The question asks to identify the article of the Indian Constitution that directs the state to establish a living wage for workers. This falls under the Directive Principles of State Policy (DPSP), which are guidelines for the state to promote social and economic democracy.
B) Article 43 of the Indian Constitution states: "The State shall endeavour to secure, by suitable legislation or economic organisation or in any other way, to all workers, agricultural, industrial or otherwise, work, a living wage, conditions of work ensuring a decent standard of life and full enjoyment of leisure and social and cultural opportunities and, in particular, the State shall endeavour to promote cottage industries on an individual or co-operative basis in rural areas." This directly addresses the establishment of a living wage for workers.
The question asks for the year in which the Battle of Buxar was fought. This is a direct factual question from Indian history, specifically related to the period of British expansion in India. Recalling the key dates of major battles is essential for competitive exams.
Correct Option: B) 1764 AD
The question asks about the meaning of "issue price" in the context of the Public Distribution System (PDS). The PDS is a government-sponsored system designed to provide essential food grains and other commodities to vulnerable sections of society at subsidized rates. Understanding the objective of PDS is key to answering this question.
A) Price lower than the market price — This is correct. The very purpose of the Public Distribution System is to provide essential commodities at subsidized rates to the economically weaker sections of society. This subsidy means the issue price is significantly lower than the prevailing market price, making these goods affordable and accessible.
To find the time it takes for a sum of money to double at a given simple interest rate, we use the simple interest formula. If the sum doubles, it means the simple interest earned is equal to the principal amount. We will set up the equation and solve for time, then convert the fractional part of a year into months.
D) 5 years \( 6\frac{2}{3} \) months — This matches our calculated value of 5 years and \(6\frac{2}{3}\) months.
The problem asks us to find the value of 'x' given a percentage relationship. We need to translate the given statement "x% of 160 = 8" into a mathematical equation and then solve for x.
Understand the percentage: 'x%' means \(\frac{x}{100}\).
Translate "of" to multiplication: In mathematical terms, "x% of 160" means \(\frac{x}{100} \times 160\).
Formulate the equation: The given statement "x% of 160 = 8" can be written as:
\[ \frac{x}{100} \times 160 = 8 \]Simplify the equation:
\[ \frac{160x}{100} = 8 \]We can simplify the fraction \(\frac{160}{100}\) by dividing both numerator and denominator by 20:
\[ \frac{8x}{5} = 8 \]Solve for x: To isolate x, multiply both sides by 5 and then divide by 8 (or simply divide both sides by 8, then multiply by 5).
Multiply both sides by 5:
\[ 8x = 8 \times 5 \] \[ 8x = 40 \]Divide both sides by 8:
\[ x = \frac{40}{8} \] \[ x = 5 \]Thus, the value of x is 5.
Correct Option: B) 5
We are given the initial ratio of two numbers and their ratio after each number is increased by a certain value. We can represent the numbers using a variable and set up an equation based on the given ratios to find the value of the variable, and subsequently, the numbers.
Represent the initial numbers: Let the two numbers be \(2x\) and \(3x\), since their ratio is \(2:3\).
Apply the increase: Each number is increased by 20. So, the new numbers will be \(2x + 20\) and \(3x + 20\).
Formulate the equation based on the new ratio: The ratio of the new numbers is given as \(3:4\). Therefore, we can write the equation:
\[ \frac{2x + 20}{3x + 20} = \frac{3}{4} \]Solve the equation for \(x\): Cross-multiply to solve for \(x\):
\[ 4(2x + 20) = 3(3x + 20) \] \[ 8x + 80 = 9x + 60 \]Subtract \(8x\) from both sides:
\[ 80 = 9x - 8x + 60 \] \[ 80 = x + 60 \]Subtract \(60\) from both sides:
\[ x = 80 - 60 \] \[ x = 20 \]Find the original numbers: Substitute the value of \(x\) back into our initial representations of the numbers:
First number \( = 2x = 2 \times 20 = 40 \)
Second number \( = 3x = 3 \times 20 = 60 \)
So, the numbers are 40 and 60.
Verify the solution: Initial ratio: \(40:60 = 2:3\) (Correct) Numbers after increasing by 20: \(40+20 = 60\) and \(60+20 = 80\) New ratio: \(60:80 = 3:4\) (Correct)
Correct Option: A) 40, 60
The question asks to identify which type of UV rays are primarily responsible for skin cancer, specifically in the context of Australia's high incidence rates. This requires knowledge of the different types of UV radiation and their biological effects.
B) UV-B rays are the main cause of sunburn and directly damage DNA in skin cells, leading to the development of skin cancer. This makes them the primary culprits for the high incidence of skin cancer in regions like Australia.
The question asks to identify the odd one out from a given set of four words. This is a classification type of question where we need to find a common characteristic among three words and identify the one that does not share that characteristic.
Correct Option: B) Speed is the odd one out because it is a physical quantity (a state or measurement) while Clutch, Brake, and Accelerator are control mechanisms or components used to operate a vehicle.
The question asks to identify the equipment that converts mechanical energy into electrical energy. We need to analyze the function of each given option.
Based on this analysis, the dynamo is the correct equipment for the specified energy transformation.
Correct Option: C) Dynamo — A dynamo (or electrical generator) converts mechanical energy into electrical energy based on Faraday's law of electromagnetic induction. When a coil is rotated in a magnetic field, an electromotive force (EMF) is induced, leading to the generation of electrical current.
The problem involves finding the perimeter of a rectangle given its area is equal to the area of a square, and the ratio of its length and width. We will first calculate the area of the square, then use this to find the dimensions of the rectangle, and finally calculate the perimeter of the rectangle.
Correct Option: B) 40 cm