To find the Least Common Multiple (LCM) of two numbers, we can use the prime factorization method. This involves finding the prime factors of each number and then taking the highest power of all common and uncommon prime factors.
Multiply the highest powers of all unique prime factors:
\[ \text{LCM}(88, 220) = 2^3 \times 5^1 \times 11^1 = 8 \times 5 \times 11 = 40 \times 11 = 440 \]Correct Option: C) 440
This problem involves setting up and solving a system of linear equations based on the given ratios of ages at two different points in time. We will use variables to represent the current ages and then form equations using the given ratios.
Let the current ages of the two persons be \(5x\) and \(7x\) years, respectively, based on the given ratio of \(5:7\).
18 years ago, their ages would have been \((5x - 18)\) years and \((7x - 18)\) years.
According to the problem, 18 years ago, their ages were in the ratio of \(8:13\). So, we can set up the equation:
\[ \frac{5x - 18}{7x - 18} = \frac{8}{13} \]Now, we cross-multiply to solve for \(x\):
\[ 13(5x - 18) = 8(7x - 18) \]\[ 65x - 234 = 56x - 144 \]Rearrange the terms to solve for \(x\):
\[ 65x - 56x = 234 - 144 \]\[ 9x = 90 \]\[ x = \frac{90}{9} \]\[ x = 10 \]Substitute the value of \(x\) back into the expressions for their current ages:
Thus, their current ages are 50 and 70 years.
Correct Option: B) 50 and 70 years
Insert mathematical symbols in the place of ‘?’ to get the result of the given equation as 87:
((150 ? 2) ? 2) ? 10 = 87
The problem requires us to find the correct set of mathematical symbols (+, -, ×, ÷) that, when inserted into the given equation, result in 87. We will test each option by substituting the symbols into the equation and performing the calculations following the order of operations (BODMAS/PEMDAS).
Let's test Option D: \(\div, +, +\)
Substitute the symbols into the equation:
\[ ((150 \div 2) + 2) + 10 \]Since the result is 87, Option D is the correct answer.
The question asks about the number of players selected by Hockey India for two specific tournaments: the Sultan Azlan Shah Cup and the Commonwealth Games. This is a factual recall question related to sports news, specifically hockey. To answer this, one needs to know the historical team selections made by Hockey India for these events.
C) 33. Hockey India had announced a 33-member squad for the Sultan Azlan Shah Cup and the Commonwealth Games, combining experienced players with young talent.
This is a blood relations puzzle. We need to deduce the relationship between P and Q based on the given statement. The key is to carefully break down the statement and consider all possibilities, especially when a negative condition ("NOT my brother") is present.
A) Sister — Based on the analysis, P and Q are siblings, and Q is not male (not P's brother), therefore Q must be P's sister.
The problem is a coding-decoding type question. We need to identify the pattern used to transform "PHONE" into "RJQPG" and then apply the same pattern to transform "WATER".
The pattern is to advance each letter by two positions in the English alphabet.
A) YCVGT is the correct code derived by applying the "+2" pattern to each letter of "WATER".
The time period of a vibrating body is 0.05 s. The frequency of waves it emits will be:
The problem asks us to find the frequency of waves emitted by a vibrating body, given its time period. We need to recall the fundamental relationship between the time period and frequency of a wave.
The frequency and time period are inversely proportional to each other. The formula connecting them is:
\[ f = \frac{1}{T} \]The time period of the vibrating body is given as \(T = 0.05 \text{ s}\).
Substitute the given time period into the formula:
\[ f = \frac{1}{0.05 \text{ s}} \]\[ f = \frac{1}{\frac{5}{100} \text{ s}} \]\[ f = \frac{100}{5} \text{ Hz} \]\[ f = 20 \text{ Hz} \]The calculated frequency is 20 Hz, which matches option B.
Correct Option: B) 20 Hz
The frequency of waves emitted by the vibrating body is 20 Hz, as it is the reciprocal of the given time period of 0.05 s.
132 × 16 ÷ 23 + 4 =?
We need to form 5-digit numbers using the digits 4, 5, 6, 7, 8, and 9 without repetition, such that the numbers are divisible by 4. A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
C) 168
Choose the mirror image of the following figure.
To find the mirror image of a figure, you need to reverse the orientation of the elements as if viewing them in a mirror placed vertically alongside the figure.
Correct Option: C) The circle is at the top of the vertical line, correctly representing the mirror image of the original figure.
