The question asks to identify the winner of the ICC Women's World Twenty20 Championship in 2016. This requires knowledge of past major cricket tournament results.
Correct Option: A) West Indies won the ICC Women's World Twenty20 Championship in 2016 by defeating Australia in the final.
The question states that two numbers are respectively 40% and 60% more than a third number. We need to express both numbers in terms of the third number and simplify their ratio to determine the ratio of the first number to the second number.
Identify the given information:
Assume the value of the third number:
For easier calculation, let the third number be 100.
Both percentage increases are calculated using this same number.
Calculate the first number:
The first number is 40% more than 100.
\[ \text{First Number}=100+\frac{40}{100}\times100 \] \[ =100+40 \] \[ =140 \]Therefore, the first number is 140.
Calculate the second number:
The second number is 60% more than 100.
\[ \text{Second Number}=100+\frac{60}{100}\times100 \] \[ =100+60 \] \[ =160 \]Therefore, the second number is 160.
Calculate the required ratio:
The ratio of the first number to the second number is:
\[ 140:160 \]Dividing both terms by their HCF, which is 20:
\[ \frac{140}{20}:\frac{160}{20} \] \[ =7:8 \]Therefore, the required ratio is 7:8.
Correct Option: D) 7:8 — Assuming the third number is 100, the first number is 140 and the second number is 160. Therefore, their ratio is:
\[ 140:160=7:8 \]
Hence, Option D is the correct answer.
A) 7:9: This is incorrect because the two numbers are 140 and 160, whose simplified ratio is 7:8, not 7:9.
B) 8:9: This is incorrect because the given percentage increases produce a ratio of 140:160, which simplifies to 7:8.
C) 8:7: This is incorrect because it reverses the required ratio. The first number is smaller than the second number, so the correct ratio is 7:8.
The problem asks us to find the missing number in a given series. We need to identify the pattern or rule that governs the sequence of numbers and then apply it to find the missing term.
A) 20 — The pattern of differences between consecutive terms is an arithmetic progression: 4, 6, 8, 10, 12, 14. Adding 8 to 12 gives 20.
The problem asks us to determine the meaning of the code word 'sen'. We are given two statements, and we need to evaluate if either statement alone or both statements together are sufficient to answer the question. This is a common type of data sufficiency question in competitive exams, often involving coding-decoding logic.
D) Both statements I and II together are necessary
As shown in the step-by-step analysis, neither statement alone provides enough information to uniquely identify what 'sen' stands for. However, by combining both statements, we can identify the common word 'you' and the common code 'sen', thus establishing that 'sen' stands for 'you'.
HCF of \( \frac{12}{5} \), \( \frac{21}{6} \), \( \frac{9}{4} \), and \( \frac{18}{3} \) is:
\( \frac{1}{20} \)
\( \frac{3}{2} \)
\( \frac{3}{5} \)
\( \frac{3}{7} \)
To find the HCF (Highest Common Factor) of fractions, we use the formula: \[\text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}}\]. We will first simplify the given fractions if possible, then find the HCF of their numerators and the LCM of their denominators.
Simplify the given fractions:
So, the fractions are \[\frac{12}{5}, \frac{7}{2}, \frac{9}{4}, \frac{6}{1}\].
Find the HCF of the numerators:
The numerators are \(12, 7, 9, 6\).
Factors of \(12\): \(1, 2, 3, 4, 6, 12\)
Factors of \(7\): \(1, 7\)
Factors of \(9\): \(1, 3, 9\)
Factors of \(6\): \(1, 2, 3, 6\)
The only common factor among \(12, 7, 9, 6\) is \(1\).
Therefore, \(\text{HCF}(12, 7, 9, 6) = 1\).
Find the LCM of the denominators:
The denominators are \(5, 2, 4, 1\).
To find the LCM, we can list multiples or use prime factorization.
Prime factorization:
\(5 = 5^1\)
\(2 = 2^1\)
\(4 = 2^2\)
\(1 = 1\)
\(\text{LCM}(5, 2, 4, 1) = 2^2 \times 5^1 = 4 \times 5 = 20\).
Calculate the HCF of the fractions:
\[ \text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{1}{20} \]
Correct Option: A) \( \frac{1}{20} \) is the HCF of the given fractions, as calculated by finding the HCF of the numerators and the LCM of the denominators.
