To solve this problem, we first need to determine the Cost Price (CP) of the fan using the initial selling price and loss percentage. Once the CP is known, we can calculate the new profit or loss percentage if the fan is sold at the second given selling price.
Calculate the Cost Price (CP):
Given:
The formula for Selling Price with a loss is:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]Substitute the given values:
\[ 3600 = \text{CP} \times \left(1 - \frac{4}{100}\right) \] \[ 3600 = \text{CP} \times \left(\frac{100 - 4}{100}\right) \] \[ 3600 = \text{CP} \times \frac{96}{100} \]Now, solve for CP:
\[ \text{CP} = \frac{3600 \times 100}{96} \] \[ \text{CP} = \frac{360000}{96} \] \[ \text{CP} = \text{₹}3750 \]Calculate the new gain or loss percent:
Given:
Since \(\text{SP}_2 > \text{CP}\), there will be a gain.
Calculate the Gain Amount:
\[ \text{Gain Amount} = \text{SP}_2 - \text{CP} \] \[ \text{Gain Amount} = 4200 - 3750 \] \[ \text{Gain Amount} = \text{₹}450 \]Calculate the Gain Percentage:
\[ \text{Gain \%} = \frac{\text{Gain Amount}}{\text{CP}} \times 100 \] \[ \text{Gain \%} = \frac{450}{3750} \times 100 \] \[ \text{Gain \%} = \frac{45000}{3750} \] \[ \text{Gain \%} = 12\% \]Correct Option: B) Gain 12%
The question asks for the location of the Kilauea volcano, known for its destructive eruptions. This requires knowledge of world geography and famous volcanic sites.
Correct Option: D) Hawaii
Kilauea is an active shield volcano in the Hawaiian Islands, located on the southeastern part of the Big Island of Hawaii. It is one of the world's most active volcanoes and has been in a state of nearly continuous eruption for decades, making it a significant geological feature and a frequent subject of news due to its destructive potential.
The problem is a word analogy based on a specific pattern. We need to identify the transformation applied to "JUMBUCKS" to get "SKCUBMUJ" and then apply the same transformation to "SHIPJACK" to find the related word.
Correct Option: D) KCAJPIHS is the correct answer because it is the reverse spelling of SHIPJACK.
The question asks to identify the metal that cannot be extracted from its ore by reduction using carbon. This involves understanding the reactivity series of metals and the principles of extractive metallurgy.
Correct Option: B) Sodium is a highly reactive metal, more reactive than carbon. Therefore, its oxides cannot be reduced by carbon. It is typically extracted by electrolytic reduction of its molten salts.
This problem can be solved using the Remainder Theorem. The Remainder Theorem states that if a polynomial \(P(x)\) is divided by \((x - c)\), the remainder is \(P(c)\). We will apply this theorem to both given conditions to form a system of two linear equations with two variables, \(a\) and \(b\), and then solve for \(a\) and \(b\).
Apply Remainder Theorem to the first polynomial:
Given the polynomial \(P_1(x) = x^2 + ax + b\). When divided by \((x - 4)\), the remainder is \(-40\).
According to the Remainder Theorem, \(P_1(4) = -40\).
Substitute \(x = 4\) into the polynomial:
\[ (4)^2 + a(4) + b = -40 \] \[ 16 + 4a + b = -40 \]Rearrange the terms to form the first equation:
\[ 4a + b = -40 - 16 \] \[ 4a + b = -56 \quad \text{(Equation 1)} \]Apply Remainder Theorem to the second polynomial:
Given the polynomial \(P_2(x) = x^2 + bx + a\). When divided by \((x - 4)\), the remainder is \(-43\).
According to the Remainder Theorem, \(P_2(4) = -43\).
Substitute \(x = 4\) into the polynomial:
\[ (4)^2 + b(4) + a = -43 \] \[ 16 + 4b + a = -43 \]Rearrange the terms to form the second equation:
\[ a + 4b = -43 - 16 \] \[ a + 4b = -59 \quad \text{(Equation 2)} \]Solve the system of linear equations:
We have two equations:
\(4a + b = -56 \quad \text{(1)}\)
\(a + 4b = -59 \quad \text{(2)}\)
We need to find the value of \(a + b\). A quick way to do this is to add the two equations:
Add Equation 1 and Equation 2:
\[ (4a + b) + (a + 4b) = -56 + (-59) \] \[ 5a + 5b = -115 \]Factor out 5 from the left side:
\[ 5(a + b) = -115 \]Divide both sides by 5 to find \(a + b\):
\[ a + b = \frac{-115}{5} \] \[ a + b = -23 \]D) The value of \(a + b\) is \(-23\).
The question asks about the origin of the quantum theory of light. This requires knowledge of key figures in the development of quantum mechanics and their specific contributions.
Max Planck introduced the concept that energy is emitted or absorbed in discrete packets, or "quanta," to explain black-body radiation. This groundbreaking idea laid the foundation for quantum theory.
While Albert Einstein later used Planck's quantum hypothesis to explain the photoelectric effect, thereby solidifying the idea of light quanta (photons), the initial concept of energy quantization, which is central to the quantum theory of light, was proposed by Planck.
B) Planck — Max Planck, in 1900, proposed that energy is radiated and absorbed in discrete units, or quanta, to explain the spectrum of black-body radiation. This revolutionary idea marked the birth of quantum theory and laid the groundwork for understanding light as composed of energy packets.
This question tests knowledge of significant ministerial portfolios in the Indian government at a specific point in time. To answer correctly, one needs to recall the Union Cabinet composition as of February 2018.
Correct Option: B) Rajnath Singh
The question asks to identify the Mughal Emperor who was deported to Rangoon by the British. This is a direct historical fact related to the Indian Rebellion of 1857.
Correct Option: A) Bahadur Shah Zafar was the last Mughal Emperor. He was involved in the Indian Rebellion of 1857, and after the British suppressed the rebellion, he was tried for treason and subsequently exiled to Rangoon, Burma, where he died in 1862.
The problem describes a rearrangement of a given alphanumeric sequence. We need to identify the element at a specific position (fifth from the right) after the rearrangement. The rearrangement involves swapping the first 10 terms with the last 10 terms in a specific order: first with last, second with second last, and so on.
B) The fifth term from the right in the new arrangement is E.
The question asks for the term that describes the number of atoms present in a molecule. We need to evaluate each given option to identify the correct scientific term.
Correct Option: C) Atomicity is the term used to describe the number of atoms constituting a molecule. For example, the atomicity of \(\text{H}_2\text{O}\) is 3 (2 hydrogen atoms + 1 oxygen atom), and the atomicity of \(\text{O}_3\) (ozone) is 3.