Staff Selection Commission Combined Graduate Level Exam
Question : The following pie charts show the data of the number of appeared and passed students of class 12 in sections A, B, C, D, and E. How many students failed in Section C?
Option 1: 250
Option 2: 200
Option 3: 300
Option 4: 400
Correct Answer: 300
Solution : Appeared students = 1800 Appeared students for section C = $1800×\frac{100}{360}=500$ Total passed students = 800 Passed students of section C = $800×\frac{25}{100}=200$ $\therefore$ Failed students of section C = 500 – 200 = 300 Hence, the correct answer is 300.
Question : What is the value of $\frac{5.6\times0.36 + 0.42 \times 3.2 }{0.8\times2.1} ?$
Option 1: $2$
Option 2: $1$
Option 3: $3$
Option 4: $\frac{3}{2}$
Correct Answer: $2$
Solution : Given: $\frac{5.6\times 0.36 + 0.42 \times 3.2 }{0.8\times 2.1}$ = $\frac{2.016 + 1.344}{1.68}$ = $\frac{3.36}{1.68}$ = 2 Hence, the correct answer is $2$.
Question : Direction: In the following question, select the related number from the given alternatives.
525 : 25 :: 315 : ?
Option 1: 10
Option 2: 15
Option 3: 5
Option 4: 25
Correct Answer: 15
Solution : Given:
The above ratio can also be written as
$$\frac{525}{25} = \frac{315}{?}$$
$$? = \frac{315\times25}{525}$$
$$? = 15$$
Hence, the second option is correct.
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 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
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