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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
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.
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
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
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.
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
Question : Directions: Two statements are given followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: I. All chains are circles. II. No chain is square. Conclusions: I. Some circles are square. II. Some circles are chains.
Option 1: Neither conclusion I nor II follows
Option 2: Only conclusion II follows
Option 3: Both conclusions I and II follow
Option 4: Only conclusion I follows
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some circles are square – It is a possibility that the circles representing circles and squares overlap. But this is not definite.
Question : Wood spirit is
Option 1: Methyl alcohol
Option 2: Ethyl alcohol
Option 3: Butyl alcohol
Option 4: Propyl alcohol
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
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
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.
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
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
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%
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
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
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
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
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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