Select the odd image
The goal is to identify the image that does not fit the pattern or sequence followed by the others. This requires analyzing the characteristics of each letter in the images.
Correct Option: B) A
The question asks about the political party that came to power in the Tripura elections in 2018. This requires knowledge of recent Indian state election results, specifically for the state of Tripura.
Correct Option: A) BJP
In the 2018 Tripura Assembly elections, the Bharatiya Janata Party (BJP) formed the government, ending the long rule of the Left Front. This was a significant political shift in the state.
The question asks about Newlands' Octave Law and the placement of iron. We need to recall the arrangement of elements in Newlands' periodic table and identify which elements iron resembles in properties and where it was placed relative to them.
Correct Option: A) Co and Ni
Iron resembles Cobalt (Co) and Nickel (Ni) in properties. However, according to Newlands' Octave Law, iron was placed far away from these elements. This was a significant drawback of his classification.
The question asks to identify the element whose atoms do not contain neutrons. To answer this, we need to recall the basic atomic structure of elements, particularly the composition of the nucleus, and then consider the specific case of the lightest element.
Correct Option: B) H is the symbol for Hydrogen. The most common isotope of hydrogen, protium (\(^{1}\text{H}\)), consists of one proton and one electron, but no neutrons in its nucleus. This makes it unique among all elements.
The question asks to identify the director of the 1928 film 'Devdas'. This requires knowledge of early Indian cinema history and specific filmography.
The first film adaptation of Sarat Chandra Chattopadhyay's novel 'Devdas' was a silent film released in 1928. This film was directed by Naresh Mitra.
Correct Option: A) Naresh Mitra was the director of the 1928 silent film 'Devdas'. This was the first cinematic adaptation of Sarat Chandra Chattopadhyay's famous novel.
________ is added to hydrocarbons in a more rapid reaction in the presence of sunlight
The question asks which substance reacts with hydrocarbons more rapidly in the presence of sunlight. This points to a free radical substitution reaction, which is characteristic of halogens with alkanes under UV light (sunlight).
D) Cl\(_2\) — Chlorine reacts with hydrocarbons (specifically alkanes) in a rapid free radical substitution reaction when exposed to sunlight (UV light). The sunlight provides the energy for the homolytic cleavage of the chlorine molecule into highly reactive chlorine free radicals, initiating a chain reaction.
To find the profit percentage, we need to determine the total cost price (CP) and total selling price (SP) of the watches. The problem states that the profit made by selling 12 watches is equal to the selling price of 2 watches. We can set up equations based on this information to find the relationship between CP and SP, and then calculate the profit percentage.
Let \( \text{CP} \) be the cost price of one watch and \( \text{SP} \) be the selling price of one watch.
The selling price of 12 watches is \( 12 \times \text{SP} \).
The cost price of 12 watches is \( 12 \times \text{CP} \).
The profit made by selling 12 watches is given by:
\[ \text{Profit} = (\text{Selling Price of 12 watches}) - (\text{Cost Price of 12 watches}) \]\[ \text{Profit} = 12 \times \text{SP} - 12 \times \text{CP} \]According to the problem statement, this profit is equal to the selling price of 2 watches:
\[ \text{Profit} = 2 \times \text{SP} \]Now, we equate the two expressions for profit:
\[ 12 \times \text{SP} - 12 \times \text{CP} = 2 \times \text{SP} \]Rearrange the equation to find the relationship between SP and CP:
\[ 12 \times \text{SP} - 2 \times \text{SP} = 12 \times \text{CP} \]\[ 10 \times \text{SP} = 12 \times \text{CP} \]From this, we can express SP in terms of CP (or vice versa):
\[ \text{SP} = \frac{12}{10} \times \text{CP} \]\[ \text{SP} = \frac{6}{5} \times \text{CP} \]Now, calculate the profit percentage. The formula for profit percentage is:
\[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{CP}} \times 100\% \]We know that for one watch, the profit is \( \text{SP} - \text{CP} \). Substitute the expression for SP:
\[ \text{Profit} = \frac{6}{5} \times \text{CP} - \text{CP} \]\[ \text{Profit} = \left(\frac{6}{5} - 1\right) \times \text{CP} \]\[ \text{Profit} = \left(\frac{6-5}{5}\right) \times \text{CP} \]\[ \text{Profit} = \frac{1}{5} \times \text{CP} \]Now, substitute this profit into the profit percentage formula:
\[ \text{Profit Percentage} = \frac{\frac{1}{5} \times \text{CP}}{\text{CP}} \times 100\% \]\[ \text{Profit Percentage} = \frac{1}{5} \times 100\% \]\[ \text{Profit Percentage} = 20\% \]Correct Option: C) 20%
Which of the following option images shows the closest resemblance to the question figures?
