The question asks to identify the personality who propounded the 'safety valve theory' regarding the formation of the Indian National Congress and attributed its origin to Lord Dufferin. This is a direct factual question from modern Indian history.
B) Lala Lajpat Rai — Lala Lajpat Rai, in his book "Young India" (1916), popularized the 'safety valve theory'. He stated that the Indian National Congress was 'a product of the brain of Lord Dufferin' and that A.O. Hume founded it with the objective of providing a safe outlet for the rising discontent among Indians, thereby safeguarding British rule from a potential rebellion.
To solve this problem, we first need to determine the Cost Price (CP) of the item using the given Selling Price (SP) and the percentage loss. Once the CP is known, we can calculate the new Selling Price required to achieve a 15% gain.
Calculate the Cost Price (CP):
Given:
The formula for SP when there is a loss is:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss}\%}{100}\right) \]\[ 1980 = \text{CP} \times \left(1 - \frac{10}{100}\right) \]\[ 1980 = \text{CP} \times \left(1 - 0.10\right) \]\[ 1980 = \text{CP} \times 0.90 \]\[ \text{CP} = \frac{1980}{0.90} \]\[ \text{CP} = 2200 \]Calculate the new Selling Price (SP) for a 15% gain:
Now that we have the Cost Price (CP = ₹2,200), we need to find the selling price to gain 15%.
The formula for SP when there is a gain is:
\[ \text{SP} = \text{CP} \times \left(1 + \frac{\text{Gain}\%}{100}\right) \]\[ \text{SP} = 2200 \times \left(1 + \frac{15}{100}\right) \]\[ \text{SP} = 2200 \times \left(1 + 0.15\right) \]\[ \text{SP} = 2200 \times 1.15 \]\[ \text{SP} = 2530 \]Therefore, the shopkeeper should sell the item for ₹2,530 to gain 15%.
Correct Option: C) 2,530
The question asks for the venue of the 2022 Asian Games, which were eventually held in 2023. This requires knowledge of major international sporting events and their host cities.
The 19th Asian Games, originally planned for September 10-25, 2022, were postponed and eventually held from September 23 to October 8, 2023. The host city for these games was Hangzhou, China.
Correct Option: B) Hangzhou
The 19th Asian Games, often referred to as Hangzhou 2022, were hosted by Hangzhou, Zhejiang, China. The event was postponed from its original 2022 dates to 2023 due to the COVID-19 pandemic.
The question asks to identify the incorrectly matched slogan with its originator among the given options. This requires knowledge of famous slogans and their respective historical figures in the Indian independence movement.
Correct Option: C) "Do or Die" – Lala Lajpat Rai
The slogan "Do or Die" was given by Mahatma Gandhi during the Quit India Movement in 1942, not by Lala Lajpat Rai.
The given series consists of terms, each having a letter, a number, and another letter. We need to identify the pattern for each component (first letter, number, second letter) separately to find the next term in the series.
The pattern for the gaps is an increasing sequence of odd numbers: 3, 5, 7. So, the next gap should be 9.
P (16th letter) + 9 letters = Y (25th letter).
The pattern is a sequence of squares of consecutive integers starting from 2. So, the next number should be \(6^2 = 36\).
The pattern for the gaps is an increasing sequence of even numbers: 4, 6, 8. So, the next gap should be 10.
U (21st letter) + 10 letters = E (31st letter, which is 5th letter after completing the alphabet once, i.e., \(26+5=31\)).
The next term will have the first letter Y, the number 36, and the second letter E. Thus, the term is Y36E.
Correct Option: C) Y36E
If cos x – 3sin x = \(\sqrt{3}\) sin x, then the value of tan x is:
\(\frac{3-\sqrt{3}}{6}\)
3 - \(\sqrt{3}\)
\(\sqrt{3}\)
3 + \(\sqrt{3}\)
The problem asks us to find the value of \(\tan x\) given a trigonometric equation involving \(\cos x\) and \(\sin x\). The strategy is to rearrange the given equation to isolate terms containing \(\sin x\) and \(\cos x\), and then divide by \(\cos x\) to express the equation in terms of \(\tan x\).
