Staff Selection Commission Combined Graduate Level Exam
Question : If $x+\frac{1}{x}=\sqrt{3}$, the value of $\left (x^{3}+\frac{1}{x^{3}} \right )$ is:
Option 1: $\sqrt{3}$
Option 2: $\frac{1}{\sqrt{3}}$
Option 3: $0$
Option 4: $1$
Correct Answer: $0$
Solution : Given: $x+\frac{1}{x}=\sqrt{3}$ Cubing both sides and simplifying the equation, ⇒ $(x+\frac{1}{x})^3=(\sqrt{3})^3$ ⇒ $x^3+\frac{1}{x^3}+3(x×\frac{1}{x})(x+\frac{1}{x})=(\sqrt{3})^3$ ⇒ $x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=3\sqrt{3}$ Putting the value of $x+\frac{1}{x}=\sqrt{3}$ ⇒ $x^3+\frac{1}{x^3}+3\sqrt{3}=3\sqrt{3}$ ⇒ $x^3+\frac{1}{x^3}=3\sqrt{3}-3\sqrt{3}$ ⇒ $x^3+\frac{1}{x^3}=0$ Hence, the correct answer is $0$.
Question : Select the most appropriate ANTONYM of the underlined word.
He was riding his bike on a bumpy surface.
Option 1: Jerky
Option 2: Uneven
Option 3: Choppy
Option 4: Steady
Correct Answer: Steady
Solution : The correct choice is the fourth option.
Steady means stable, consistent, and not subject to abrupt or uneven movements. It is the antonym of bumpy, as it conveys the opposite meaning of a smooth and even surface.
The meanings of the other options are
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the options given. Select the most appropriate option for each number. Castles are home to a rich history. From blood feuds to tragic pasts, (1)______ love affairs to alleged ghosts, no castle is ever (2)______ a secret to unveil. Known locally as Chateaux Picomtal, Picomtal Castle (3)______ came under new ownership. During the renovation of the (4)______, a surprising discovery was made. Messages (5)______long ago were found on the floorboards of (6)______ upper chambers. The messages were written (7)______1880 and 1881 by Joachim Martin; the carpenter (8)______ installed the flooring. His messages were a diary of 72 entries of his daily (9)______, personal thoughts along with his emotions and feelings. Joachim’s (10)______is indeed a very personal account of the history of those times. The discovery gives us an honest look at an average person’s daily life over 135 years ago. Question: Select the most appropriate option to fill in the blank no. 2.
Option 1: with
Option 2: including
Option 3: without
Option 4: excluding
Correct Answer: without
Solution : The correct choice will be the third option.
The word without is the most appropriate option in this context, as it suggests the absence of secrets, indicating that every castle has some secrets or historical stories associated with it.
Therefore, the completed sentence would read:
Question : Which of the following is a phylum of animals found in freshwater ponds, lakes, and swamps that provides setae, or parapodia for locomotion?
Option 1: Ctenophora
Option 2: Porifera
Option 3: Annelida
Option 4: Platyheiminthes
Correct Answer: Annelida
Solution : The correct option is Annelida.
Annelids, belonging to the phylum Annelida, are aquatic creatures commonly found in freshwater environments like ponds, lakes, and swamps. They possess specialised structures known as setae or parapodia, which are bristle-like appendages used for locomotion. These segments aid in gripping
Question : Select the correct indirect form of the given sentence. Mahesh said to Priya,“How will you pay off your debts?”
Option 1: Mahesh asked Priya how she would pay off your debts.
Option 2: Mahesh asked Priya how will she pay off her debts.
Option 3: Mahesh asked Priya how she would pay off her debts.
Option 4: Mahesh asked Priya that how you will pay off your debts.
Correct Answer: Mahesh asked Priya how she would pay off her debts.
Solution : The correct choice is the third option.
The steps of conversion are as follows:
Question : Ram sold an item costing INR 1,250 at a gain of 18% to Ramesh. It was again sold by Ramesh to Shyam at a loss of 10%. Find the selling price of Ramesh.
Option 1: INR 1,328.50
Option 2: INR 1,428.50
Option 3: INR 1,427.50
Option 4: INR 1,327.50
Correct Answer: INR 1,327.50
Solution : Ram sold the item to Ramesh at a gain of 18%. So, Ramesh's cost price (CP) is 118% of the original cost price. Ramesh's CP = $\frac{118}{100} \times 1250$ = INR 1475 Ramesh sold the item to Shyam at a loss of 10%. So,
Question : Find the remainder when we divide $3x^4-2x^2+4x-1$ by $(2x-1)$.
Option 1: $2$
Option 2: $3$
Option 3: $\frac{11}{16}$
Option 4: $\frac{15}{16}$
Correct Answer: $\frac{11}{16}$
Solution : Assume, $2x-1$ = 0 ⇒ $x$ = $\frac{1}{2}$ Let $f(x)=3x^4-2x^2+4x-1$ So, the remainder when $3 x^4-2 x^2+4 x-1$ is divided by $(2x-1)$ is $f(\frac{1}{2})$ = $3 (\frac{1}{2})^4-2 (\frac{1}{2})^2+4(\frac{1}{2})-1$ = $\frac{3}{16} - \frac{1}{2} + 2 - 1$ = $\frac{3}{16} + \frac{1}{2}$ = $\frac{11}{16}$ Hence, the correct
Question : Which group of Kingdom Animalia has unsegmented, bilaterally symmetrical, soft bodies, with a triploblastic construction (comprising three layers of cells) and a lacking coelom, skeleton and anus?
Option 1: Cnidaria
Option 2: Ctenophora
Option 3: Platyhelminthes
Option 4: Porifera
Correct Answer: Platyhelminthes
Solution : The correct answer is Platyhelminthes.
The group of Kingdom Animalia with unsegmented, bilaterally symmetrical, soft bodies, with a triploblastic construction and a lacking coelom, skeleton and anus is the phylum Platyhelminthes, also known as flatworms. Flatworms are a different group of about 25,000 species found
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
As an old friend, may I (give you an advice)?
(1) give you some advice
(2) give you an advise
(3) offer you an advice
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The correct choice to improve the sentence is the first option.
Explanation: The word "advice" is an uncountable noun in English, so we should use "some advice" instead of "an advice".
Question : Directions: Select the figure from among the given options that can replace the question mark (?) in the following series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Here the pattern is as follows — In box 1, there is only an empty square. In box 2, there is a square with one line inside the square. In box 3, there is a square with 2 lines inside the square. In box 4, there
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