The question asks to identify the award received by the book 'Soul of a New Machine'. This requires knowledge of famous literary awards and the works that have won them.
Correct Option: D) Pulitzer
The question asks to identify the largest compartment of the stomach in hoofed animals, specifically ruminants. Ruminants have a unique digestive system with a multi-compartmented stomach, each serving a specific function in breaking down plant material.
B) Rumen — The rumen is the largest compartment of the stomach in ruminant animals, serving as the primary site for microbial fermentation of ingested plant material.
The question asks to identify the first Indian newspaper that made its content available on the Internet. This requires knowledge of the history of Indian newspapers and their adoption of digital platforms.
Correct Option: B) The Hindu
The Hindu was the first Indian newspaper to launch an online edition in 1995. This marked a significant step in the digitalization of news media in India, making its content accessible to a global audience via the Internet.
Rama can finish a task in 50 days. He worked for 10 days then Ravi finished the remaining task alone in 32 days. How much time will Rama and Ravi take, working together, to finish the task?
24 \( \frac{2}{9} \) days
22 \( \frac{2}{9} \) days
22 \( \frac{4}{9} \) days
24 \( \frac{1}{9} \) days
This problem involves work and time. We need to determine the individual work rates of Rama and Ravi, then combine them to find their joint work rate and the time taken to complete the task together.
Rama can finish a task in 50 days. So, in one day, Rama completes:
\[ \text{Rama's 1-day work} = \frac{1}{50} \text{ of the task} \]Rama worked for 10 days. The amount of work he completed is:
\[ \text{Work done by Rama} = 10 \times \frac{1}{50} = \frac{10}{50} = \frac{1}{5} \text{ of the task} \]The total work is 1. The remaining work after Rama worked for 10 days is:
\[ \text{Remaining work} = 1 - \frac{1}{5} = \frac{4}{5} \text{ of the task} \]Ravi finished the remaining \(\frac{4}{5}\) of the task in 32 days. So, Ravi's 1-day work rate is:
\[ \text{Ravi's 1-day work} = \frac{\frac{4}{5}}{32} = \frac{4}{5 \times 32} = \frac{4}{160} = \frac{1}{40} \text{ of the task} \]When working together, their daily work rates add up:
\[ \text{Combined 1-day work} = \text{Rama's 1-day work} + \text{Ravi's 1-day work} \]\[ \text{Combined 1-day work} = \frac{1}{50} + \frac{1}{40} \]\[ \text{Combined 1-day work} = \frac{4}{200} + \frac{5}{200} = \frac{9}{200} \text{ of the task} \]If they complete \(\frac{9}{200}\) of the task in one day, the total time to complete the entire task (1 unit of work) is the reciprocal of their combined daily work rate:
\[ \text{Time taken together} = \frac{1}{\text{Combined 1-day work}} = \frac{1}{\frac{9}{200}} = \frac{200}{9} \text{ days} \]Divide 200 by 9:
\[ 200 \div 9 = 22 \text{ with a remainder of } 2 \]\[ \text{Time taken together} = 22 \frac{2}{9} \text{ days} \]B) 22 \(\frac{2}{9}\) days
To find the speed of the cyclist in km/h, we first need to convert the given distance to kilometers and the given time to hours. Then, we use the formula \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\) to calculate the speed.
The given distance is 650 m.
\[ 1 \text{ km} = 1000 \text{ m} \]\[ \text{Distance in km} = \frac{650}{1000} \text{ km} = 0.65 \text{ km} \]The given time is 2 min 10 s.
\[ 1 \text{ min} = 60 \text{ s} \]\[ 2 \text{ min} = 2 \times 60 \text{ s} = 120 \text{ s} \]\[ \text{Total time in seconds} = 120 \text{ s} + 10 \text{ s} = 130 \text{ s} \]\[ 1 \text{ hour} = 3600 \text{ s} \]\[ \text{Time in hours} = \frac{130}{3600} \text{ hours} \]Using the formula \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\)
\[ \text{Speed} = \frac{0.65 \text{ km}}{\frac{130}{3600} \text{ hours}} \]\[ \text{Speed} = \frac{0.65 \times 3600}{130} \text{ km/h} \]\[ \text{Speed} = \frac{2340}{130} \text{ km/h} \]\[ \text{Speed} = 18 \text{ km/h} \]Correct Option: B) 18
If the height of a pole is 6\(\sqrt{3}\) m and the length of its shadow is 6 m, then the angle of elevation of the sun is:
This problem involves trigonometry, specifically the tangent function, to find the angle of elevation. We are given the height of a pole and the length of its shadow, which form a right-angled triangle with the angle of elevation of the sun.
Let the height of the pole be \(h\) and the length of its shadow be \(l\). Let the angle of elevation of the sun be \(\theta\).
