This question asks for the full form of the abbreviation UPU, specifically in the context of its relation to the United Nations. This requires knowledge of international organizations and their acronyms.
Correct Option: C) Universal Postal Union
The Universal Postal Union (UPU) is indeed a specialized agency of the United Nations. It was established in 1874 and became a specialized agency of the UN in 1948. Its primary role is to ensure a truly universal network of postal services, allowing for the free flow of international mail.
This problem involves the properties of co-prime numbers and the relationship between the product of two numbers, their HCF (Highest Common Factor), and their LCM (Least Common Multiple).
D) 119 — As derived, the LCM of two co-prime numbers whose product is 119 is 119.
If tan 3θ · tan 6θ = 1, then the value of tan 30θ is:
0
\( 3\sqrt{3} \)
-\(\sqrt{3}\)
-\(\frac{1}{\sqrt{3}}\)
The problem provides a trigonometric equation involving the tangent function and asks for the value of another tangent expression. We will use the trigonometric identity \(\tan A \cdot \tan B = 1 \implies A + B = 90^\circ\) (or \( (2n+1)90^\circ \)) to find the value of the angle, and then substitute this value to calculate the required tangent expression.
Given the equation:
\[ \tan 3\theta \cdot \tan 6\theta = 1 \]Recall the trigonometric identity: If \(\tan A \cdot \tan B = 1\), then \(A + B = 90^\circ\) (for acute angles, or more generally \(A+B = (2n+1)90^\circ\), where \(n\) is an integer). Assuming \(3\theta\) and \(6\theta\) are acute angles for simplicity, or that their sum falls into a quadrant where the identity holds.
Apply the identity to the given equation:
\[ 3\theta + 6\theta = 90^\circ \]Solve for \(\theta\):
\[ 9\theta = 90^\circ \]\[ \theta = \frac{90^\circ}{9} \]\[ \theta = 10^\circ \]Now, we need to find the value of \(\tan 30\theta\). Substitute the value of \(\theta\):
\[ \tan 30\theta = \tan (30 \cdot 10^\circ) \]\[ \tan 30\theta = \tan 300^\circ \]To evaluate \(\tan 300^\circ\), we can use the property \(\tan (360^\circ - x) = -\tan x\):
\[ \tan 300^\circ = \tan (360^\circ - 60^\circ) \]\[ \tan 300^\circ = -\tan 60^\circ \]We know that \(\tan 60^\circ = \sqrt{3}\).
Therefore:
\[ \tan 300^\circ = -\sqrt{3} \]C) The value of \(\tan 30\theta\) is \(-\sqrt{3}\).
The question asks to identify which country was NOT a member of the UN Security Council as of October 2020. This requires knowledge of the composition of the UN Security Council, specifically its permanent and non-permanent members during that period.
Malaysia was not a member of the UN Security Council in October 2020. Its last term on the Security Council was from 2015-2016.
The question asks to identify the host country of the 2022 FIFA World Cup. This is a factual question related to major international sporting events, which is a common topic in general knowledge sections of competitive exams.
D) Qatar — Qatar hosted the 2022 FIFA World Cup, which took place from November 20 to December 18, 2022. This was a historic event as it was the first time the tournament was held in the Middle East.
To find the area of an equilateral triangle, we use the standard formula involving the length of its side. We will substitute the given side length into the formula and calculate the area, then compare it with the given options.
The area of an equilateral triangle with side length \(a\) is given by:
\[ \text{Area} = \frac{\sqrt{3}}{4} a^2 \]The side length \(a = 10 \text{ m}\).
Substitute \(a = 10\) into the formula:
\[ \text{Area} = \frac{\sqrt{3}}{4} (10)^2 \]The approximate value of \(\sqrt{3}\) is \(1.732\).
The calculated area is \(43.3 \text{ m}^2\). We need to find the option closest to this value.
Correct Option: B) 43.25 m² is the closest value to \(43.3 \text{ m}^2\).
At what rate per cent of simple interest does a sum of money double itself in 12 years?
9 \( \frac{1}{3} \) %
8 \( \frac{1}{3} \) %
8 \( \frac{2}{3} \) %
9 \( \frac{2}{3} \) %
This problem involves calculating the rate of simple interest required for a sum of money to double itself over a given period. We will use the formula for simple interest to solve this.
Let the principal amount be \(P\).
If the sum of money doubles itself, the amount \(A\) will be \(2P\).
The simple interest \(SI\) earned is the difference between the amount and the principal:
\[ SI = A - P = 2P - P = P \]The time period \(T\) is given as 12 years.
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]where \(R\) is the rate of interest per annum.Substitute the known values into the formula:
\[ P = \frac{P \times R \times 12}{100} \]To find \(R\), we can cancel \(P\) from both sides (assuming \(P \neq 0\)):
\[ 1 = \frac{R \times 12}{100} \]Now, solve for \(R\):
\[ R = \frac{100}{12} \]Simplify the fraction:
\[ R = \frac{25}{3} \]Convert the improper fraction to a mixed fraction:
\[ R = 8 \frac{1}{3} \% \]Correct Option: B) 8 \( \frac{1}{3} \) %
A boy bought some toffee at the rate of 15 toffees for ₹3 and sold all of them at the rate of 3 toffee for ₹2. Find the gain or loss.
233 \( \frac{1}{3} \) % loss
233 \( \frac{2}{3} \) % loss
233 \( \frac{2}{3} \) % gain
233 \( \frac{1}{3} \)% gain
To find the gain or loss percentage, we need to calculate the cost price (CP) and selling price (SP) of a certain number of toffees. A common approach is to find the CP and SP of a single toffee or to equate the number of toffees bought and sold.
D) 233 \( \frac{1}{3} \)% gain
This problem involves work and time, where the efficiency of two individuals is related. We can use the concept of work rate to solve this. If A is twice as efficient as B, it means A can do twice the amount of work B does in the same amount of time, or A takes half the time B takes to complete the same work. We will express their individual work rates and then combine them to find the total work and the time A takes alone.
C) 30 days — As calculated, A alone can finish the work in 30 days.
The problem presents an analogy where we need to find the relationship between pairs of numbers. We are given two complete pairs and one incomplete pair. By analyzing the pattern in the complete pairs, we can deduce the missing number in the incomplete pair.
Both 2 and 7 are prime numbers. The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...
Starting from 2, the next prime number is 3, then 5, and then 7. So, 7 is the 3rd prime number after 2 (excluding 2 itself).
Both 23 and 37 are prime numbers.
Starting from 23, the next prime number is 29, then 31, and then 37. So, 37 is also the 3rd prime number after 23 (excluding 23 itself).
The pattern is that the second number in each pair is the 3rd prime number following the first number in the pair.
We need to find the 3rd prime number after 11.
Therefore, the missing number is 19.
Correct Option: A) 19