The question asks for the standard keyboard shortcut used to paste content that has been previously copied or cut. This is a fundamental computer operation frequently tested in competitive exams to assess basic computer literacy.
B) Ctrl + V — This is the universally recognized keyboard shortcut for the "Paste" command in most operating systems and applications (e.g., word processors, web browsers, file explorers). After content has been copied (Ctrl + C) or cut (Ctrl + X), pressing Ctrl + V will insert that content at the current cursor position or selected location.
A hollow spherical shell is made of a metal of density 28 g/cm³. Its internal and external radii are 2 cm and 5 cm, respectively. What is the approximate weight (in kg) of the shell? (Take π = \( \frac{22}{7} \), \(\text{Density}=\frac{\text{Mass}}{\text{Volume}}\))
To find the weight of the hollow spherical shell, we first need to calculate its volume. Since it's a hollow sphere, the volume of the metal will be the difference between the volume of the external sphere and the internal sphere. Once the volume is found, we can use the given density to calculate the mass, and then convert the mass to kilograms to get the weight (assuming weight is asked in terms of mass in kg, which is common in such problems).
The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^3\).
\[ V_{\text{external}} = \frac{4}{3} \times \frac{22}{7} \times (5 \text{ cm})^3 \]\[ V_{\text{external}} = \frac{4}{3} \times \frac{22}{7} \times 125 \text{ cm}^3 \]\[ V_{\text{external}} = \frac{11000}{21} \text{ cm}^3 \]\[ V_{\text{external}} \approx 523.81 \text{ cm}^3 \]The volume of the metal is the difference between the external and internal volumes.
\[ V_{\text{shell}} = V_{\text{external}} - V_{\text{internal}} \]\[ V_{\text{shell}} = \frac{11000}{21} \text{ cm}^3 - \frac{704}{21} \text{ cm}^3 \]\[ V_{\text{shell}} = \frac{11000 - 704}{21} \text{ cm}^3 \]\[ V_{\text{shell}} = \frac{10296}{21} \text{ cm}^3 \]\[ V_{\text{shell}} = 490.2857 \text{ cm}^3 \]Given \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\), so \(\text{Mass} = \text{Density} \times \text{Volume}\).
\[ \text{Mass} = 28 \text{ g/cm}^3 \times 490.2857 \text{ cm}^3 \]\[ \text{Mass} = 13728 \text{ g} \]Since \(1 \text{ kg} = 1000 \text{ g}\).
\[ \text{Mass (kg)} = \frac{13728 \text{ g}}{1000 \text{ g/kg}} \]\[ \text{Mass (kg)} = 13.728 \text{ kg} \]A) 13.728 kg is the calculated mass of the shell, which represents its weight in kilograms.
The question asks about the first instance where Mahatma Gandhi used a hunger strike as a weapon. To answer this, we need to recall the various struggles led by Gandhi in India and identify which one marked the first use of a hunger strike.
B) Ahmedabad Mill Workers' Struggle — Mahatma Gandhi undertook his first hunger strike in India during the Ahmedabad Mill Workers' Struggle in March 1918. He did this to support the textile mill workers who were demanding a wage increase and to strengthen their resolve against the mill owners.
To find the value of \( \alpha^4 + \beta^4 \) where \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 - x - 6 = 0 \), we will first find the sum and product of the roots using Vieta's formulas. Then, we will use algebraic identities to express \( \alpha^4 + \beta^4 \) in terms of \( \alpha + \beta \) and \( \alpha \beta \).
Identify coefficients and apply Vieta's formulas:
The given quadratic equation is \( x^2 - x - 6 = 0 \). Comparing this with the standard form \( ax^2 + bx + c = 0 \), we have \( a = 1 \), \( b = -1 \), and \( c = -6 \).
