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Question : If $\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)^2=9$, then what is the value of $\mathrm{k}^3+\frac{1}{\mathrm{k}^3} ?$

Option 1: 27

Option 2: 18

Option 3: 15

Option 4: 21

Team Careers360 25th Jan, 2024

Correct Answer: 18


Solution : $\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)^2=9$ 
$⇒\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right) = 3$
$⇒\left(\mathrm{k}+\frac{1}{\mathrm{k}}\right)^3 = 3^3$
$⇒\mathrm{k}^3+ \frac{1}{\mathrm{k}^3}+3×\mathrm{k}×\frac{1}{\mathrm{k}}(\mathrm{k}+\frac{1}{\mathrm{k}})=27$
$⇒ \mathrm{k}^3 + \frac{1}{\mathrm{k}^3}=27- 3(\mathrm{k} + \frac{1}{\mathrm{k}} )$
$⇒\mathrm{k}^3 + \frac{1}{\mathrm{k}^3} = 27 - 3\times3$
$⇒\mathrm{k}^3 + \frac{1}{\mathrm{k}^3}=18$
Hence, the correct answer is 18.

27 Views

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.
The solar system is made up of the sun, planets, moons, asteroids, and comets that 1.______ around it. Its mysteries and wonders have captured the imagination of people from all walks of life, and it continues to be an area of active research and exploration. The sun is at the centre of the solar system and is the largest object in it. The eight planets in the solar system, 2._________ Earth, orbit around the sun in nearly circular paths. While the sun is at the centre of the solar system and dominates its gravitational pull, each planet has its own unique set of characteristics that makes it a fascinating object to study. Each planet in the solar system has unique characteristics and features. 3._________ planets, such as Mercury and Venus, are small and rocky, while others, like Jupiter and Saturn, are much larger and made up mostly of gas. The outer planets, Uranus and Neptune, are 4._______ as 'ice giants' because they contain more water, ammonia, and methane than the gas giants. In addition to the planets, the solar system also has numerous moons, asteroids, and comets. These objects provide important 5.______ about the formation and evolution of the solar system.
Question:
Select the most appropriate option to fill in the blank 2.

Option 1: excluding

Option 2: diluting

Option 3: dissolving

Option 4: including

Team Careers360 24th Jan, 2024

Correct Answer: including


Solution : The most appropriate option is the fourth option.

Explanation: Including means to contain as part of a whole. In this context, it implies that among the eight planets in the solar system, Earth is one of them. "The eight planets in the solar system, including

88 Views

Question : Select the option that expresses the given sentence in active voice.

Because of his caring nature, he is appreciated by all.

Option 1: Because of his caring nature all appreciate him.

Option 2: Because of his caring nature everyone appreciate him.

Option 3: Because of his caring nature all will appreciate him.

Option 4: Because of his caring nature, all appreciated him.

Team Careers360 24th Jan, 2024

Correct Answer: Because of his caring nature all appreciate him.


Solution : The first option is the correct choice.

Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.

The

10 Views

Question : Wood spirit is 

Option 1: Methyl alcohol 

Option 2: Ethyl alcohol 

Option 3: Butyl alcohol 

Option 4: Propyl alcohol 

Team Careers360 24th Jan, 2024

Correct Answer: Methyl alcohol 


Solution : The correct option is - Methyl alcohol 

Other names for methanol include methyl alcohol, wood alcohol, and wood spirits and its chemical formula is CH3OH. It got the name "wood alcohol" because, in the past, it was mostly produced as a byproduct

14 Views

Question : If $\left(x-\frac{1}{x-2}\right)=7$, then the value of $(x-2)^3-\frac{1}{(x-2)^3}$ is:

Option 1: 130

Option 2: 115

Option 3: 140

Option 4: 125

Team Careers360 25th Jan, 2024

Correct Answer: 140


Solution : Given:
$\left(x-\frac{1}{x-2}\right)=7$
⇒ $\left(x-2-\frac{1}{x-2}\right)=5$
⇒ $\left(x-2-\frac{1}{x-2}\right)^3=5^3$
⇒ $(x-2)^3 - (\frac{1}{x-2})^3-3×(x-2)×(\frac{1}{x-2})\left(x-2-\frac{1}{x-2}\right)=125$
⇒ $(x-2)^3 - (\frac{1}{x-2})^3=125+(3×5)$
$\therefore (x-2)^3 - (\frac{1}{x-2})^3=140$
Hence, the correct answer is 140.

20 Views

Question : The Bailadila range of Chhattisgarh is famous for which of the following minerals?

Option 1: Copper

Option 2: Bauxite

Option 3: Iron ore

Option 4: Coal

Team Careers360 24th Jan, 2024

Correct Answer: Iron ore


Solution : The correct answer is Iron ore.

Bailadila is a hill range in Chhattisgarh and is famous for producing iron. The iron produced is used for manufacturing steel. Bailadila's name is due to its shape, like that of the mound of a bull. Bailadila is

50 Views

Question : If the area of a square is decreased by 19%, then the diagonal of the square is decreased by:

Option 1: 10%

Option 2: 15%

Option 3: 5%

Option 4: 12%

Team Careers360 25th Jan, 2024

Correct Answer: 10%


Solution : Use: Length of a diagonal in a square = $\sqrt2$ × side of the square
Let the side of the square be 10 cm.
Area of square = 10 × 10 = 100 cm2
Diagonal of the square = $10\sqrt{2}$ cm
Now,
Decrease in

26 Views

Question : The waste water management technique that involves the use of micro - organisms to remove or neutralize pollutants from contaminated site is called:

Option 1: Bio sensor

Option 2: Bio magnification

Option 3: Bio remediation

Option 4: Bio concentration

Team Careers360 25th Jan, 2024

Correct Answer: Bio remediation


Solution : The correct option is Bioremediation.

The approach of waste water management that involves the employment of microorganisms to remove or neutralise contaminants from polluted places is known as "bioremediation". Bioremediation uses microorganisms' inherent metabolic activities to break down or change contaminants into less dangerous

27 Views

Question : Directions: A man walks from a point towards the south. He turns right at the right angle, then turns right again at the right angle. In what direction is he walking now?

Option 1: West

Option 2: North

Option 3: South

Option 4: East

Team Careers360 24th Jan, 2024

Correct Answer: North


Solution : First, we will draw the diagram as per the given instructions –

Therefore, from the above diagram, it is clear that the man is walking North. Hence, the second option is correct.

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