The task is to identify which option image closely resembles the given question figures. We need to analyze the shapes, orientations, and positions of elements within the images.
Correct Option: B) Option B closely resembles the question figures with the triangle and star in the correct orientation.
The question asks for the full form of the acronym HIV. This is a factual recall question related to common diseases and their causative agents, which is a standard topic in general science sections of competitive exams.
Correct Option: D) Human Immunodeficiency Virus. This is the universally recognized full form of HIV, the virus that causes AIDS (Acquired Immunodeficiency Syndrome).
If 2x = sec A and \( \frac{2}{x} \) = tan A, then find the value of 2\(\left[x^2-\frac{1}{x^2}\right]\)=
1
\( \frac{1}{2} \)
\( \frac{1}{4} \)
\( \frac{1}{3} \)
The problem provides two equations relating \(x\), \(\text{sec A}\), and \(\text{tan A}\). We need to find the value of an expression involving \(x^2\) and \(\frac{1}{x^2}\). We can use the given equations to express \(x\) and \(\frac{1}{x}\) in terms of trigonometric functions, then substitute these into the expression and simplify using a fundamental trigonometric identity.
From the first given equation:
\[ 2x = \text{sec A} \]\[ x = \frac{\text{sec A}}{2} \]From the second given equation:
\[ \frac{2}{x} = \text{tan A} \]\[ \frac{1}{x} = \frac{\text{tan A}}{2} \]Now, we need to find \(x^2\) and \(\frac{1}{x^2}\):
\[ x^2 = \left(\frac{\text{sec A}}{2}\right)^2 = \frac{\text{sec}^2 \text{A}}{4} \]\[ \frac{1}{x^2} = \left(\frac{\text{tan A}}{2}\right)^2 = \frac{\text{tan}^2 \text{A}}{4} \]Substitute these values into the expression \(2\left[x^2-\frac{1}{x^2}\right]\):
\[ 2\left[x^2-\frac{1}{x^2}\right] = 2\left[\frac{\text{sec}^2 \text{A}}{4} - \frac{\text{tan}^2 \text{A}}{4}\right] \]Factor out \(\frac{1}{4}\) from the terms inside the bracket:
\[ 2\left[x^2-\frac{1}{x^2}\right] = 2 \times \frac{1}{4} \left[\text{sec}^2 \text{A} - \text{tan}^2 \text{A}\right] \]Simplify the constant term:
\[ 2\left[x^2-\frac{1}{x^2}\right] = \frac{1}{2} \left[\text{sec}^2 \text{A} - \text{tan}^2 \text{A}\right] \]Recall the fundamental trigonometric identity: \(\text{sec}^2 \text{A} - \text{tan}^2 \text{A} = 1\).
Substitute this identity into the expression:
\[ 2\left[x^2-\frac{1}{x^2}\right] = \frac{1}{2} \times 1 \]\[ 2\left[x^2-\frac{1}{x^2}\right] = \frac{1}{2} \]B) The value of the expression is \(\frac{1}{2}\).