Staff Selection Commission Combined Graduate Level Exam
Question : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:
Option 1: $\frac{2}{7}$
Option 2: $\frac{7}{8}$
Option 3: $\frac{7}{2}$
Option 4: $\frac{8}{7}$
Correct Answer: $\frac{7}{8}$
Solution : Given: $2x+\frac{2}{x}=3$ ⇒ $x+\frac{1}{x}=\frac{3}{2}$ (Dividing both sides by 2) Now, $(x+\frac{1}{x})^3=(\frac{3}{2})^3$ (Taking cube on both sides) ⇒ $x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})=\frac{27}{8}$ ⇒ $x^3+\frac{1}{x^3}+3(\frac{3}{2})=\frac{27}{8}$ ⇒ $x^3+\frac{1}{x^3}=\frac{27}{8}–\frac{9}{2}$ ⇒ $x^3+\frac{1}{x^3}+2=\frac{27}{8}–\frac{9}{2}+2=\frac{27–36+16}{8}=\frac{7}{8}$ Hence, the correct answer is = $\frac{7}{8}$.
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: CBED
Option 2: JILK
Option 3: TSVU
Option 4: VZXY
Correct Answer: VZXY
Solution : Let's check the options – First option: CBED; C – 1 = B; B + 3 = E; E – 1 = D Second option: JILK; J – 1 = I; I + 3 = L; L – 1 = K Third option: TSVU; T
Question : Select the most appropriate ANTONYM of the underlined word.
The antonym of a word is sometimes a prefix added to the actual word.
Option 1: metaverse
Option 2: synonym
Option 3: symphony
Option 4: metonymy
Correct Answer: synonym
Solution : The second option is correct.
Explanation: In this case, the antonym is synonym, the word itself. A synonym is a word that has the same or similar meaning as another word, while an antonym is a word that has the opposite meaning.
Question : Directions: The table given below shows the number of applicants who have applied for exams at various centres as a percentage of the total number of applicants. The table also shows the number of online applicants and absent applicants as a percentage of the total applicants for each centre. The total number of applicants is 12,00,000.
What is the ratio of the total number of present applicants from exam centre K to the total number of offline applicants from exam centre J?
Option 1: 40 : 41
Option 2: 80 : 81
Option 3: 10 : 9
Option 4: 7 : 11
Correct Answer: 80 : 81
Solution : The total number of applicants is 12,00,000. For exam centre K, The total number of applicants = 16% of 12,00,000 = 1,92,000 The number of absent applicants = 20% of 1,92,000 = 38,400 The number of present applicants = 1,92,000 – 38,400 =
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".
Due to his negligence, (1) / he failed (2) / in the examination. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : The correct choice is the fourth option.
There is no error in the sentence as the sentence structure is grammatically correct since it follows the format of subject + verb + object indicating that this is meaningful.
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.
A marketplace is always abuzz with activity. It is especially (1)_________a visit in the evenings. A (2)______range of items is on display. (3) __________and getting a satisfactory (4) __________give the necessary sense of (5) ___________to the bored housewife and bring a smile (6) _________her face. People from all (7) __________of life, rich and poor, (8) ___________shoulders with each other. From their busy (9). __________, here people find time to (10) __________a greeting with friends or neighbours.
Question: Select the most appropriate option to fill in the blank number 9.
Option 1: pattern
Option 2: system
Option 3: schedule
Option 4: custom
Correct Answer: schedule
Solution : The correct choice is the third option.
In this context, schedule implies that people take time out of their busy routines to exchange greetings with friends or neighbours at the marketplace.
It highlights the social aspect of the marketplace, where individuals from various walks of
Question : Directions: Select the option figure in which the given figure is embedded. (Rotation is NOT allowed)
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of the question figure with all the option figures, the given question figure is embedded only in the third option figure.
Hence, the third option is
Question : Direction: A mother is five times older than her daughter. After 5 years, she would be 3 times older than her daughter. Find the mother's present age.
Option 1: 20 years
Option 2: 22 years
Option 3: 25 years
Option 4: 29 years
Correct Answer: 25 years
Solution : Let the present age of the daughter be x years.
So, the present age of the mother is 5x years.
After 5 years, she would be 3 times older than her daughter. The following equation is formed.
5x + 5 = 3 (x +
Question : Directions: If K ÷ L means that K is the mother of L, K – L means that K is the father of L, and K × L means that K is the sister of L, then which of the following expressions shows that P is the paternal grandmother of R?
Option 1: P ÷ Q × R
Option 2: R – Q ÷ P
Option 3: P ÷ Q – R
Option 4: Q ÷ P – R
Correct Answer: P ÷ Q – R
Solution : Let's check the given options – First option: P ÷ Q × R As per the given information, the family tree will be as follows –
Here, the quadrilateral represents the male, and the circular figure represents the female in the
Question : Directions: Select the option that is related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster. HERO : JGPM :: FLOW : HNMU :: DIAL : ?
Option 1: KYFJ
Option 2: JFYK
Option 3: FLIJ
Option 4: FKYJ
Correct Answer: FKYJ
Solution : Given: HERO : JGPM :: FLOW : HNMU :: DIAL : ?
Add 2 to the place value of the first and second letters and subtract 2 from the place value of the third and fourth letters of HERO, and FLOW to get their required
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