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Staff Selection Commission Combined Graduate Level Exam

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Question : In $\triangle {PQR} $, PQ = PR and S is a point on QR such that $\angle {PSQ}=96^{\circ}+\angle {QPS}$ and $\angle {QPR} = 132^{\circ}$. What is the measure of $\angle {PSR}$?

Option 1: 45°

Option 2: 56°

Option 3: 54°

Option 4: 52°

Team Careers360 9th Jan, 2024

Correct Answer: 54°


Solution :
Let $\angle QPS$ be $\theta$
⇒ $\angle PSQ = 96^\circ + \theta$
Now, In $\triangle PQR$
⇒ $\angle Q + \angle R = 180^\circ - \angle P$
$= 180^\circ -132^\circ$
$=48^\circ$
Since $PQ = PR$
$\angle Q = \angle R$
$\therefore \angle Q = \angle

33 Views

Question : In $\triangle ABC$, M and N are the points on side BC such that AM $\perp$ BC, AN is the bisector of $\angle A$, and M lies between B and N. If $\angle B=68^{\circ}$, and $\angle \\{C}=26^{\circ}$, then the measure of $\angle MAN$ is:

Option 1: 21º

Option 2: 28º

Option 3: 24º

Option 4: 22º

Team Careers360 9th Jan, 2024

Correct Answer: 21º


Solution :
$\triangle$ABC, M and N are the side on BC such that AM $\perp$ BC, AN is the bisector $\angle$A, and M lies between B and N
$\angle$B = 68$^\circ$, and $\angle$C = 26$^\circ$
Concept used:
$\triangle$ABC, M and N are the sides on BC such

117 Views

Question : The price of a scooter increases successively by 10%, 5%, and 15%. What is the total percentage increase in the price of the scooter?

Option 1: $32 \frac{33}{40}$%

Option 2: $34 \frac{21}{40}$%

Option 3: $30 \frac{11}{40}$%

Option 4: $36 \frac{31}{40}$%

Team Careers360 8th Jan, 2024

Correct Answer: $32 \frac{33}{40}$%


Solution : Let the initial price of the scooter be 100.
After successive increment of 10%, 5%, and 15%, the price becomes
= $100\times\frac{110}{100}\times\frac{105}{100}\times\frac{115}{100}$
= $100\times\frac{11}{10}\times\frac{21}{20}\times\frac{23}{20}$
= $\frac{11\times21\times23}{40}$
= $\frac{5313}{40}$
Difference = Price after increment – initial price = $\frac{5313}{40}-100=\frac{5313-4000}{40}=\frac{1313}{40}$
$\therefore$ Percentage increased
= $\frac{\text{Difference}}{\text{Initial price}}\times

13 Views

Question : Select the most appropriate option that can substitute the underlined segment in the given sentence.
He was sitting besides his best friend during the event.

Option 1: was sitting about his

Option 2: was sitting beside his

Option 3: were sitting besides his

Option 4: was sitting besides her

Team Careers360 13th Jan, 2024

Correct Answer: was sitting beside his


Solution : The correct choice is the second option.

Explanation: Beside means at the side of or next to someone or something. In this context, it refers to the location of someone sitting next to their best friend.
The correct preposition to use

11 Views

Question : Directions: Which letter cluster will replace the question mark (?) to complete the given series?
abCD, fgHI, ?, stUV, abCD

Option 1: kIMO

Option 2: ImNO

Option 3: mnOP

Option 4: InMO

Team Careers360 17th Jan, 2024

Correct Answer: ImNO


Solution : Given:
abCD, fgHI, ?, stUV, abCD

Add consecutive natural numbers (starting from 5) to the place value of the letters of the previous term to get the next term.
abCD→a + 5 = f; b + 5 = g; C + 5 = H; D

28 Views

Question : Directions: Select the option that represents the correct order of the given words as they would appear in an English dictionary.
1. Mistaken
2. Missing
3. Mistyped
4. Mistrust
5. Mission
6. Mistress

Option 1: 2, 5, 6, 4, 3, 1

Option 2: 2, 5, 1, 6, 4, 3

Option 3: 5, 2, 1, 6, 4, 3

Option 4: 2, 5, 1, 4, 6, 3

Team Careers360 17th Jan, 2024

Correct Answer: 2, 5, 1, 6, 4, 3


Solution : Given:
1. Mistaken 2. Missing 3. Mistyped 4. Mistrust 5. Mission 6. Mistress

Step 1: The first three letters of each word are the same – m, i, s, so move on to the next letter.
Step

32 Views

Question : The following figure shows the scores of students in three tests organised by a coaching institution. Who scored the best on average?

Option 1: D

Option 2: C

Option 3: E

Option 4: B

Team Careers360 14th Jan, 2024

Correct Answer: E


Solution : Let's find the average first,
For A = $\frac{84+71+95}{3} = \frac{250}{3} = 83.33$
For B = $\frac{93+76+101}{3} = \frac{270}{3} = 90$
For C = $\frac{99+79+71}{3} = \frac{249}{3} = 83$
For D = $\frac{80+90+94}{3} = \frac{264}{3} = 88$
For E = $\frac{88+93+90}{3} = \frac{271}{3} = 90.33$

58 Views

Question : The probabilities of solving a problem by three students A, B, and C are $\frac{3}{7}, \frac{5}{9}$ and $\frac{1}{5}$, respectively. The probability that the problem will be solved is:

Option 1: $\frac{155}{315}$

Option 2: $\frac{64}{315}$

Option 3: $\frac{251}{315}$

Option 4: $\frac{32}{315}$

Team Careers360 19th Jan, 2024

Correct Answer: $\frac{251}{315}$


Solution : Let A, B, and C respectively denote the events that the problem is solved by A, B, and C respectively and A', B', and C' respectively denote the events that the problem will not be solved.
P(A) = $\frac{3}{7}$; P(A') = $\frac{4}{7}$
P(B) = $\frac{5}{9}$;

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