In a row of 37 persons, Aneesha is 12th from the left end. What is her position from the right end?
This problem involves determining a person's position from the opposite end of a row when their position from one end and the total number of persons are known. We can use a standard formula for this type of ranking problem.
The relationship between the total number of persons, a person's position from the left, and their position from the right is given by:
\[ N = L + R - 1 \]We need to find \(R\), so we can rearrange the formula as:
\[ R = N - L + 1 \]Therefore, Aneesha's position from the right end is 26th.
B) 26 — As calculated, Aneesha's position from the right end is 26th.
The question asks to identify the name of the exercise in which the Indian Air Force (IAF) participated in Malaysia, with its contingent returning on August 10, 2024. This requires knowledge of recent joint military exercises involving the IAF.
Correct Option: C) Udara Shakti is the bilateral air exercise between the Indian Air Force and the Royal Malaysian Air Force. The inaugural exercise took place in August 2022 in Malaysia, making it the correct answer for an IAF contingent participating in Malaysia.
The question asks to identify the government initiative or mission that serves as a roadmap for achieving development and child protection priorities aligned with the Sustainable Development Goals (SDGs). This requires knowledge of various government programs related to child welfare.
Correct Option: C) Mission Vatsalya is a scheme of the Ministry of Women and Child Development, Government of India. It aims to secure a healthy and happy childhood for every child in India, ensuring their development, protection, and well-being. It consolidates and strengthens various child protection services and schemes, aligning with the Sustainable Development Goals related to child health, education, and protection (e.g., SDG 3: Good Health and Well-being, SDG 4: Quality Education, SDG 16: Peace, Justice, and Strong Institutions). The scheme provides support for statutory bodies, service delivery structures, institutional care, non-institutional care, emergency outreach, training, and capacity building.
The question asks to identify the Indian Paralympian who won a gold medal in the Women's 10 m air rifle standing SH1 Shooting category at the Paralympics. This requires knowledge of prominent Indian Paralympians and their achievements.
C) Avani Lekhara is an Indian Paralympian and rifle shooter. She won a gold medal in the Women's 10 m air rifle standing SH1 event at the 2020 Tokyo Paralympics, becoming the first Indian woman to win a Paralympic gold medal. She also won a bronze medal in the Women's 50 m rifle 3 positions SH1 event at the same Games.
The problem states that after a 24% decrease, the price of an article is ₹988. We need to find the original (actual) cost of the article. We can set up an equation where the actual cost minus 24% of the actual cost equals the decreased price.
Let the actual cost of the article be \(P\).
The decrease in price is 24% of the actual cost. This can be written as \(0.24 \times P\).
After the decrease, the new price is the actual cost minus the decrease:
\[ \text{New Price} = P - (0.24 \times P) \]We are given that the new price is ₹988. So, we can set up the equation:
\[ P - 0.24P = 988 \]Combine the terms involving \(P\):
\[ (1 - 0.24)P = 988 \]\[ 0.76P = 988 \]To find \(P\), divide both sides by 0.76:
\[ P = \frac{988}{0.76} \]Perform the division:
\[ P = \frac{98800}{76} \]\[ P = 1300 \]Therefore, the actual cost of the article is ₹1,300.
C) ₹1,300. This is the actual cost calculated by reversing the 24% decrease.
To find the arithmetic mean (or average) of a set of observations, we sum all the observations and then divide the sum by the total number of observations.
Thus, the arithmetic mean of the given observations is 14.
Correct Option: C) 14
If x + \( \frac{1}{x} \) = 4, then x² + \( \frac{1}{x^2} \) = ?
The problem asks us to find the value of \(x^2 + \frac{1}{x^2}\) given the equation \(x + \frac{1}{x} = 4\). This can be solved by squaring both sides of the given equation and then rearranging the terms using the algebraic identity \((a+b)^2 = a^2 + b^2 + 2ab\).
We are given the equation:
\[ x + \frac{1}{x} = 4 \]To find \(x^2 + \frac{1}{x^2}\), we can square both sides of the given equation:
\[ \left(x + \frac{1}{x}\right)^2 = (4)^2 \]Apply the algebraic identity \((a+b)^2 = a^2 + b^2 + 2ab\) to the left side of the equation, where \(a=x\) and \(b=\frac{1}{x}\):
\[ x^2 + \left(\frac{1}{x}\right)^2 + 2 \cdot x \cdot \frac{1}{x} = 16 \]Simplify the terms:
\[ x^2 + \frac{1}{x^2} + 2 \cdot 1 = 16 \]\[ x^2 + \frac{1}{x^2} + 2 = 16 \]Subtract 2 from both sides of the equation to isolate \(x^2 + \frac{1}{x^2}\):
\[ x^2 + \frac{1}{x^2} = 16 - 2 \]\[ x^2 + \frac{1}{x^2} = 14 \]Correct Option: C) 14
To find the depth of water, we will use the formula for the volume of a rectangular tank, which is the product of its base area and height (depth). We need to ensure all units are consistent before performing calculations. The given base area is in cm² and the volume is in cubic meters, so we will convert them to a common unit, preferably meters.
It's generally easier to work with meters for volume and depth. Let's convert the base area from cm² to m².
We know that 1 m = 100 cm.
Therefore, 1 m² = (100 cm) \(\times\) (100 cm) = 10000 cm².
So, to convert cm² to m², we divide by 10000.
\[ A = 6500 \text{ cm}^2 = \frac{6500}{10000} \text{ m}^2 = 0.65 \text{ m}^2 \]The volume of a rectangular tank is given by the formula:
\[ V = A \times h \]where \(V\) is the volume, \(A\) is the base area, and \(h\) is the height (depth) of the water.We need to find \(h\), so we can rearrange the formula:
\[ h = \frac{V}{A} \]Substitute the converted values into the formula:
\[ h = \frac{2.6 \text{ m}^3}{0.65 \text{ m}^2} \]\[ h = \frac{260}{65} \text{ m} \]\[ h = 4 \text{ m} \]Correct Option: B) 4 m
The question asks for the location of the Khalubar War Memorial, which was opened to tourists by the Indian Army in June 2024. This is a factual question related to current affairs and geography.
Correct Option: B) Ladakh
The question asks to identify the longest cell in the human body. We need to recall the general characteristics and relative sizes of the cells listed in the options.
A) Nerve cell (Neuron) has an axon that can extend up to a meter or more, making it the longest cell in the human body. These long extensions are crucial for transmitting signals over long distances.