The sum of \( \frac{5}{11} \) and \( \frac{11}{5} \) is:
\( \frac{16}{55} \)
\( \frac{110}{55}\)
\( \frac{146}{55} \)
\( \frac{16}{16} \)
To find the sum of two fractions, we need to find a common denominator. The least common multiple (LCM) of the denominators will serve as the common denominator. Once the fractions have the same denominator, we can add their numerators.
Identify the fractions: The given fractions are \( \frac{5}{11} \) and \( \frac{11}{5} \).
Find the LCM of the denominators: The denominators are 11 and 5. Since 11 and 5 are prime numbers, their LCM is their product.
\[ \text{LCM}(11, 5) = 11 \times 5 = 55 \]
Convert each fraction to an equivalent fraction with the common denominator:
\[ \frac{5}{11} = \frac{5 \times 5}{11 \times 5} = \frac{25}{55} \]
\[ \frac{11}{5} = \frac{11 \times 11}{5 \times 11} = \frac{121}{55} \]
Add the equivalent fractions: Now that both fractions have the same denominator, add their numerators.
\[ \frac{25}{55} + \frac{121}{55} = \frac{25 + 121}{55} = \frac{146}{55} \]
Correct Option: C) The sum is \( \frac{146}{55} \), which matches the calculated result.
The question asks to identify the author of the book 'Half Girlfriend'. This is a direct factual recall question related to Indian literature and popular authors.
Correct Option: C) Chetan Bhagat is the author of the popular novel 'Half Girlfriend', which was also adapted into a Bollywood film.
The question asks to identify which common household substance contains tartaric acid. This requires knowledge of the chemical composition of the given options.
A) Baking powder
Baking powder is a mixture of sodium bicarbonate (\(\text{NaHCO}_3\)), a weak acid (often tartaric acid, cream of tartar, or monocalcium phosphate), and a starch (as a buffer). The tartaric acid reacts with sodium bicarbonate in the presence of moisture to produce carbon dioxide gas, which makes baked goods rise.
To find the number, we need to set up an equation where 63% of the unknown number is equal to 315. We can then solve for the unknown number.
Thus, the number is 500.
Correct Option: A) 500
The problem asks us to find the next term in a given numerical series. We need to identify the pattern or rule governing the sequence of numbers to predict the subsequent term.
A) 1458 — This is the correct term derived from identifying the series as a geometric progression with a common ratio of 9.
The question asks to identify the element known as "Eka-silicon". This refers to a prediction made by Dmitri Mendeleev in his periodic table.
A) Germanium is the element that was predicted as Eka-silicon by Mendeleev.
The question asks to identify the winner of the 2016 Premier Badminton League. This is a factual recall question related to sports history, specifically badminton tournaments in India. To answer this, one needs to know the results of the 2016 Premier Badminton League.
Correct Option: A) Delhi Acers won the 2016 Premier Badminton League by defeating Mumbai Rockets in the final.
The volume of a right circular cone, whose radius of the base is one-third of its altitude and the volume of a sphere are equal. The ratio of the radius of the cone to the sphere is:
\(\sqrt[3]{9}:\sqrt[3]{4}\)
1 : 1
\(\sqrt[3]{4}:\sqrt[3]{3}\)
\(\sqrt[3]{3}:\sqrt[3]{2}\)
To find the ratio of the radius of the cone to the sphere, we need to set up equations for the volumes of the cone and the sphere based on the given conditions. We will then equate these volumes and solve for the ratio of their radii.
Define variables for the cone:
Let the radius of the base of the cone be \(r_c\).
Let the altitude (height) of the cone be \(h_c\).
Use the given condition for the cone:
The radius of the base of the cone is one-third of its altitude.
So, \(r_c = \frac{1}{3} h_c\), which implies \(h_c = 3r_c\).
Write the formula for the volume of the cone:
The volume of a right circular cone, \(V_c\), is given by:
\[ V_c = \frac{1}{3} \pi r_c^2 h_c \]
Substitute \(h_c\) in terms of \(r_c\) into the volume formula: \[ V_c = \frac{1}{3} \pi r_c^2 (3r_c) \] \[ V_c = \pi r_c^3 \]
Define variables for the sphere:
Let the radius of the sphere be \(r_s\).
Write the formula for the volume of the sphere:
The volume of a sphere, \(V_s\), is given by:
\[ V_s = \frac{4}{3} \pi r_s^3 \]
Equate the volumes of the cone and the sphere:
Given that the volume of the cone and the volume of the sphere are equal, \(V_c = V_s\).
\[ \pi r_c^3 = \frac{4}{3} \pi r_s^3 \]
Solve for the ratio \(r_c : r_s\):
Cancel \(\pi\) from both sides:
\[ r_c^3 = \frac{4}{3} r_s^3 \]
Rearrange to find the ratio of cubes:
\[ \frac{r_c^3}{r_s^3} = \frac{4}{3} \]
Take the cube root of both sides:
\[ \frac{r_c}{r_s} = \sqrt[3]{\frac{4}{3}} \]
This can be written as:
\[ r_c : r_s = \sqrt[3]{4} : \sqrt[3]{3} \]
Correct Option: C) \(\sqrt[3]{4}:\sqrt[3]{3}\)
Who among the following won a gold medal at the World Weightlifting Championship 2017?
Segura Ana
Mirabai Chanu
Sukcharoen Thunya
Karanam Malleswari
The question asks to identify the weightlifter who won a gold medal at the World Weightlifting Championship in 2017. This requires knowledge of significant sporting achievements, particularly those of Indian athletes, in international competitions.
In 2017, Mirabai Chanu won a gold medal at the World Weightlifting Championship held in Anaheim, USA. She competed in the women's 48 kg category, lifting a total of 194 kg (85 kg in snatch and 109 kg in clean & jerk).
B) Mirabai Chanu — Mirabai Chanu indeed won a gold medal at the 2017 World Weightlifting Championship in the women's 48 kg category, making her the second Indian weightlifter after Karnam Malleswari to achieve this feat.
Which does NOT belong to this group?
A.Rack
B.Window
C.Door
D.Shutter
The question asks to identify the item that does not belong to the group. We need to find a common characteristic among three of the items and identify the one that lacks this characteristic.
Correct Option: B) A. Rack is the item that does not belong to the group because it is a storage unit, whereas Window, Door, and Shutter are all elements related to openings in a building structure.