From the problem statement, we have:
Height of the pole, \(h = 6\sqrt{3}\) m
Length of the shadow, \(l = 6\) m
In the right-angled triangle formed by the pole, its shadow, and the line of sight from the tip of the shadow to the top of the pole, the height of the pole is the 'opposite' side to the angle \(\theta\), and the length of the shadow is the 'adjacent' side to the angle \(\theta\).
We can use the tangent function, which is defined as:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]Substitute the given values into the formula:
\[ \tan(\theta) = \frac{h}{l} = \frac{6\sqrt{3}}{6} \]Simplify the expression:
\[ \tan(\theta) = \sqrt{3} \]Now, we need to find the angle \(\theta\) whose tangent is \(\sqrt{3}\). We know that:
\[ \tan(60^\circ) = \sqrt{3} \]Therefore, the angle of elevation of the sun is \(60^\circ\).
B) 60° is the correct answer because the tangent of the angle of elevation is the ratio of the height of the pole to the length of its shadow, which calculates to \(\sqrt{3}\). The angle whose tangent is \(\sqrt{3}\) is \(60^\circ\).
A box contains 2 black, 6 green and 4 yellow balls. If 2 balls are picked up at random, the probability that both are green is:
\( \frac{1}{22} \)
\( \frac{1}{6} \)
\( \frac{3}{11} \)
\( \frac{5}{22} \)
To solve this problem, we need to calculate the probability of picking two green balls from a box containing balls of different colors. This involves using combinations, specifically the formula for combinations \(C(n, k) = \frac{n!}{k!(n-k)!}\), where \(n\) is the total number of items, and \(k\) is the number of items to choose.
Calculate the total number of ways to pick 2 balls from 12 balls: This is a combination problem, as the order of picking the balls does not matter.
\[ \text{Total ways to pick 2 balls} = C(12, 2) = \frac{12!}{2!(12-2)!} = \frac{12!}{2!10!} = \frac{12 \times 11}{2 \times 1} = 6 \times 11 = 66 \]Calculate the number of ways to pick 2 green balls from 6 green balls:
\[ \text{Ways to pick 2 green balls} = C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2!4!} = \frac{6 \times 5}{2 \times 1} = 3 \times 5 = 15 \]Calculate the probability that both balls picked are green: Probability is defined as the ratio of favorable outcomes to the total possible outcomes.
\[ \text{Probability (both green)} = \frac{\text{Ways to pick 2 green balls}}{\text{Total ways to pick 2 balls}} = \frac{15}{66} \]Simplify the probability: Divide both the numerator and the denominator by their greatest common divisor, which is 3.
\[ \frac{15}{66} = \frac{15 \div 3}{66 \div 3} = \frac{5}{22} \]D) \( \frac{5}{22} \) is the correct probability that both balls picked are green.
This problem involves calculating successive profit percentages. We need to find the selling price of the horse from A to B, and then from B to C. The amount paid by C will be the final selling price after two transactions.
A bought the horse for ₹4,500 and sold it to B at a profit of 5%.
\[ \text{Profit for A} = 5\% \text{ of } \text{₹}4,500 \]\[ \text{Profit for A} = \frac{5}{100} \times 4500 = \text{₹}225 \]
\[ \text{Selling Price (A to B)} = \text{Cost Price for A} + \text{Profit for A} \]
\[ \text{Selling Price (A to B)} = 4500 + 225 = \text{₹}4,725 \]
So, B bought the horse for ₹4,725.
B bought the horse for ₹4,725 and sold it to C at a gain (profit) of 20%.
\[ \text{Profit for B} = 20\% \text{ of } \text{₹}4,725 \]
\[ \text{Profit for B} = \frac{20}{100} \times 4725 = \frac{1}{5} \times 4725 = \text{₹}945 \]
\[ \text{Selling Price (B to C)} = \text{Cost Price for B} + \text{Profit for B} \]
\[ \text{Selling Price (B to C)} = 4725 + 945 = \text{₹}5,670 \]
The amount paid by C to purchase the horse is ₹5,670.
D) ₹5,670 is the correct amount paid by C, as calculated through the successive profit percentages.
The question asks to identify the planet known as 'Earth's Twin'. This nickname is given to a planet that shares significant similarities with Earth in terms of size, mass, and composition. We need to evaluate the characteristics of each option provided.
Correct Option: C) Venus is known as 'Earth's Twin' due to its similar size, mass, density, and volume to Earth.
The question asks about the starting and ending points of the human digestive process. To answer this, we need to recall the journey of food through the alimentary canal and where significant chemical digestion begins and concludes.
A) mouth; small intestine — This option correctly identifies the mouth as the starting point of digestion (both mechanical and chemical) and the small intestine as the primary site where the digestion of all major food components is completed and absorption takes place.