The question asks to identify the state that was the highest producer of raw silk in India as of 2016. This requires knowledge of the agricultural and industrial statistics related to sericulture in India.
As per various reports and government data (such as from the Central Silk Board, Ministry of Textiles, Government of India), Karnataka has consistently been the largest producer of raw silk in India for many years, including and around 2016. It accounts for a significant share of the country's total raw silk production.
C) Karnataka — Karnataka has historically been and continues to be the largest producer of raw silk in India. As of 2016, it contributed over 50% of India's total raw silk production, making it the undisputed leader in sericulture.
Mohan invested Rs. 100,000 in a garment business. After a few months, Sohan joined him with Rs. 40,000. At the end of the year, the total profit was divided between them in ratio 3:1. After how many months did Sohan join the business?
This problem involves calculating the duration of investment for partners in a business and relating it to their profit-sharing ratio. The profit is typically divided in the ratio of the product of the capital invested and the time for which it was invested. We will set up an equation based on this principle and solve for the unknown duration.
Mohan invested at the beginning and stayed for the entire year. So, Mohan's investment duration (T1) = 12 months.
Let Sohan join after 'x' months. Then Sohan's investment duration (T2) = \((12 - x)\) months.
The profit share is proportional to (Capital \(\times\) Time). Therefore, the ratio of their profits is:
\[ \frac{\text{Mohan's Profit}}{\text{Sohan's Profit}} = \frac{\text{C1} \times \text{T1}}{\text{C2} \times \text{T2}} \]We are given the profit ratio is 3:1. So,
\[ \frac{3}{1} = \frac{100,000 \times 12}{40,000 \times (12 - x)} \]Cancel out common factors:
\[ 3 = \frac{100 \times 12}{40 \times (12 - x)} \]\[ 3 = \frac{10 \times 12}{4 \times (12 - x)} \]\[ 3 = \frac{5 \times 12}{2 \times (12 - x)} \]\[ 3 = \frac{60}{2 \times (12 - x)} \]\[ 3 = \frac{30}{(12 - x)} \]Now, cross-multiply:\[ 3 \times (12 - x) = 30 \]\[ 36 - 3x = 30 \]\[ 36 - 30 = 3x \]\[ 6 = 3x \]\[ x = \frac{6}{3} \]\[ x = 2 \]Sohan joined the business after 2 months.
Correct Option: B) Sohan joined after 2 months. This is derived by setting up the profit-sharing ratio based on capital and time, and solving for the unknown time duration.
If two complementary angles are in the ratio of 4:5, find the greater angle.
The problem involves finding the measures of two complementary angles given their ratio. Complementary angles are two angles whose sum is 90 degrees. We will use the given ratio to represent the angles and then form an equation to solve for their values.
Correct Option: B) The greater angle is \(50^\circ\).
If HEAR is written as KJHA, then MILK can be written as
This is a coding-decoding problem where a word is coded using a specific pattern. We need to identify the pattern by comparing the given word and its code, and then apply the same pattern to decode the new word.
The word is HEAR and its code is KJHA.
The pattern for the positional value of letters is \(+3, +5, +7, +9\).
P, N, S, T
So, MILK is coded as PNST.
Correct Option: C) PNST
The problem involves calculating the value of a new observation when the mean of a set of observations changes after adding that observation. We will use the formula for the mean, which is the sum of all observations divided by the number of observations.
So, for the initial set:
\[ 15 = \frac{\text{Sum}_{12}}{12} \]Multiplying both sides by 12, we get the sum of the first 12 observations:
\[ \text{Sum}_{12} = 15 \times 12 = 180 \]Multiplying both sides by 13, we get the sum of the 13 observations:
\[ \text{Sum}_{13} = 16 \times 13 = 208 \]Subtract 180 from both sides to find \(x\):
\[ x = 208 - 180 \]\[ x = 28 \]
Thus, the 13th observation is 28.
Correct Option: D) 28
Which tissue directly connects one bone to another bone in the human body?
By tendons
By ligaments
By muscles
By small bones
The question asks to identify the tissue responsible for connecting one bone to another bone in the human body. This is a fundamental concept in human anatomy and physiology, specifically related to the skeletal system and connective tissues.
