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Staff Selection Commission Combined Graduate Level Exam

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Question : In a triangle PQR, $\angle$Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circumcircle of the triangle?

Option 1: $5$

Option 2: $6$

Option 3: $6.5$

Option 4: $6\sqrt2$

Team Careers360 10th Jan, 2024

Correct Answer: $6.5$


Solution : Given: In a triangle PQR, $\angle$Q=90°, PQ = 12 cm, and QR = 5 cm.

Let the hypotenuse of the triangle be $h$ cm.
So, $h^2=12^2+5^2$
⇒ $h=\sqrt{169}$
⇒ $h=13$ cm
We know,
The circumradius of a right-angled triangle is half of its hypotenuse.
So,

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Question : The smallest fraction which should be added to the sum of $2\frac{1}{2}, 3\frac{1}{3}, 4\frac{1}{4}$ and $5\frac{1}{5}$ to make the result a whole number is:

Option 1: $\frac{13}{60}$

Option 2: $\frac{1}{4}$

Option 3: $\frac{17}{60}$

Option 4: $\frac{43}{60}$

Team Careers360 21st Jan, 2024

Correct Answer: $\frac{43}{60}$


Solution : Given: $2\frac{1}{2} +3\frac{1}{3} + 4\frac{1}{4} +5\frac{1}{5}$
To make this expression a whole number, add fractions:
$ = (\frac{1}{2} +\frac{1}{3} + \frac{1}{4} +\frac{1}{5})$
$ = \frac{(30+20+15+12)}{60}$
$ = \frac{77}{60}$
$ = 1 +\frac{17}{60}$
The smallest fraction to be added = $1 -\frac{17}{60} =\frac{43}{60}$
Hence, the correct

12 Views

Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series.
$\frac{W}{S}$, $\frac{U}{O}$, $\frac{S}{K}$, $\frac{Q}{G}$, ?

Option 1: $\frac{P}{R}$

Option 2: $\frac{C}{O}$

Option 3: $\frac{R}{J}$

Option 4: $\frac{O}{C}$

Team Careers360 21st Jan, 2024

Correct Answer: $\frac{O}{C}$


Solution : Given:
$\frac{W}{S}$, $\frac{U}{O}$, $\frac{S}{K}$, $\frac{Q}{G}$, ?

In the given series, subtract 2 from the place value of the letter in the numerator and subtract 4 from the place value of the letter in the denominator to obtain the missing term –
$\frac{W\text{ – }2}{S\text{ –

16 Views

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:

Team Careers360 9th Jan, 2024

Correct Answer:


Solution : Since the rotation of the figure is not allowed, so we will check where the question figure can exactly fit itself in the given option figures.

From the above, it is clear that the given question figure is embedded in the third option figure. Hence, the 

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Question : Select the most appropriate synonym for the highlighted word.

The government's utilitarian stance was appreciated by all.

Option 1: thrust

Option 2: fanciful

Option 3: useful

Option 4: distasteful

Team Careers360 14th Jan, 2024

Correct Answer: useful


Solution : The correct answer is the third option.

Utilitarian means designed to be useful or practical rather than attractive. In the given sentence, the government's utilitarian stance suggests that their approach prioritises practicality and usefulness.

Therefore, useful is the most suitable synonym in this context, which

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