The question asks to identify the deity whose images are predominantly depicted in Tahngka paintings. This requires knowledge of the origin and subject matter of Tahngka art.
Correct Option: C) Buddha
If the numerator of a fraction is decreased by 80% and the denominator of the fraction is decreased by 60%, then the resultant fraction is \( \frac{5}{6} \). What is the original fraction?
\( \frac{3}{5} \)
\( \frac{7}{3} \)
\( \frac{5}{3} \)
\( \frac{6}{5} \)
To find the original fraction, we will represent the original fraction as \( \frac{x}{y} \). Then, we will apply the given percentage decreases to the numerator and denominator to form a new fraction. We will equate this new fraction to the given resultant fraction and solve for \( \frac{x}{y} \).
Let the original fraction be \( \frac{x}{y} \).
The numerator is decreased by 80%. This means the new numerator will be \( x - 80\% \text{ of } x \).
New Numerator \( = x - 0.80x = 0.20x \).
The denominator is decreased by 60%. This means the new denominator will be \( y - 60\% \text{ of } y \).
New Denominator \( = y - 0.60y = 0.40y \).
The resultant fraction is the new numerator divided by the new denominator:
\[ \frac{0.20x}{0.40y} \]
We are given that the resultant fraction is \( \frac{5}{6} \). So, we set up the equation:
\[ \frac{0.20x}{0.40y} = \frac{5}{6} \]
Simplify the left side of the equation:
\[ \frac{0.20}{0.40} \times \frac{x}{y} = \frac{5}{6} \]
\[ \frac{1}{2} \times \frac{x}{y} = \frac{5}{6} \]
Solve for \( \frac{x}{y} \) by multiplying both sides by 2:
\[ \frac{x}{y} = \frac{5}{6} \times 2 \]
\[ \frac{x}{y} = \frac{10}{6} \]
Simplify the fraction:
\[ \frac{x}{y} = \frac{5}{3} \]
Correct Option: C) The original fraction is \( \frac{5}{3} \).
This problem involves calculating the principal amount when the final amount, time period, and varying compound interest rates for each year are given. We will use the compound interest formula for varying rates to work backward from the final amount to find the principal.
B) ₹14,276.58 is the closest value to our calculated principal amount of approximately ₹14,286.58. The slight difference is likely due to rounding in the options or during intermediate calculations.
The question asks to identify the government program specifically launched to trace missing and destitute children and reunite them with their families. This requires knowledge of various government initiatives and their objectives.
Correct Option: D) Operation Muskaan
Operation Muskaan (later renamed "Operation Smile") is an initiative of the Ministry of Home Affairs, Government of India. It was launched with the primary objective of tracing missing children, rescuing them from various vulnerable situations (like child labor, begging, sexual exploitation), and reuniting them with their families. Police personnel are trained and deployed to conduct special drives to achieve these goals.
The question asks to identify the historian who famously stated, "Neither first, nor national not war of independence" in the context of the 1857 Revolt. This statement reflects a particular historical interpretation of the event.
Correct Option: C) RC Majumadar
R.C. Majumdar, in his work on the Sepoy Mutiny and the Revolt of 1857, concluded that the uprising was not "first, nor national, nor a war of independence." He based this on the lack of a unified national sentiment, the localized nature of many revolts, and the diverse motivations of the participants, which often included personal grievances and religious fanaticism rather than a collective desire for national independence.
The question asks to identify the emblem of the Reserve Bank of India (RBI). This is a factual question requiring knowledge of the RBI's official symbol.
Correct Option: D) The emblem of the Reserve Bank of India (RBI) is a Bengal tiger in front of a palm tree. This imagery was adopted from the East India Company's original seal, with the lion replaced by a tiger, symbolizing India's national animal and natural heritage.
To find the area of the circle, we first need to determine its radius. The problem states that the diameter of the circle is equal to the diagonal of a square. We are given the area of the square, which allows us to find the side length of the square and then its diagonal. Once the diagonal is found, we can determine the circle's diameter and subsequently its radius and area.
Find the side length of the square:
Given the area of the square is 32 sq units.
Let \(s\) be the side length of the square.
\[ \text{Area of square} = s^2 \] \[ 32 = s^2 \] \[ s = \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \text{ units} \]Find the diagonal of the square:
Let \(d\) be the diagonal of the square. Using the Pythagorean theorem, or the formula for the diagonal of a square:
\[ d = s\sqrt{2} \]Substitute the value of \(s\):
\[ d = (4\sqrt{2})\sqrt{2} = 4 \times 2 = 8 \text{ units} \]Determine the diameter and radius of the circle:
The problem states that the diameter of the circle is equal to the diagonal of the square.