We are given the initial ratio of boys to girls and information about an increase in the number of boys. We need to find the initial number of girls. We can set up algebraic expressions for the number of boys and girls based on the given ratio, then use the percentage increase information to form an equation and solve for the unknown.
Define initial numbers: Let the initial number of boys be \(4x\) and the initial number of girls be \(5x\), based on the given ratio of 4:5.
Calculate the new number of boys: Four new boys joined the class, so the new number of boys is \(4x + 4\).
Relate the increase to the percentage: The number of boys increased by 20%. This means the new number of boys is \(120\%\) of the original number of boys.
So, we can write the equation:
\[ 4x + 4 = 4x \times \left(1 + \frac{20}{100}\right) \]\[ 4x + 4 = 4x \times \left(1 + 0.20\right) \]\[ 4x + 4 = 4x \times 1.2 \]Solve for \(x\):
\[ 4x + 4 = 4.8x \]\[ 4 = 4.8x - 4x \]\[ 4 = 0.8x \]\[ x = \frac{4}{0.8} \]\[ x = \frac{40}{8} \]\[ x = 5 \]Find the number of girls: The number of girls was initially \(5x\).
Substitute the value of \(x\):
\[ \text{Number of girls} = 5 \times 5 = 25 \]Correct Option: D) The number of girls in the class is 25.
The question asks to identify which of the given compounds is insoluble in water. This requires knowledge of the solubility rules for ionic compounds, particularly those involving carbonates and halides of alkali and alkaline earth metals.
A) Calcium Carbonate is insoluble in water. This aligns with the general solubility rule that most carbonates are insoluble, with alkali metal carbonates being the primary exception. Calcium is an alkaline earth metal, not an alkali metal.
The question asks about the tool used by a computer to convert a procedure-oriented language program (like C, C++, Java) into a machine language program (binary code that the CPU can understand). This process is known as compilation or interpretation.
Correct Option: C) Compiler
A compiler is a software program that translates source code written in a high-level programming language (like C, C++, Java) into machine code or another intermediate code that a computer's processor can execute. It translates the entire program before execution.
This problem can be solved using the concept of work rates. We will calculate the individual work rate of X and the combined work rate of X and Y. Then, we can find Y's individual work rate and use it to determine the number of days Y alone would take to complete the work.
Define Work Rates:
If a person can complete a work in \(N\) days, their one-day work rate is \(\frac{1}{N}\) of the total work.
Calculate Combined Work Rate of X and Y:
X and Y together complete the work in 15 days. So, their combined one-day work rate is:
\[ (\text{X} + \text{Y})'s \text{ one-day work} = \frac{1}{15} \]Calculate Work Rate of X:
X alone can complete the work in 30 days. So, X's one-day work rate is:
\[ \text{X}'s \text{ one-day work} = \frac{1}{30} \]Calculate Work Rate of Y:
The one-day work of Y can be found by subtracting X's one-day work from the combined one-day work of X and Y:
\[ \text{Y}'s \text{ one-day work} = (\text{X} + \text{Y})'s \text{ one-day work} - \text{X}'s \text{ one-day work} \]\[ \text{Y}'s \text{ one-day work} = \frac{1}{15} - \frac{1}{30} \]Perform the Subtraction:
To subtract the fractions, find a common denominator, which is 30:
\[ \text{Y}'s \text{ one-day work} = \frac{2}{30} - \frac{1}{30} \]\[ \text{Y}'s \text{ one-day work} = \frac{2-1}{30} \]\[ \text{Y}'s \text{ one-day work} = \frac{1}{30} \]Determine Days Y Takes to Complete the Work:
If Y's one-day work is \(\frac{1}{30}\) of the total work, then Y alone will take the reciprocal of this rate to complete the entire work:
\[ \text{Days Y takes} = \frac{1}{\text{Y}'s \text{ one-day work}} = \frac{1}{\frac{1}{30}} = 30 \text{ days} \]C) 30 days — As calculated, Y alone will take 30 days to complete the same work.
The question asks to identify which substance is NOT secreted by the stomach as a component of gastric juice. Gastric juice is a mixture of various secretions from the gastric glands in the stomach lining, essential for digestion.
B) Sulphuric acid. The stomach secretes hydrochloric acid (HCl), which is a strong acid, but it does not secrete sulphuric acid (\(H_2SO_4\)). Sulphuric acid is not a biological component of gastric juice.