Which of the following languages has NOT been mentioned in the 8th Schedule of the Indian Constitution?
The question asks to identify which of the given languages is NOT included in the Eighth Schedule of the Indian Constitution. This requires knowledge of the languages listed in the Eighth Schedule.
Correct Option: B) Awadhi is a dialect of Hindi and is not independently listed as one of the 22 scheduled languages in the Eighth Schedule of the Indian Constitution.
The question asks to identify the Chairman of the Rajya Sabha as of a specific date (August 12, 2022). This requires knowledge of the constitutional position of the Chairman of the Rajya Sabha and the individuals holding that office around the specified time.
Correct Option: B) Shri Jagdeep Dhankhar was elected as the 14th Vice-President of India and assumed office on August 11, 2022. As the Vice-President is the ex-officio Chairman of the Rajya Sabha, he held this position as of August 12, 2022.
The question asks to identify the first Indian state to adopt the Panchayati Raj system in 1959. This is a factual question related to the history of local self-governance in India. Recalling the key historical events and states involved in the implementation of Panchayati Raj is crucial.
B) Rajasthan was the first state in India to adopt the Panchayati Raj system on October 2, 1959, in Nagaur district.
This question tests fundamental geometric definitions related to triangles. We need to identify the specific point of concurrency formed by the medians of a triangle.
D) Centroid is the correct answer because it is defined as the point of intersection of the medians of a triangle. It is also the center of mass of the triangle.
The question asks us to determine if materials A and B follow Ohm's law based on their V-I graphs. Ohm's law states that for a conductor, the current flowing through it is directly proportional to the voltage across its ends, provided the temperature and other physical conditions remain unchanged. Graphically, this means the V-I characteristic (or I-V characteristic) should be a straight line passing through the origin.
Correct Option: C) Both A and B follow Ohm's law.
The problem asks us to find the rate of simple interest given the principal amount, the interest paid, and the time period. We can use the standard formula for simple interest to solve this.
The formula for simple interest is:
\[ \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \]where:
We need to find R. So, we can rearrange the formula to solve for R:
\[ \text{R} = \frac{\text{SI} \times 100}{\text{P} \times \text{T}} \]Now, substitute the given values:
\[ \text{R} = \frac{2000 \times 100}{10000 \times 2} \]Perform the multiplication in the numerator and denominator:
\[ \text{R} = \frac{200000}{20000} \]Now, divide to find R:
\[ \text{R} = 10 \]So, the rate of interest is 10% per annum.
D) 10%
The problem requires us to modify a given number based on specific rules for its odd and even digits, and then find the sum of two specific digits from the modified number. We will first apply the given rules to each digit of the original number to form a new number. Then, we will identify the second digit from the left and the third digit from the right in the new number and calculate their sum.
A) 15 — As calculated in the step-by-step explanation, the sum of the second digit from the left (7) and the third digit from the right (8) in the modified number is \(7 + 8 = 15\).
When partners invest in a business, their share of the profit is proportional to their respective investments. First, we need to find the ratio of their investments. Then, we can distribute the total annual profit according to this ratio to find each partner's share.
Determine the investments:
Find the ratio of their investments:
The ratio of investments (Lakshman : Bharath) is:
\[ 48,000 : 72,000 \]To simplify the ratio, divide both numbers by their greatest common divisor. We can start by dividing by 1000, then by 24:
\[ 48 : 72 \]Dividing by 24:
\[ \frac{48}{24} : \frac{72}{24} \] \[ 2 : 3 \]So, the ratio of Lakshman's investment to Bharath's investment is \( 2:3 \).
Calculate the sum of the ratio parts:
Sum of ratio parts \( = 2 + 3 = 5 \)
Determine Bharath's share of the profit:
The total annual profit is \( \text{₹}6,530 \).
Bharath's share will be his ratio part divided by the sum of the ratio parts, multiplied by the total profit:
\[ \text{Bharath's share} = \frac{\text{Bharath's ratio part}}{\text{Sum of ratio parts}} \times \text{Total Profit} \] \[ \text{Bharath's share} = \frac{3}{5} \times 6,530 \] \[ \text{Bharath's share} = 3 \times \frac{6,530}{5} \] \[ \text{Bharath's share} = 3 \times 1,306 \] \[ \text{Bharath's share} = 3,918 \]Therefore, Bharath's share out of the annual profit is ₹3,918.
Correct Option: B) ₹3,918
The problem asks us to identify a set of three numbers that follow the same mathematical relationship as the given sets: (12, 112, 9) and (6, 28, 4). We need to find a pattern involving the first, second, and third numbers in these sets.
Let the numbers be \(A=12\), \(B=112\), and \(C=9\).
We need to find a relationship between \(A\), \(B\), and \(C\). Let's try operations involving multiplication, addition, and subtraction.
Consider the product of the first and third numbers: \(A \times C = 12 \times 9 = 108\).
The middle number is \(B = 112\). We can see that \(B = A \times C + 4\).
So, \(112 = 108 + 4\). This relationship seems plausible.
Let the numbers be \(A=6\), \(B=28\), and \(C=4\).
Using the same relationship: \(B = A \times C + 4\).
Calculate \(A \times C = 6 \times 4 = 24\).
Now, add 4: \(24 + 4 = 28\).
This matches the middle number \(B=28\). So, the established rule is: The middle number is equal to the product of the first and third numbers plus 4.
B) (18, 94, 5)
To determine the correct option, we need to recall the structure and functional group of propanone. This involves understanding organic nomenclature and common functional groups.
Therefore, propanone has 3 carbons and a ketone functional group.
D) 3, ketone — Propanone (also known as acetone) has the chemical formula \(CH_3COCH_3\). It contains three carbon atoms and the \(C=O\) group is a ketone functional group.