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Question : Directions: Which number from among the given options can replace the question mark (?) in the following series? 83, ?, 92, 107, 101, 116
Option 1: 81
Option 2: 89
Option 3: 91
Option 4: 98
Correct Answer: 98
Solution : Given: 83, ?, 92, 107, 101, 116
Add 9 to each term to obtain the next alternate term of the series. 83 + 9 = 92; {(?) + 9 = 107 ⇒ (?) = 107 – 9 = 98}; 92 + 9 = 101; 107
Question : If $x+\frac{1}{x}=-2$, then what is the value of $x^{17}+x^{-17}+x^{12}+x^{-12} ?(x<0)$
Option 1: –2
Option 2: –1
Option 3: 1
Option 4: 0
Correct Answer: 0
Solution : Given $x+\frac{1}{x}=-2$ $⇒x^2+1=-2x$ $⇒x^2+2x+1=0$ $⇒(x+1)^2=0$ $⇒x=-1$ Now, putting the value of $x=-1$ in $x^{17}+x^{-17}+x^{12}+x^{-12}$ we get: $=(-1)^{17}+(-1)^{-17}+(-1)^{12}+(-1)^{-12}$ $=-1-1+1+1=0$ Hence, the correct answer is 0.
Question : Study the following table and answer the question that follows. A school has four sections A, B, C, and D of Class IX students. The results of the Science and Mathematics examinations are shown in the following table.
Section A
What is the ratio of the number of students who failed in Science but passed in Mathematics of section B and section D together to the number of students of section A that passed in both subjects?
Option 1: 9 : 17
Option 2: 3 : 7
Option 3: 4 : 9
Option 4: 5 : 11
Correct Answer: 3 : 7
Solution : Number of students who failed in Science but passed in Mathematics of section B and section D together = 12 + 15 = 27 Number of students in section A passed in both subjects = 63 Ratio = 27 : 63 = 3
Question : Select the option that expresses the given sentence in passive voice.
People say Shyam is wise and honest.
Option 1: It is believed that Shyam is wise and honest.
Option 2: Let's say that Shyam is wise and honest.
Option 3: Shyam is wise and honest is said by people.
Option 4: It is said that Shyam is wise and honest.
Correct Answer: It is said that Shyam is wise and honest.
Solution : The fourth option is the correct answer.
Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject
Question : Directions: What should come in place of the question mark (?) in the given series? 71, 73, 79, ?, 89, 97
Option 2: 83
Option 3: 90
Option 4: 84
Correct Answer: 83
Solution : Given: 71, 73, 79, ?, 89, 97
The numbers given in the series are the consecutive prime numbers (starting from 71). So, the next prime number after 79 is 83.
So, 83 is the missing number of the series. Hence, the second option is correct.
Question : The following sentence has been divided into parts. One of them may contain an error. Select the part that contains the error from the given options. The investigation conducting by the research team / yielded statistically significant results / providing substantial evidence / to support the hypothesis.
Option 1: to support the hypothesis.
Option 2: yielded statistically significant results
Option 3: providing substantial evidence
Option 4: The investigation conducting by the research team
Correct Answer: The investigation conducting by the research team
Solution : The correct choice is the fourth option.
The correct structure should use the verb form that matches the subject and the tense of the sentence. Instead of "conducting", it should be "conducted" to make the sentence grammatically accurate.
The
Question : If the birth rate of a country is more than the death rate then the population will ___________.
Option 1: decrease by 50%
Option 2: decrease gradually
Option 3: increase
Option 4: remain constant
Correct Answer: increase
Solution : The correct option is to increase.
If the birth rate of a country is more than the death rate, the population of that country will increase. If the birth rate of a country is equal to the death rate, the population of that country
Question : In which state of India is the Airavatesvara temple situated?
Option 1: Tamil Nadu
Option 2: West Bengal
Option 3: Rajasthan
Option 4: Telangana
Correct Answer: Tamil Nadu
Solution : The correct answer is Tamil Nadu.
One of Tamil Nadu's most significant Shaiva temples is the Airavatesvara Temple, located in Thanjavur in Tamil Nadu and dedicated to Lord Shiva. It was built in the 8th century and is dedicated to the household deity
Question : If $a+b+c=5, a^3+b^3+c^3=85$, and $abc=25$, then find the value of $a^2+b^2+c^2-a b- bc - ca$.
Option 1: 2
Option 2: 4
Option 3: 6
Option 4: 8
Correct Answer: 2
Solution : $a+b+c=5$ Squaring both sides, ⇒ $(a+b+c)^2 = 25$ ⇒ $a^2 + b^2 + c^2 +2(ab+bc+ca) = 25 $ ⇒ $a^2 + b^2 + c^2 - ab - bc - ca + 3(ab+bc+ca) = 25$ ........(1) Now we have to find the value of $(ab +
Question : In which session of Congress was the demand of "Poorna Swaraj" accepted as the aim of the Congress?
Option 1: Calcutta
Option 2: Madras
Option 3: Nagpur
Option 4: Lahore
Correct Answer: Lahore
Solution : The correct answer is Lahore.
Purna Swaraj was established as the aim of the Indian National Congress in its Lahore Session. Jawaharlal Nehru served as the President of this session. The Indian National Congress decided to observe January 26, 1930, as Purna Swaraj Day.
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