The HCF of \( \frac{9}{10} \), \( \frac{3}{25} \), \( \frac{6}{15} \) and \( \frac{12}{5} \) is:
\( \frac{1}{150} \)
\( \frac{1}{50} \)
\( \frac{9}{50} \)
\( \frac{3}{70} \)
To find the HCF (Highest Common Factor) of fractions, we use the formula:
\[ \text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} \]First, identify the numerators and denominators of the given fractions:
Calculate the HCF of the numerators (\( 9, 3, 6, 12 \)):
Calculate the LCM (Least Common Multiple) of the denominators (\( 10, 25, 15, 5 \)):
Apply the formula for HCF of fractions:
\[ \text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{3}{150} \]Simplify the resulting fraction:
\[ \frac{3}{150} = \frac{1}{50} \]B) \( \frac{1}{50} \) is the correct HCF of the given fractions.
The question asks for the definition of "spam." This is a fundamental concept in computer literacy and internet usage, commonly tested in competitive exams. We need to identify the option that accurately describes spam.
Based on this evaluation, "unsolicited e-mail" is the most accurate and direct definition of spam among the given options.
Correct Option: A) unsolicited e-mail
The question asks to identify the Schedule of the Indian Constitution that deals with the division of powers between the Union (Central) government and the State governments. This is a direct factual question about the Schedules of the Indian Constitution.
C) VII
The Seventh Schedule of the Indian Constitution contains three lists that define and allocate powers between the Union and the States:
The question asks to identify the animal with a three-chambered heart from the given options. This requires knowledge of the circulatory systems of different animal groups, specifically the number of heart chambers in amphibians, fish, birds, and cartilaginous fish.
Correct Option: A) Salamander has a three-chambered heart, typical of amphibians. Its heart consists of two atria and one ventricle, leading to incomplete double circulation.
The question asks about the specific year when the number of overs in a Cricket World Cup tournament was first reduced to 50. This is a factual question related to the history of the Cricket World Cup.
Correct Option: B) 1987. The 1987 Cricket World Cup was the first tournament to feature 50 overs per innings, a format that has been maintained ever since.
Atulit has 100 apples. He gave 10% of the apples to Arnav, 15% of the apples to Keshav and \( \frac{2}{5} \) th of the apples to Rinku. How many apples are left with Atulit after distribution?
To find the number of apples left with Atulit, we need to calculate the total number of apples distributed to Arnav, Keshav, and Rinku, and then subtract this total from the initial number of apples Atulit had.
Correct Option: C) 35
The problem presents a series of letter-clusters. To find the missing cluster, we need to identify the pattern in the progression of each letter's position within the English alphabet.
The pattern for the first letter is a consecutive alphabetical increment. So, the next letter should be H (8th letter).
The pattern for the second letter is also a consecutive alphabetical increment. So, the next letter should be T (20th letter).
The pattern for the third letter is a consecutive alphabetical increment, wrapping around from Z to A. So, the next letter should be B (2nd letter).
Based on the patterns identified:
The next letter-cluster in the series is HTB.
Correct Option: C) HTB
The question asks for the original language in which Babur's autobiography, Tuzuk-i-Baburi (also known as Baburnama), was written. This requires knowledge of the historical context of Babur and the languages prevalent during his time.
Correct Option: B) Tuzuk-i-Baburi/Baburnama was originally written in Chagatai Turkic. It is a significant work of Chagatai literature and provides valuable insights into Babur's life, observations, and the history of the region.
To find the area of the rectangle, we first need to determine its length and width. We are given two pieces of information: the relationship between length and width, and the perimeter of the rectangle. We will use these to set up equations and solve for the dimensions.
Let the width of the rectangle be \(w\) cm.
According to the problem, the length is 1 cm more than its width. So, the length \(l\) will be:
\[ l = w + 1 \]The perimeter \(P\) of a rectangle is given by the formula \(P = 2(l + w)\).
We are given that the perimeter is 14 cm. Substitute the values into the formula:
\[ 14 = 2((w + 1) + w) \]Simplify the equation:
\[ 14 = 2(2w + 1) \]\[ 14 = 4w + 2 \]\[ 14 - 2 = 4w \]\[ 12 = 4w \]\[ w = \frac{12}{4} \]\[ w = 3 \text{ cm} \]Now that we have the width, we can find the length:
\[ l = w + 1 \]\[ l = 3 + 1 \]\[ l = 4 \text{ cm} \]The area \(A\) of a rectangle is given by the formula \(A = l \times w\).
Substitute the calculated length and width:
\[ A = 4 \text{ cm} \times 3 \text{ cm} \]\[ A = 12 \text{ cm}^2 \]Correct Option: D) 12 cm²
If x = \( \frac{y}{2} \) and y = \( \frac{z}{6} \), then x : y : z is equal to:
To find the ratio \(x : y : z\), we need to express \(x\), \(y\), and \(z\) in terms of a common variable or find their proportional relationship. We are given two equations relating these variables.
We are given the first equation:
\[ x = \frac{y}{2} \]From this, we can express the ratio of \(x\) to \(y\):
\[ \frac{x}{y} = \frac{1}{2} \implies x : y = 1 : 2 \]We are given the second equation:
\[ y = \frac{z}{6} \]From this, we can express the ratio of \(y\) to \(z\):
\[ \frac{y}{z} = \frac{1}{6} \implies y : z = 1 : 6 \]Now we have two ratios: \(x : y = 1 : 2\) and \(y : z = 1 : 6\). To combine these into a single ratio \(x : y : z\), we need to make the common term, \(y\), the same in both ratios.
In the first ratio, \(x : y = 1 : 2\), the value of \(y\) is 2.
In the second ratio, \(y : z = 1 : 6\), the value of \(y\) is 1. To make it 2, we multiply the entire ratio by 2:
\[ y : z = (1 \times 2) : (6 \times 2) = 2 : 12 \]Now we have:
Since the value of \(y\) is now 2 in both ratios, we can combine them directly.
Therefore, the combined ratio is \(x : y : z = 1 : 2 : 12\).
C) The step-by-step calculation shows that \(x : y : z = 1 : 2 : 12\).