According to Vieta's formulas:
Calculate \( \alpha^2 + \beta^2 \):
We know the identity \( (\alpha + \beta)^2 = \alpha^2 + \beta^2 + 2\alpha\beta \). Rearranging this, we get:
\[ \alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta \]\[ \alpha^2 + \beta^2 = (1)^2 - 2(-6) \]\[ \alpha^2 + \beta^2 = 1 + 12 \]\[ \alpha^2 + \beta^2 = 13 \]Calculate \( \alpha^4 + \beta^4 \):
We can express \( \alpha^4 + \beta^4 \) in terms of \( \alpha^2 + \beta^2 \) and \( \alpha^2\beta^2 \):
\[ \alpha^4 + \beta^4 = (\alpha^2 + \beta^2)^2 - 2\alpha^2\beta^2 \]\[ \alpha^4 + \beta^4 = (\alpha^2 + \beta^2)^2 - 2(\alpha\beta)^2 \]Substitute the values:
Substitute the values we found for \( \alpha^2 + \beta^2 \) and \( \alpha\beta \):
\[ \alpha^4 + \beta^4 = (13)^2 - 2(-6)^2 \]\[ \alpha^4 + \beta^4 = 169 - 2(36) \]\[ \alpha^4 + \beta^4 = 169 - 72 \]\[ \alpha^4 + \beta^4 = 97 \]Thus, the value of \( \alpha^4 + \beta^4 \) is 97.
D) 97 is the correct answer, as calculated through the step-by-step process using Vieta's formulas and algebraic identities.
To find the mode of a set of observations, we need to identify the observation that appears most frequently in the given data set. We will count the occurrences of each unique number.
Correct Option: C) 24 is the mode because it appears 4 times, which is the highest frequency among all the observations.
The question asks for a key difference in accountability to the legislature between the Indian Prime Minister and the American President. This requires understanding the fundamental differences between parliamentary and presidential systems of government.
B) The American President and his cabinet are not members of Congress, whereas the Indian Prime Minister and his ministers must be part of Parliament. This statement accurately captures a fundamental difference between the presidential system (USA) and the parliamentary system (India). In a presidential system, there is a clear separation of powers, meaning the executive (President and cabinet) are distinct from the legislature (Congress). In a parliamentary system, the executive (Prime Minister and ministers) are drawn from and remain part of the legislature (Parliament), and are directly accountable to it.
The question asks to identify the financial institution established by the 74th Constitutional Amendment, 1992, specifically for reviewing the finances of Urban Local Government Bodies. This requires knowledge of the provisions of the 74th Amendment related to urban local self-governance.
Correct Option: C) State Finance Commission. The 74th Constitutional Amendment Act, 1992, through Article 243Y, mandated the establishment of a State Finance Commission to review the financial position of Urban Local Government Bodies (Municipalities) and make recommendations regarding their finances.
If 56% of a number is equal to \( \frac{5}{9} \) of another number, then what is the ratio of the first number to the second number?
The problem asks for the ratio of two numbers given a relationship between their percentages and fractions. We will represent the two numbers with variables, translate the given information into an algebraic equation, and then solve for the ratio of the first number to the second number.
Let the first number be \(A\) and the second number be \(B\).
Translate the given condition into an equation:
"56% of a number is equal to \( \frac{5}{9} \) of another number"
This can be written as:
\[ 56\% \text{ of } A = \frac{5}{9} \text{ of } B \]Convert the percentage to a fraction or decimal:
\[ \frac{56}{100} \times A = \frac{5}{9} \times B \]Simplify the fraction \( \frac{56}{100} \). Both 56 and 100 are divisible by 4:
\[ \frac{14}{25} \times A = \frac{5}{9} \times B \]We need to find the ratio of the first number to the second number, which is \( A : B \) or \( \frac{A}{B} \).
To find \( \frac{A}{B} \), rearrange the equation:
\[ \frac{A}{B} = \frac{\frac{5}{9}}{\frac{14}{25}} \]To divide by a fraction, multiply by its reciprocal:
\[ \frac{A}{B} = \frac{5}{9} \times \frac{25}{14} \]Perform the multiplication:
\[ \frac{A}{B} = \frac{5 \times 25}{9 \times 14} \]\[ \frac{A}{B} = \frac{125}{126} \]The ratio of the first number to the second number is \( 125 : 126 \).
D) 125 : 126 is the correct ratio derived from the calculations.
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This stands for Brackets/Parentheses, Orders/Exponents, Division/Multiplication (from left to right), and Addition/Subtraction (from left to right).
The expression inside the parentheses is \(5 + 2\).
\[ 5 + 2 = 7 \]Now the expression becomes:
\[ 81 - 4 \times 7 + 54 \]The multiplication operation is \(4 \times 7\).
\[ 4 \times 7 = 28 \]Now the expression becomes:
\[ 81 - 28 + 54 \]First, perform the subtraction:
\[ 81 - 28 = 53 \]Now, add \(54\) to the result:
\[ 53 + 54 = 107 \]C) 107 is the simplified value of the given expression.