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Staff Selection Commission Combined Graduate Level Exam

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Question : As part of his journey, a person travels 120 km at 80 km/h, the next 100 km at 40 km/h, and returns to the starting point at 75 km/h. The average speed of the person throughout the journey is:

Option 1: 63.46 km/h

Option 2: 58.74 km/h

Option 3: 68.15 km/h

Option 4: 49.58 km/h

Team Careers360 25th Jan, 2024

Correct Answer: 63.46 km/h


Solution : Time taken for the first journey $= \frac{120}{80} = \frac{3}{2}$ hr
Time taken for the second journey $= \frac{100}{40} = \frac{5}{2}$ hr
Distance covered in first and second journeys = 120 + 100 = 220 km
While returning, the time taken $=\frac{220}{75 }= \frac{44}{15}$

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Question : If $a+b+c=15$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{71}{abc}$, then the value of $a^{3}+b^{3}+c^{3}-3abc$ is:

Option 1: 160

Option 2: 180

Option 3: 200

Option 4: 220

Team Careers360 22nd Jan, 2024

Correct Answer: 180


Solution : Given: $a+b+c=15$
$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{71}{abc}$
Taking LCM of (a, b, c), we have:
⇒ $\frac{bc+ac+ab}{abc}=\frac{71}{abc}$
⇒ $bc+ac+ab=71$
We know that $a^{2}+b^{2}+c^{2}=(a+b+c)^{2}-2(ab+bc+ca)$
By putting the values, we have,
$a^{2}+b^{2}+c^{2}=(15)^{2}-2×71$
⇒ $a^{2}+b^{2}+c^{2}=225-142$
⇒ $a^{2}+b^{2}+c^{2}=83$
We know that $a^{3}+b^{3}+c^{3}-3abc=(a+b+c)(a^{2}+b^{2}+c^{2}-(ab+bc+ca))$
By putting the values, we have,
$a^{3}+b^{3}+c^{3}-3abc=(15)(83-71)$
Or, $a^{3}+b^{3}+c^{3}-3abc=15×12=180$
Hence, the

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Question : ____________ measures the aggregate production of final goods and services taking place within the domestic economy during a year.

Option 1: Gross national income

Option 2: Gross domestic product

Option 3: Net national product

Option 4: National income at factor price

Team Careers360 24th Jan, 2024

Correct Answer: Gross domestic product


Solution : The correct answer is Gross domestic product.

Gross Domestic Product (GDP) measures the aggregate production of final goods and services taking place within the domestic economy during a specific time, typically in a year. GDP is a key indicator of the overall

18 Views

Question : Directions: By interchanging the given two signs which of the following equations will be not correct?
+ and ÷

Option 1: 18 + 6 – 6 ÷ 3 × 3 = 6

Option 2: 18 + 2 × 6 ÷ 3 – 7 = 50

Option 3: 7 × 8 ÷ 4 + 2 – 6 = 49

Option 4: 6 × 9 + 3 – 24 ÷ 8 = 2

Team Careers360 21st Jan, 2024

Correct Answer: 7 × 8 ÷ 4 + 2 – 6 = 49


Solution : Given: 
Interchange + and ÷

First option: 18 + 6 – 6 ÷ 3 × 3 = 6
Interchanging + and ÷, and solving the L.H.S. we get,
18 ÷ 6 – 6 + 3

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Question : If $k$ is the largest possible real number such that $p^{4}+q^{4}=(p^{2}+kpq+q^{2})(p^{2}-kpq+q^{2})$, then the value of $k$ is:

Option 1: $1$

Option 2: $–\sqrt{2}$

Option 3: $2$

Option 4: $\sqrt{2}$

Team Careers360 14th Jan, 2024

Correct Answer: $\sqrt{2}$


Solution : Given: $p^{4}+q^{4}=(p^{2}+kpq+q^{2})(p^{2}-kpq+q^{2})$ -----(1)
 $p^{4}+q^{4}$
$=(p^{2})^{2}+(q^{2})^{2}$
$=(p^{2}+q^{2})^{2}-2p^{2}q^{2}$
$=(p^{2}+q^{2})^{2}-(\sqrt{2}pq)^{2}$
$=(p^{2}+\sqrt{2}pq+q^{2})(p^{2}-\sqrt{2}pq+q^{2})$
By comparing this with equation (1), we get,
$k=\sqrt{2}$
Hence, the correct answer is $\sqrt{2}$.

10 Views

Question : Select the most appropriate option that can substitute the underlined segment in the given sentence.

The yellow dress purchased by you is not much different than the one I have brought.

Option 1: different then the one

Option 2: different as the one

Option 3: different above the one

Option 4: different from the one

Team Careers360 25th Jan, 2024

Correct Answer: different from the one


Solution : The fourth option is the correct choice.

Explanation: The correct preposition to use in this context is from when making comparisons. In English, when expressing the idea of being unlike or distinct from something else, we use different from. The preposition

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