So, diameter of circle \(= D = d = 8 \text{ units}\).
The radius of the circle \[= r = \frac{D}{2} = \frac{8}{2} = 4 \text{ units}\].
Calculate the area of the circle:
The formula for the area of a circle is \(\text{Area} = \pi r^2\).
Substitute the value of \(r\):
\[ \text{Area of circle} = \pi (4)^2 = \pi \times 16 = 16\pi \text{ sq units} \]Correct Option: A) 16π sq units
The question asks to identify the UN organization responsible for addressing illicit trafficking and drug abuse. This requires knowledge of the mandates of various UN bodies.
Correct Option: B) UNODC (United Nations Office on Drugs and Crime) is the UN entity mandated to assist Member States in their struggle against illicit drugs, crime, and terrorism. This includes addressing illicit trafficking and drug abuse.
Arrange the given fractions in decreasing order.
\( \frac{7}{8} \),\( \frac{8}{9} \), \( \frac{9}{10} \)
\( \frac{7}{8} \), \( \frac{8}{9} \),\( \frac{9}{10} \)
\( \frac{9}{10} \), \( \frac{7}{8} \), \( \frac{8}{9} \)
\( \frac{8}{9} \), \( \frac{7}{8} \), \( \frac{9}{10} \)
\( \frac{9}{10} \), \( \frac{8}{9} \), \( \frac{7}{8} \)
To arrange fractions in decreasing order, we need to compare their values. This can be done by converting them to decimals, finding a common denominator, or by observing a pattern if one exists. In this case, all fractions have a numerator one less than the denominator, which is a useful pattern to exploit.
D) The decreasing order of the fractions is \( \frac{9}{10} \), \( \frac{8}{9} \), \( \frac{7}{8} \), which matches option D.
The remainder in the expression 27 \( \frac{3}{4} \) is:
The question asks for the remainder when the number \(27 \frac{3}{4}\) is considered. The expression \(27 \frac{3}{4}\) represents a mixed fraction. To find the remainder, we first need to understand what the question implies. In the context of remainders, it usually refers to the remainder when an integer is divided by another integer. However, \(27 \frac{3}{4}\) is a mixed fraction. If the question implies finding the remainder of the fractional part when expressed in a certain way, or if it's a poorly phrased question asking for the numerator of the fractional part, we should interpret it in the most common mathematical sense for competitive exams.
A mixed fraction \(A \frac{B}{C}\) can be written as \(A + \frac{B}{C}\). Here, \(A\) is the integer part and \(\frac{B}{C}\) is the fractional part. When we talk about remainder in division, if a number \(N\) is divided by \(D\), we write \(N = Q \times D + R\), where \(R\) is the remainder and \(0 \le R < D\).
Given the options, it seems the question is asking for the numerator of the fractional part, or perhaps the remainder when the numerator of the improper fraction form is divided by the denominator. Let's analyze the expression \(27 \frac{3}{4}\).
Understand the expression: The expression given is \(27 \frac{3}{4}\). This is a mixed fraction.
Convert to an improper fraction (optional but helpful for clarity): A mixed fraction \(A \frac{B}{C}\) can be converted to an improper fraction as \(\frac{(A \times C) + B}{C}\).
For \(27 \frac{3}{4}\), this would be:
\[ \frac{(27 \times 4) + 3}{4} = \frac{108 + 3}{4} = \frac{111}{4} \]Interpret "remainder": In the context of fractions, the term "remainder" can be ambiguous. However, in a mixed fraction \(A \frac{B}{C}\), \(B\) is often referred to as the remainder when the numerator of the improper fraction is divided by the denominator, provided \(B < C\).
If we divide \(111\) by \(4\):
\[ 111 \div 4 \]\(111 = 4 \times 27 + 3\)
Here, \(27\) is the quotient and \(3\) is the remainder. This directly corresponds to the integer part and the numerator of the fractional part in the mixed fraction \(27 \frac{3}{4}\).
Identify the remainder: From the mixed fraction \(27 \frac{3}{4}\), the integer part is \(27\) and the fractional part is \(\frac{3}{4}\). The numerator of this fractional part is \(3\). When \(111\) is divided by \(4\), the remainder is \(3\).
Correct Option: B) 3
The remainder in the expression \(27 \frac{3}{4}\) is the numerator of the fractional part, which is \(3\). This is also the remainder when the equivalent improper fraction's numerator (\(111\)) is divided by its denominator (\(4\)).