Start with the given equation:
\[ \cos x - 3\sin x = \sqrt{3}\sin x \]Move all terms involving \(\sin x\) to one side of the equation:
\[ \cos x = \sqrt{3}\sin x + 3\sin x \]Factor out \(\sin x\) from the right side:
\[ \cos x = (\sqrt{3} + 3)\sin x \]To find \(\tan x\), which is \(\frac{\sin x}{\cos x}\), divide both sides of the equation by \(\cos x\). Assume \(\cos x \neq 0\).
\[ 1 = (\sqrt{3} + 3) \frac{\sin x}{\cos x} \]\[ 1 = (\sqrt{3} + 3) \tan x \]Now, solve for \(\tan x\):
\[ \tan x = \frac{1}{\sqrt{3} + 3} \]Rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is \((3 - \sqrt{3})\):
\[ \tan x = \frac{1}{3 + \sqrt{3}} \times \frac{3 - \sqrt{3}}{3 - \sqrt{3}} \]Apply the difference of squares formula \((a+b)(a-b) = a^2 - b^2\) in the denominator:
\[ \tan x = \frac{3 - \sqrt{3}}{3^2 - (\sqrt{3})^2} \]\[ \tan x = \frac{3 - \sqrt{3}}{9 - 3} \]\[ \tan x = \frac{3 - \sqrt{3}}{6} \]A) \(\frac{3-\sqrt{3}}{6}\) is the correct value for \(\tan x\) as derived from the step-by-step solution.
The question asks for the establishment year of NABARD (National Bank for Agriculture and Rural Development). This is a factual question requiring knowledge of key dates related to Indian financial institutions.
Correct Option: B) 1982 — NABARD was established on July 12, 1982, by an Act of Parliament (National Bank for Agriculture and Rural Development Act 1981).
This is a blood relations question. We need to deduce the relationship between Rashi and Rahul by breaking down the given statement step-by-step.
C) Wife — Rahul's mother-in-law is the mother of Rahul's wife. If Rashi is the daughter of Rahul's mother-in-law, and assuming Rashi is the only daughter or the primary daughter in this context, then Rashi is Rahul's wife.
A retailer buys a bag containing 54 kg oranges at ₹25 per kg. Later upon sorting he finds that 4 kg oranges are rotten, he throws them and sells the remaining ones at ₹36 per kg. Find his profit percent.
To find the profit percentage, we need to calculate the total cost price (CP) and the total selling price (SP). The cost price is based on the initial purchase of all oranges. The selling price is based on the sale of the remaining good oranges after discarding the rotten ones. The profit percentage is then calculated using the formula: \[\text{Profit Percent} = \frac{\text{Profit}}{\text{CP}} \times 100\].
The retailer buys 54 kg of oranges at ₹25 per kg.
\[ \text{CP} = \text{Quantity purchased} \times \text{Cost per kg} \]\[ \text{CP} = 54 \text{ kg} \times \text{₹}25/\text{kg} = \text{₹}1350 \]Out of 54 kg, 4 kg are rotten and thrown away.
\[ \text{Quantity sold} = \text{Total quantity} - \text{Rotten quantity} \]\[ \text{Quantity sold} = 54 \text{ kg} - 4 \text{ kg} = 50 \text{ kg} \]The remaining 50 kg of oranges are sold at ₹36 per kg.
\[ \text{SP} = \text{Quantity sold} \times \text{Selling price per kg} \]\[ \text{SP} = 50 \text{ kg} \times \text{₹}36/\text{kg} = \text{₹}1800 \]Profit is the difference between the Selling Price and the Cost Price.
\[ \text{Profit} = \text{SP} - \text{CP} \]\[ \text{Profit} = \text{₹}1800 - \text{₹}1350 = \text{₹}450 \]Profit percent is calculated with respect to the Cost Price.
\[ \text{Profit Percent} = \frac{\text{Profit}}{\text{CP}} \times 100 \]\[ \text{Profit Percent} = \frac{\text{₹}450}{\text{₹}1350} \times 100 \]\[ \text{Profit Percent} = \frac{1}{3} \times 100 \]\[ \text{Profit Percent} = 33 \frac{1}{3} \% \]Correct Option: C) \(33 \frac{1}{3} \%\)
The question asks to identify a member country of BIMSTEC (Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation). To answer this, one needs to know the member countries of BIMSTEC.
A) Sri Lanka is one of the seven member countries of BIMSTEC. The other members are Bangladesh, Bhutan, India, Myanmar, Nepal, and Thailand.