Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $x+\frac{1}{x}=\mathrm{\frac{K}{2}}$, then what is the value of $\frac{x^8+1}{x^4} ?$
Option 1: $\frac{\mathrm{K}^4-16 \mathrm{~K}^2+32}{16}$
Option 2: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2-36}{32}$
Option 3: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2-32}{16}$
Option 4: $\frac{\mathrm{K}^4-8 \mathrm{~K}^2+32}{16}$
Correct Answer: $\frac{\mathrm{K}^4-16 \mathrm{~K}^2+32}{16}$
Solution : $x + \frac{1}{x} = \frac{K}{2}$ $⇒\left(x + \frac{1}{x}\right)^2 = \mathrm{\left(\frac{K}{2}\right)^2}$ $⇒x^2 + 2 + \frac{1}{x^2} = \mathrm{\frac{K^2}{4}}$ $⇒x^2 + \frac{1}{x^2} =\mathrm{ \frac{K^2}{4} - 2}$ Now, square this equation: $⇒\left(x^2 + \frac{1}{x^2}\right)^2 = \mathrm{\left(\frac{K^2}{4} - 2\right)^2}$ $⇒x^4 + 2 + \frac{1}{x^4} = \mathrm{\left(\frac{K^2}{4} - 2\right)^2}$
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.
Globalisation is not a new (1)_______. Traders travelled vast distances in ancient times to buy commodities that were (2) ______and expensive for sale in their homelands. The Industrial Revolution brought (3)_________ in transportation and communication in the 19th century that eased trade across borders. The think tank, Peterson Institute for International Economics (PIIE), states globalisation (4)________after World War I and nations moved toward (5)________ as they launched import taxes to more closely guard their industries in the aftermath of the conflict.
Select the most appropriate option to fill in the blank number 2.
Option 1: plentiful
Option 2: common
Option 3: preserved
Option 4: rare
Correct Answer: rare
Solution : The correct choice is the fourth option.
The sentence talks about traders travelling long distances to buy commodities that were not easily available or common in their homelands. The word rare fits in this context, indicating that the commodities were not commonly found or abundant
Question : The first Indian woman powerlifter who participated in the Tokyo Paralympics 2020 was:
Option 1: Arifa Bilal
Option 2: Sakina Khatun
Option 3: Manpreet Kaur
Option 4: Kunjarani Devi
Correct Answer: Sakina Khatun
Solution : The correct answer is Sakina Khatun.
The first Indian woman powerlifter to participate in the Tokyo Paralympics 2020 was Sakina Khatun. She qualified for the Games by winning the silver medal in the 45 kg category at the Para-Powerlifting World Cup in Dubai.
Question : A metallic sphere of radius 21 cm is melted and then recast into smaller cones, each with a 7 cm radius and a height of 3 cm. Find the number of cones obtained.
Option 1: 225
Option 2: 325
Option 3: 522
Option 4: 252
Correct Answer: 252
Solution : Let the number of cones made be $n$. In this case, the metallic sphere is melted and then cast into smaller cones. So, Volume of Sphere $= n\times$ Volume of cone ⇒ $\frac{4}{3}\pi r{_s}^3=n\times\frac{1}{3}\pi r{_c}^2h$ where $r_s$ is the radius of the sphere, $r_c$ is
Question : Fill in the blank with an appropriate option. Have you ever had a ______ bath using a bath wash?
Option 1: barbaric
Option 2: extinguishing
Option 3: refreshing
Option 4: killing
Correct Answer: refreshing
Solution : The correct choice is the third option.
The word "refreshing" is correct in the context of the sentence because it aligns with the positive and invigorating experience one typically associates with taking a bath using a bath wash.
The meanings of the other options are
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error."
I remember him as (1) / someone who was a lot nicer (2) / than circumstances warranted. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : The correct option is the fourth option, as there is no error in the sentence.
As it is grammatically accurate, the sentence doesn't need any change.
So, the correct sentence is, "I remember him as someone who was a lot nicer than circumstances warranted."
Question : Directions: In the given question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
Rama took his ______ for the wrong done to him.
Option 1: avenge
Option 2: vengeance
Option 3: revenge
Option 4: ravage
Correct Answer: revenge
Revenge is a noun that means to harm someone in return for a wrongdoing. This is the correct choice according to the context of the sentence, as "revenge" is used when the same person punishes someone for the
Question : Study the given table and answer the question that follows. The table shows the total score scored by 8 batsmen in the year 2022.
Who is the second-highest scorer in the year 2022?
Option 1: E
Option 2: B
Option 3: A
Option 4: H
Correct Answer: H
Solution : The second-highest scorer in the year 2022 is H with a score of 1365. Hence, the correct answer is H.
Question : Parts of the following sentence have been given as options. Select the option that contains an error.
He was that angry that he slammed the book on the table.
Option 1: that he slammed the book
Option 2: that angry
Option 3: He was
Option 4: on the table.
Correct Answer: that angry
Solution : The correct choice is the second option.
The error lies in the use of "that" before angry. It should be replaced with the adverb so, which means "to such a great degree", to make the sentence grammatically accurate and convey the intended
Question : Study the given bar graph and answer the question that follows. The production of cement (in lakh tonnes) by a company during the last six years is presented by the bar graph. What is the average cement production (in lakh tonnes) during the given six years?
Option 1: 40.0
Option 2: 39.0
Option 3: 39.5
Option 4: 40.5
Correct Answer: 39.5
Solution : Average cement production = $\frac{\text{Total production in 6 years}}{\text{Number of years}}$ Total production in 6 years = 35 + 40 + 45 + 35 + 35 + 47 = 237 ⇒ Average = $\frac{237}{6}$ = 39.5 Hence, the correct answer is 39.5.
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
Topic Tagged to the Question are not relevant to Question
Question drives traffic to external sites for promotional or commercial purposes
The Question is not relevant to User
And never miss an important update
