The question asks to identify which of the given options is NOT a constitutional body. A constitutional body is an organization or institution that derives its power and authority directly from the Constitution of India. They are established by specific articles of the Constitution.
Based on the evaluation, NITI Aayog is the only body among the options that is not established by the Constitution.
Correct Option: B) NITI Aayog
Study the given diagram carefully and answer the question that follows.
The numbers in different sections indicate the number of people who have coffee, tea, and ice cream.
How many people have all three i.e. Ice cream, Tea as well as Coffee?
To find how many people have all three items: Ice cream, Tea, and Coffee, we need to identify the section in the diagram where all three shapes (rectangle, circle, and triangle) overlap.
Correct Option: B) 6
The question asks to identify the term represented by \(\bar{C}\) in the consumption function. Understanding the components of the consumption function is key to answering this question.
B) Autonomous Consumption. In the consumption function \(C = \bar{C} + bY\), \(\bar{C}\) represents the level of consumption that is independent of income. This is precisely the definition of autonomous consumption.
This problem involves the relationship between resistance, resistivity, length, and cross-sectional area of a wire. We will use the formula for resistance and the given ratios to find the ratio of resistivities.
Recall the formula for the resistance of a wire:
\[ R = \rho \frac{L}{A} \]where:
We are given that the two wires have the same length and the same resistance. Let's denote the properties of the first wire with subscript 1 and the second wire with subscript 2.
Given:
Write the resistance formula for both wires:
\[ R_1 = \rho_1 \frac{L_1}{A_1} \]\[ R_2 = \rho_2 \frac{L_2}{A_2} \]Since \(R_1 = R_2\) and \(L_1 = L_2\), we can set the two expressions equal:
\[ \rho_1 \frac{L}{A_1} = \rho_2 \frac{L}{A_2} \]Cancel out \(L\) from both sides:
\[ \frac{\rho_1}{A_1} = \frac{\rho_2}{A_2} \]Rearrange the equation to find the ratio of resistivities \(\rho_1 : \rho_2\):
\[ \frac{\rho_1}{\rho_2} = \frac{A_1}{A_2} \]Substitute the given ratio of cross-sectional areas:
\[ \frac{\rho_1}{\rho_2} = \frac{1}{8} \]Therefore, the ratio of their resistivities is \(1 : 8\).
B) 1 : 8 is the correct ratio of their resistivities, as derived from the relationship between resistance, resistivity, length, and cross-sectional area.
The problem presents a series of terms, each consisting of three letters and a number. To find the missing term, we need to identify the pattern in both the letters and the numbers separately.
The numbers in the series are 15, 18, 21, 24. Let's find the difference between consecutive numbers:
The numerical sequence is an arithmetic progression with a common difference of 3. So, the next number in the series will be \(24 + 3 = 27\).
The first letters are M, Q, U, Y. Let's find their positions in the alphabet (A=1, B=2, ...):
The differences are:
The first letter sequence also follows a pattern of adding 4 to the alphabetical position. So, the next first letter will be \(25 + 4 = 29\). Since there are only 26 letters, we wrap around: \(29 - 26 = 3\). The 3rd letter is C.
The second letters are S, W, A, E. Let's find their positions:
The differences are:
This sequence also follows a pattern of adding 4 to the alphabetical position, wrapping around after Z. So, the next second letter will be \(5 + 4 = 9\). The 9th letter is I.
The third letters are N, R, V, Z. Let's find their positions:
The differences are:
This sequence also follows a pattern of adding 4 to the alphabetical position. So, the next third letter will be \(26 + 4 = 30\). Wrapping around: \(30 - 26 = 4\). The 4th letter is D.
The next term will have the first letter C, the second letter I, the third letter D, and the number 27. Combining these, we get CID27.
B) CID27 is the correct option as it matches all the patterns identified for the letters and the number.
The question asks to identify the infection where the virus specifically targets and damages the immune system. We need to recall the primary mode of action of the pathogens listed in the options.
