were built to provide living quarters for Buddhist monks (bhikkhus) and nuns (bhikkhunis) during their monastic life. These structures typically included cells for individual monks, a common hall, and sometimes a shrine or a stupa within the complex.