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Question : Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph.
A. The olive tree grows slowly yet lives a long time. B. The normal lifespan of an olive tree is 300-400 years, but olive trees as ancient as 3000 years have been discovered. C. The olive is a well-known Mediterranean-native evergreen tree whose fruit and oil are used in cuisine and cooking. D. As a result, the olive tree is known as the 'immortal tree' in mythology and botany.
Option 1: CDAB
Option 2: CABD
Option 3: DBCA
Option 4: ABCD
Correct Answer: CABD
Solution : The correct answer is the second option.
Sentence (C) introduces the olive tree and its significance in Mediterranean cuisine. The sentence (A) provides information about the growth and lifespan of the olive tree. Sentence (B) discusses the typical lifespan of an olive tree and highlights
Question : If $x+\frac{1}{x}=2 \cos \theta$, then $x^3+\frac{1}{x^3}=?$
Option 1: $2 \cos 2θ$
Option 2: $\cos 3θ$
Option 3: $2 \cos 3θ$
Option 4: $\cos 2θ$
Correct Answer: $2 \cos 3θ$
Solution : Given: $x+\frac{1}{x}=2 \cos \theta$. Cubing both sides, we get: $⇒\left(x^3+\frac{1}{x^3}\right) + 3\left(x+\frac{1}{x}\right) = 8\cos^3 \theta$ Putting the values, we get: $⇒x^3+\frac{1}{x^3} = 8\cos^3 \theta- 3(2 \cos \theta)$ $⇒x^3+\frac{1}{x^3}= 8\cos^3 \theta- 6 \cos \theta$ $⇒x^3+\frac{1}{x^3}=2(4\cos^3 \theta- 3 \cos \theta)$ $⇒x^3+\frac{1}{x^3}=2 \cos 3 \theta$ Hence,
Question : As per the UN criteria, a city qualifies as a mega city when its population is a minimum of:
Option 1: 12 million
Option 2: 15 million
Option 3: 10 million
Option 4: 5 million
Correct Answer: 10 million
Solution : The correct answer is 10 million.
A megacity refers to a highly populous urban area. As per the UN criteria, a city qualifies as a mega city when its population exceeds 10 million people. Some examples of megacities in India are Mumbai, Delhi, Kolkata,
Question : If $\cot A=\frac{12}{5}$, then the value of $(\sin A+\cos A) \times \operatorname{cosec} A$ is_____.
Option 1: $\frac{13}{5}$
Option 2: $\frac{17}{5}$
Option 3: $\frac{14}{5}$
Option 4: 1
Correct Answer: $\frac{17}{5}$
Solution : Given: $\cot A=\frac{12}{5}$ Now, $(\sin A+\cos A)×\operatorname{cosec}A$ $= (\sin A×\operatorname{cosec}A)+(\cos A×\operatorname{cosec}A)$ $= 1+\cot A$ $= (1+\frac{12}{5})$ $= \frac{17}{5}$ Hence, the correct answer is $\frac{17}{5}$.
Question : If $l+m+n=9$ and $l^{2}+m^{2}+n^{2}=31$, then the value of $(lm+mn+nl )$ will be:
Option 1: 22
Option 2: 50
Option 3: 25
Option 4: –25
Correct Answer: 25
Solution : Given: $l^{2}+m^{2}+n^{2}=31$ And $l+m+n=9$ Squaring both sides, $(l+m+n)^2=81$ ⇒ $l^2+m^2+n^2+2(lm+mn+nl)= 81$ ⇒ $31+2(lm+mn+nl) = 81$ ⇒ $2(lm+mn+nl) = 81 – 31 = 50$ Thus, $(lm+mn+nl)=\frac{50}{2}=25$ Hence, the correct answer is 25.
Question : Directions: In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows the given statements. Statements: I. All J is Y. II. No X is Y. Conclusions: I. Some X is not Y. II. Some J is not X.
Option 1: Neither conclusion follows
Option 2: Both conclusions I and II follow
Option 3: Only conclusion I follows
Option 4: Only conclusion II follows
Correct Answer: Both conclusions I and II follow
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion I: Some X is not Y – From the Venn diagram, it is evident that there is a negative relation between
Question : Which of the following countries is regarded as the home of 'Fabian Socialism '?
Option 1: Russia
Option 2: England
Option 3: France
Option 4: Italy
Correct Answer: England
Solution : The correct option is England.
England is considered as the place of origin of Fabian Socialism. The Fabian Society, which was established in 1884, was instrumental in advancing this socialist philosophy. The society preferred incremental transformation to revolutionary upheaval in order to attain its socialist
Question : Which among the following planets rotates in a direction opposite to that of the others?
Option 1: Jupiter
Option 2: Saturn
Option 3: Mercury
Option 4: Venus
Correct Answer: Venus
Solution : The correct answer is Venus.
Venus is the planet that rotates in a direction opposite to most other planets in our solar system. While most planets, including Earth, rotate counterclockwise on their axes, Venus rotates clockwise. Venus is the second planet from the Sun
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
__________ is the way to the zoo?
Option 1: What
Option 2: Which
Option 3: Where
Option 4: When
Correct Answer: Which
Solution : The correct choice is the second option "which".
''Which'' fits perfectly in the sentence. "Which" is used when asking about a specific choice or option among a group of things or directions.
The meanings of the other options are as follows:
Question : When the offices of both the President and Vice President of India are vacant, who will discharge their functions?
Option 1: The Prime Minister
Option 2: The Chief Minister
Option 3: The Chief Justice of India
Option 4: The Speaker of the Lok Sabha
Correct Answer: The Chief Justice of India
Solution : The correct answer is The Chief Justice of India.
When the offices of President and Vice President are vacant, the Chief Justice of India should discharge the functions of the President, and if the Chief Justice of India is also
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