The problem asks us to determine the sixth letter from the right in a modified word. The modification involves interchanging letters in pairs: the first and second, third and fourth, and so on. We need to apply this rule to the given word and then count from the right to find the required letter.
The sixth letter from the right in the new word is R.
B) R — As determined in the step-by-step analysis, the sixth letter from the right in the modified word is R.
To solve this problem, we need to compare the positions of the digits in the original number with their positions after arranging the digits in ascending order. We will list the original number and its digits, then sort the digits to form a new number, and finally compare the positions.
A) One — As determined in the step-by-step analysis, only one digit (the digit '2') retains its original position after the digits are arranged in ascending order.
The question asks to identify the term for the price point where the quantity consumers wish to purchase (demand) exactly matches the quantity producers are willing to supply. This is a fundamental concept in microeconomics related to market equilibrium.
Correct Option: B) Equilibrium price is the price where the quantity the consumer purchases is equal to the quantity the producers supply. This is the point where the demand curve and supply curve intersect.
If a square has a side of (5x − 8) cm, then the area of the square (in cm²) is:
To find the area of a square, we use the formula \( \text{Area} = (\text{side})^2 \). Given the side length of the square as an algebraic expression, we need to square this expression using the algebraic identity \((a-b)^2 = a^2 - 2ab + b^2\).
Correct Option: D) \(25x^2 - 80x + 64\)
The question asks about the number of Fundamental Duties in the Indian Constitution as of July 2022. This requires knowledge of the original inclusion of Fundamental Duties and subsequent amendments.
Correct Option: A) 11. There are currently 11 Fundamental Duties in the Indian Constitution.
The question asks which type of solution can scatter light. This phenomenon is known as the Tyndall effect. We need to identify the solution type where particles are large enough to scatter light but small enough not to settle.
B) Colloidal solution — Colloidal solutions contain particles (1-100 nm) that are large enough to scatter light but small enough to remain suspended, thus exhibiting the Tyndall effect. When a beam of light passes through a colloidal solution, its path becomes visible due to scattering.
The question asks about the specific compound used by Friedrich Wöhler in his groundbreaking synthesis of urea. This is a historical milestone in chemistry, marking the first time an organic compound was synthesized from inorganic precursors.
This experiment disproved the vital force theory and opened the door for the synthesis of many other organic compounds in the laboratory.
D) Ammonium cyanate was the compound that Friedrich Wöhler heated, which then rearranged to form urea. This experiment was crucial in disproving the vital force theory.
The question asks about the primary organisms used in vermicomposting. Vermicomposting is a process that uses certain types of worms to convert organic waste into a nutrient-rich material called vermicompost. Identifying the specific type of worm involved is key to answering this question.
A) Earthworms — Earthworms are the primary organisms used in vermicomposting. They break down organic waste into nutrient-rich compost.
Find the roots of the quadratic equation x2+x−2=0.
To find the roots of a quadratic equation of the form \(ax^2 + bx + c = 0\), we can use either factorization, completing the square, or the quadratic formula. In this case, factorization is a straightforward method.
Correct Option: C) \((1,-2)\) is the correct pair of roots for the given quadratic equation.
Convert \( \frac{23}{11} \) to its recurring decimal form.
2.\(\overline{32}\)
2.\(\overline{09}\)
2.\(\overline{23}\)
2.\(\overline{18}\)
To convert a fraction to its decimal form, we perform long division. If the division results in a repeating sequence of digits, it's a recurring decimal. We need to identify this repeating block of digits.
We need to divide 23 by 11.
First, divide 23 by 11:
\[ 23 \div 11 = 2 \text{ with a remainder of } 1 \]So, the integer part of the decimal is 2. We write this as 2.
Now, we continue with the remainder. Place a decimal point after 2 and add a zero to the remainder, making it 10. Divide 10 by 11:
\[ 10 \div 11 = 0 \text{ with a remainder of } 10 \]So, the first digit after the decimal point is 0. Our number is now 2.0
Add another zero to the remainder, making it 100. Divide 100 by 11:
\[ 100 \div 11 = 9 \text{ with a remainder of } 1 \]So, the second digit after the decimal point is 9. Our number is now 2.09
Add another zero to the remainder, making it 10. Divide 10 by 11:
\[ 10 \div 11 = 0 \text{ with a remainder of } 10 \]So, the third digit after the decimal point is 0. Our number is now 2.090
Add another zero to the remainder, making it 100. Divide 100 by 11:
\[ 100 \div 11 = 9 \text{ with a remainder of } 1 \]So, the fourth digit after the decimal point is 9. Our number is now 2.0909
We can see a pattern emerging. The sequence of digits '09' is repeating. Therefore, the recurring decimal form of \( \frac{23}{11} \) is 2.\( \overline{09} \).
B) 2.\( \overline{09} \) is the correct recurring decimal form obtained through long division.