Correct Option: D) HIV-AIDS is caused by the Human Immunodeficiency Virus, which directly attacks and destroys CD4+ T-cells, a vital part of the immune system, leading to its dysfunction and eventual collapse.
The question asks for the name of the Parsi New Year, which is celebrated in Maharashtra and Gujarat and marks the beginning of the Iranian calendar. We need to identify the correct term from the given options.
D) Nowruz — Nowruz is the traditional Iranian New Year, which literally means "new day". It is celebrated by various ethnolinguistic communities worldwide as the beginning of the New Year, and it marks the vernal equinox. The Parsi community in India celebrates Nowruz, often referred to as Parsi New Year, especially in states like Maharashtra and Gujarat where a significant Parsi population resides. It aligns with the beginning of the Iranian calendar.
To answer this question, we need to recall the basic requirements for the process of photosynthesis in plants. Photosynthesis is the process by which green plants and some other organisms use sunlight to synthesize foods with carbon dioxide and water.
Correct Option: D) Carbon dioxide, water, sunlight and chlorophyll
This option correctly lists all the essential components required for photosynthesis: carbon dioxide and water as raw materials, sunlight as the energy source, and chlorophyll as the light-absorbing pigment.
If x − \( \frac{1}{x} \) = 5, then the value of x⁴ + \( \frac{1}{x^4} \) is:
To find the value of \(x^4 + \frac{1}{x^4}\) given \(x - \frac{1}{x} = 5\), we will use the algebraic identity \((a-b)^2 = a^2 - 2ab + b^2\) and \((a+b)^2 = a^2 + 2ab + b^2\) twice. First, we'll find \(x^2 + \frac{1}{x^2}\), and then use that result to find \(x^4 + \frac{1}{x^4}\).
Square the given equation:
We are given the equation:
\[ x - \frac{1}{x} = 5 \]
Square both sides of the equation:
\[ \left(x - \frac{1}{x}\right)^2 = 5^2 \]
Apply the identity \((a-b)^2 = a^2 - 2ab + b^2\), where \(a=x\) and \(b=\frac{1}{x}\):
\[ x^2 - 2 \cdot x \cdot \frac{1}{x} + \left(\frac{1}{x}\right)^2 = 25 \]
\[ x^2 - 2 + \frac{1}{x^2} = 25 \]
\[ x^2 + \frac{1}{x^2} = 25 + 2 \]
\[ x^2 + \frac{1}{x^2} = 27 \]
Square the result again:
Now we have \(x^2 + \frac{1}{x^2} = 27\). To get \(x^4 + \frac{1}{x^4}\), we square both sides of this new equation:
\[ \left(x^2 + \frac{1}{x^2}\right)^2 = 27^2 \]
Apply the identity \((a+b)^2 = a^2 + 2ab + b^2\), where \(a=x^2\) and \(b=\frac{1}{x^2}\):
\[ (x^2)^2 + 2 \cdot x^2 \cdot \frac{1}{x^2} + \left(\frac{1}{x^2}\right)^2 = 729 \]
\[ x^4 + 2 + \frac{1}{x^4} = 729 \]
\[ x^4 + \frac{1}{x^4} = 729 - 2 \]
\[ x^4 + \frac{1}{x^4} = 727 \]
B) The value of \(x^4 + \frac{1}{x^4}\) is 727, as derived from the step-by-step calculation.
The question asks about the mission under which the Child Protection Services Scheme of 2017 was subsumed by the Government of India as of August 2022. This requires knowledge of recent government initiatives related to child welfare.
Correct Option: B) Vatsalya
Mission Vatsalya is a scheme of the Ministry of Women and Child Development that aims to ensure a healthy and happy childhood for every child in India. It supports children in difficult circumstances and provides services for their protection, care, and rehabilitation. The Child Protection Services Scheme (CPS) of 2017 was integrated into Mission Vatsalya as part of a broader restructuring of child welfare programs.