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Question : If the third proportion to 10 and X is 90 and the third proportion of 12 and Y is 27. Find the value of (X + Y).
Option 1: 56
Option 2: 44
Option 3: 48
Option 4: 50
Correct Answer: 48
Solution : Given: Third proportion to 10 and X = 90 ⇒ 10 : X : : X : 90 ⇒ $\frac{10}{X} = \frac{X}{90}$ ⇒ $X = \sqrt{10 \times 90} = 30$ Similarly, the third proportion to 12 and Y = 27 ⇒ 12 : Y :
Question : If $l+m+n=0$, then what will be the value of $(\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})^2$?
Option 1: 9
Option 2: 16
Option 3: 4
Option 4: 1
Correct Answer: 9
Solution : Given, $l+m+n=0$ $(\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})^2$ $= (\frac{l^3+m^3+n^3}{lmn})^2$ We know, if $l+m+n=0$, then $l^3+m^3+n^3=3lmn$ $= (\frac{3lmn}{lmn})^2$ $= 9$ Hence, the correct answer is 9.
Question : Four sentences are given, out of which three have spelling errors. Choose the sentence with all the correctly spelled words.
Option 1: I don't know weather to eat it or rubb it on.
Option 2: Goodbye untill later now, foks. Have a good night.
Option 3: She always says something humerous.
Option 4: Had I known what was coming, I could have prepared myself better.
Correct Answer: Had I known what was coming, I could have prepared myself better.
Solution : The fourth option is the correct answer.
This sentence does not contain any spelling errors. All the words are spelt correctly, and the sentence is grammatically sound.
In contrast, the other sentences have various
Question : A car completed a journey of 400 km in $12\frac{1}{2}$ hours. The first $\frac{3}{4}$th of the journey was done at 30 km/hr. Calculate the speed for the rest of the journey.
Option 1: 45 km/hr
Option 2: 25 km/hr
Option 3: 40 km/hr
Option 4: 30 km/hr
Correct Answer: 40 km/hr
Solution : Total journey = 400 km Speed of the car for $\frac{3}{4}$th journey = 30 km/hr $\frac{3}{4}$th journey= $400\times(\frac{3}{4})$km = 300 km Remaining journey = 400 – 300 = 100 km Let the speed of the car for the rest of the journey be $x$
Question : Directions: If the 14th of March 2007 is Wednesday, what will be the day of the week on the 17th of June 2013?
Option 1: Thursday
Option 2: Friday
Option 3: Monday
Option 4: Saturday
Correct Answer: Monday
Solution : Given: 14th of March 2007 is Wednesday.
Let's calculate the total number of days from the 14th of March 2007 to the 17th of June 2013 –
Number of days from 14 March 2007 to 31 December 2007 = 17 + 30 + 31 +
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Primitive cultures are those that exist in societies that have not yet developed advanced technology or complex social (1)__________ These cultures are often characterised by their close relationship with the natural world. Despite being considered 'primitive', these cultures have a rich history and a unique way of life that is (2)__________ studying and preserving. These cultures often have a deep understanding of the environment and its cycles, and they have developed intricate systems of knowledge and belief that are closely tied to nature. For example, indigenous cultures in the Amazon rainforest have an (3)__________ knowledge of the medicinal properties of plants and the cycles of the seasons, which they use to sustain themselves and their communities. Another important aspect is that these cultures often have complex systems of kinship and social hierarchy. Despite many challenges that primitive cultures face, including the (4)___________ of modern societies and environmental degradation, these cultures have an important role to play in our understanding of the human experience. They offer a different (5)____________ on the world and its complexities, and their traditions and knowledge have the potential to inform and enrich our modern lives. Select the most appropriate option to fill in the blank 4.
Option 1: migration
Option 2: possession
Option 3: encroachment
Option 4: estimation
Correct Answer: encroachment
Solution : The correct choice is the third option.
Explanation: The word "encroachment" refers to the intrusion or invasion of a territory, and in the context of the passage, it accurately reflects the challenges that primitive cultures face, including the intrusion of modern societies and environmental
Question : Directions: In the following question, select the missing number from the given responses.