Correct Option: B) By ligaments — Ligaments are bands of tough, fibrous connective tissue that connect bones to other bones, forming joints and providing stability.
To find the least number that leaves specific remainders when divided by different numbers, we first need to find the Least Common Multiple (LCM) of the divisors. Then, we observe the pattern of the differences between the divisors and their respective remainders. If this difference is constant, the required number can be found by subtracting this constant difference from the LCM.
Identify the divisors and remainders:
Calculate the difference between each divisor and its remainder:
Since the difference is constant (which is 2), the required number will be of the form \(\text{LCM}(\text{divisors}) - \text{constant difference}\).
Find the LCM of the divisors (12, 15, 18, 27):
To find the LCM, we take the highest power of each prime factor present in the factorizations:
\[ \text{LCM}(12, 15, 18, 27) = 2^2 \times 3^3 \times 5^1 \]\[ = 4 \times 27 \times 5 \]\[ = 108 \times 5 \]\[ = 540 \]Calculate the required least number:
The least number is \(\text{LCM} - \text{constant difference}\).
\[ \text{Least Number} = 540 - 2 \]\[ = 538 \]B) 538 — This is the least number that satisfies all the given conditions. When 538 is divided by 12, the remainder is 10 (\(538 = 12 \times 44 + 10\)). When divided by 15, the remainder is 13 (\(538 = 15 \times 35 + 13\)). When divided by 18, the remainder is 16 (\(538 = 18 \times 29 + 16\)). When divided by 27, the remainder is 25 (\(538 = 27 \times 19 + 25\)).
A) 540 — This is the LCM of 12, 15, 18, and 27. If 540 were the answer, it would leave a remainder of 0 when divided by any of these numbers, not the specified remainders.
C) 542 — This number is \(540 + 2\). If this were the answer, it would leave a remainder of 2 when divided by 12, 15, 18, and 27, which is not what the problem states (the remainders are 10, 13, 16, 25 respectively).
D) 552 — This number is \(540 + 12\). It would leave a remainder of 0 when divided by 12, and different remainders for the other numbers, which do not match the given conditions.
To find the sum of the given decimal numbers, we need to align them by their decimal points and then add them column by column, starting from the rightmost digit.
The numbers are:
\[\begin{array}{r} 6732.80000 \ 673.28000 \ 67.32800 \ 6.73280 \ + \quad 0.67328 \ \hline \end{array}\]Now, add the numbers column by column from right to left:
The sum is \(7480.81408\).
D) The sum calculated by aligning the decimal points and adding column by column is \(7480.81408\).
The question asks to identify the Indian state that has been declared a 'complete Digital State'. This requires knowledge of recent government initiatives and declarations related to digital literacy and infrastructure in various Indian states.
Correct Option: B) Kerala was declared India's first complete Digital State in 2016 due to its high digital literacy rates, extensive mobile and internet penetration, and successful e-governance initiatives.
The question asks us to evaluate an Assertion (A) and a Reason (R) related to climate change and their cause-and-effect relationship. We need to determine if both statements are true and if the Reason correctly explains the Assertion.
Carbon dioxide (\(\text{CO}_2\)) is a greenhouse gas. An increase in its concentration in the atmosphere traps more heat, leading to a rise in global temperatures. This global warming causes glaciers and polar ice caps to melt. Therefore, Assertion (A) is true.
As explained above, an increase in greenhouse gases like carbon dioxide leads to the greenhouse effect, which results in a rise in the Earth's average temperature. Therefore, Reason (R) is true.
The increase in carbon dioxide (as stated implicitly in A) leads to an increase in the Earth's temperature (R). This increase in temperature (R) is precisely what causes the polar ice to melt (A). Thus, Reason (R) provides a direct and correct explanation for Assertion (A).
C) Both A and R are true and R is the correct explanation of A. This option correctly identifies that both statements are factually accurate and that the increase in Earth's temperature (R) is the direct cause of polar ice melting (A), which is driven by increased carbon dioxide.