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Question : The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be $\alpha$ and $\beta(\alpha>\beta)$. The height of the tower is $h$ units. A possible distance (in the same unit) between the points is:

Option 1: $\frac{h(\cot\beta–\cot\alpha)}{\cos(\alpha+\beta)}$

Option 2: $h(\cot\alpha–\cot\beta)$

Option 3: $\frac{h(\tan\beta–\tan\alpha)}{\tan\alpha\tan\beta}$

Option 4: $h(\cot\alpha+\cot\beta)$

Team Careers360 27th Jan, 2024

Correct Answer: $h(\cot\alpha+\cot\beta)$


Solution :
$AD=h$ unit
In $\Delta ADB$,
$\tan\alpha=\frac{AD}{BD}$
$⇒\tan\alpha=\frac{h}{BD}$
$⇒BD=h\cot\alpha$ --------------------------------------(1)
In $\Delta ADC$,
$\tan\beta=\frac{AD}{DC}$
$⇒\tan\beta=\frac{h}{DC}$
$⇒DC=h\cot\beta$ -------------------------------------(2)
Now $BC=BD+DC$
$⇒BC=h\cot\alpha+h\cot\beta$
$\therefore BC=h(\cot\alpha+\cot\beta)$
Hence, the correct answer is $h(\cot\alpha+\cot\beta)$.

43 Views

Question : Comprehension:
Read the given passage carefully and answer the questions that follow.

As the world's population approaches 8 billion and resource use intensifies, pollution is becoming more extensive, pervasive, and persistent. It affects our health through the food we eat, the water we drink, and the air we breathe. By 2025, the world's cities will produce 2.2 billion metric tonnes of waste every year, more than three times the amount produced in 2009. That said, pollution is not a new phenomenon and is largely controllable and often avoidable, as shown in some countries and cities that have succeeded in decoupling economic growth from pollution and waste accumulation.

With the end goal of eradicating all forms of pollution by 2030, the UN Environment Programme was tasked by the UN Environment Assembly to coordinate the implementation of a global plan reiterating that pollution is not only an environmental priority, it's a priority for the achievement of the Sustainable Development Goals.

Question:
Which is the best description of the tone of the passage?

Option 1: Technical

Option 2: Sarcastic

Option 3: Dogmatic

Option 4: Humanistic

Team Careers360 27th Jan, 2024

Correct Answer: Humanistic


Solution : The correct answer is the fourth option.

The best description of the tone of the passage is likely "humanistic". The passage discusses the challenges of pollution and its impact on health and the environment and emphasises the goal of eradicating all forms of pollution by

62 Views

Question : How many oxygen atoms are there in an acetone molecule?

Option 1: 3

Option 2: 1

Option 3: 2

Option 4: 4

Team Careers360 26th Jan, 2024

Correct Answer: 1


Solution : The correct option is 1.

Acetone has the molecular formula C3H6O.

  1. Carbon (C) atoms: There are 3 carbon atoms.
  2. Hydrogen (H) atoms: There are 6 hydrogen atoms.
  3. Oxygen (O) atoms: There is 1 oxygen atom.

Therefore, in 1 molecule of

14 Views

Question : Which of the following is correct?

Option 1: $\frac{2}{3}< \frac{3}{5}< \frac{11}{15}$

Option 2: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$

Option 3: $\frac{11}{15}< \frac{3}{5}< \frac{2}{3}$

Option 4: $\frac{3}{5}< \frac{11}{15}< \frac{2}{3}$

Team Careers360 27th Jan, 2024

Correct Answer: $\frac{3}{5}< \frac{2}{3}< \frac{11}{15}$


Solution : Given: The numbers are $\frac{2}{3}, \frac{3}{5}, \frac{11}{15}$.
To find the greatest fraction, we have to find the LCM of denominators.
LCM of denominators $=$ LCM $(3, 5, 15) = {(3×5)} = 15$
We have to make all denominators the same for comparison,
$

4 Views

Question : Directions: Rajiv is the brother of Arun. Sonia is the sister of Sunil. Arun is the son of Sonia. How is Rajiv related to Sunil?

Option 1: Nephew

Option 2: Son

Option 3: Brother

Option 4: Father

Team Careers360 26th Jan, 2024

Correct Answer: Nephew


Solution : As per the given information, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.

So, from the above family tree, Rajiv is the nephew of Sunil. Hence, the first option 

7 Views

Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold parts at 1, 2, and 3, which may improve the sentence. Choose the correct alternative. If no improvement is needed, your answer is 4.

The difficulty level of this problem is extremely great.

  1. perplexity
  2. hindrance
  3. intricacy
  4. No improvement

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Team Careers360 26th Jan, 2024

Correct Answer: 4


Solution : The correct choice is the fourth option.

Difficulty means a thing that is hard to accomplish, deal with or understand. It is the appropriate choice according to the context of the sentence. 

Difficulty is the correct usage, as it implies that the level of the

15 Views

Question : PARAM supercomputer belongs to which generation of computers?

Option 1: Second

Option 2: First

Option 3: Fifth

Option 4: Third

Team Careers360 26th Jan, 2024

Correct Answer: Fifth


Solution : The correct option is the Fifth.

The Indian Centre for Development of Advanced Computing (C-DAC) is the developer of the PARAM series of supercomputers. These supercomputers are from the fifth generation, and over time, several iterations of PARAM have been created.

15 Views

Question : Which union territory has a high court of its own?

Option 1: Delhi

Option 2: Andaman and Nicobar Islands

Option 3: Dadra and Nagar Haveli

Option 4: Chandigarh

Team Careers360 27th Jan, 2024

Correct Answer: Delhi


Solution : The correct answer is Delhi.

High courts play a crucial role in a state's judicial system, with 25 in the nation and four overseeing multiple states. Delhi is the only union territory with a high court. The President appoints additional judges, including the chief

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