Option 1: 175
Option 2: 147
Option 3: 171
Option 4: 417
Correct Answer: 175
Solution : In the given figure, multiply the previous number by three and then add 1 to get the next number in the clockwise direction. 6 × 3 + 1 = 18 + 1 = 19; 19 × 3 + 1 = 57 + 1 = 58;
Question : The ratio of three numbers is 6 : 5 : 9. If 20% of the first number is 30, then what would be 50% of the difference between the third and second numbers?
Option 1: 40
Option 2: 50
Option 3: 30
Option 4: 45
Correct Answer: 50
Solution : Given that the ratio of the three numbers is 6 : 5 : 9. Let the three numbers be 6a, 5a, and 9a respectively. We know that 20% of the first number is 30. ⇒ $\frac{20}{100}$ × 6a = 30 ⇒ a = 25 The
Question : Rachit invests Rs. 12,000 for a 2-year period at a certain rate of simple interest per annum. Prasad invests Rs. 12,000 for a 2-year period at the same rate of interest per annum as Rachit, but in Prasad's case, the interest is compounded annually. Find the rate of interest per annum if Prasad receives Rs. 172.80 more as interest than Rachit at the end of the 2-year period.
Option 1: 10%
Option 2: 8%
Option 3: 12%
Option 4: 5%
Correct Answer: 12%
Solution : Given, Rachit invests Rs. 12,000 for 2 years at a certain rate of simple interest Prasad invests Rs. 12,000 for 2 years at the same interest rate per annum as Rachit, but in Prasad's case, the interest is compounded annually. Difference in interest is Rs.
Question : Comprehension: Read the passage and answer the questions. Ever wondered how efficiently the brain works on waking up in the morning, even before the system has had a chance to ingest the hot cuppa! If I could replace myself with a robot, the latter would need to train through 39 steps across different levels (kitchen platform, refrigerator, and stove), three states (solid, liquid, and gas), and manage several timed intervals between sub-tasks. Yet, once done, it will be a spectacle to watch; steps executed with such precision and dependability, will be a given. What’s more, it will address multiple tasks in an interleaved fashion by harvesting the in-betweens. The time between putting the oil in the wok and dropping the seasoning once the oil is heated, between placing the rolled chapati on the tava and flipping the partially roasted piece—such snippets of time that the human uses up to ponder will be efficiently utilised by a robot. To a robot, thinking is a challenge! But it will turn its thinking disability to its advantage. Time division multiplexing in its finest resolution will be in action. Imagine chopping a pair of beans in between flipping chapatis or shelling boiled eggs as the oil in the wok gets heated Who can give up the joy of watching a phoolka puff into a ball on the fire, each puff bringing added cheer? Yet, to a robot, it will be a sight lost in vain. For, our busybody will be placing a bottle under the water purifier to fill water when a phoolka puffs and switching off the button when the next one repeats the feat. Imagine what will happen when such a robot does come into shape. Mad with joy at gaining one hour of precious morning time, humanity will buy it. Next, the additional hour will be played with. The workaholic will add that hour to work hours. Those committed to physical well-being will hit the gym, and a handful will go jogging. Yet, soon, deeper realisations will set in. Sleeping off the extra hour will seem like a logically stable state and will be welcomed by all. Until even sleeping gets boring, in due course, the fate of my robot will be no different from that of the many fancies mankind has evolved through. The “going back to roots” movement will find a new entrant. Like the shift from refined to whole, from polished to brown, from cooked to raw, we will retrace our steps. The robot would be discarded in the e-waste bin, and we would make our way back into the kitchen. Many of the once-familiar sights and smells would then drift slowly back into our senses. Question: “Harvesting the in-betweens” refers to:
Option 1: Utilising the in-between time while multi-tasking
Option 2: The interval between many cups of tea in the course of the day.
Option 3: eating in between chores in the kitchen
Option 4: messing up the kitchen while working there.
Correct Answer: Utilising the in-between time while multi-tasking
Solution : The correct choice is the first option.
Explanation: According to the passage, harvesting the in-betweens refers to efficiently using the intervals or moments between different tasks to address multiple activities simultaneously.
Therefore, the correct answer would be: U
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