Staff Selection Commission Combined Graduate Level Exam
Question : A man takes 15 minutes to row 16 km downstream, which is 25% less than the time he takes to row the same distance upstream. How many kilometres can the man row in an hour in still water? (Rounded off to the nearest whole number)
Option 1: 56
Option 2: 60
Option 3: 58
Option 4: 54
Correct Answer: 56
Solution : Given: A man takes 15 minutes to row 16 km downstream. 15 minutes $= \frac{15}{60}=\frac{1}{4}$ hours Downstream speed $= \frac{16}{\frac{1}{4}} = 64$ km/h Man takes 25% more time in upstream, So, upstream speed = $64×\frac{75}{100}=48$ km/h Speed of boat in still water = $\frac{64+48}{2}=56$ km/h
Question : In which of the following game, ball is not used ?
Option 1: Football
Option 2: Cricket
Option 3: Badminton
Option 4: Tennis
Correct Answer: Badminton
Solution : The correct answer is Badminton.
Badminton is a racquet sport played using racquet and shuttle cock. India's most famous badminton player is P.V. Sindhu.
Additional information-
In the 32nd edition of the Thomas Cup in 2022, India's men's badminton team defeated 14-time champion Indonesia 3-0
Question : If $x^4+\frac{16}{x^4}=15617, x>0$, then find the value of $x+\frac{2}{x}$.
Option 1: $\sqrt{121}$
Option 2: $\sqrt{129}$
Option 3: $\sqrt{123}$
Option 4: $\sqrt{127}$
Correct Answer: $\sqrt{129}$
Solution : Given: $x^4+\frac{16}{x^4}=15617$ ⇒ $(x^2)^2 + (\frac{4}{x^2})^2 + 2\times x^2 \times \frac{4}{x^2} = 15617 + 2\times x^2 \times \frac{4}{x^2}$ ⇒ $(x^2+\frac{4}{x^2})^2 = 15625$ ⇒ $x^2 + \frac{4}{x^2} = 125$ ⇒ $x^2 + (\frac{2}{x})^2 + 2\times x \times \frac{2}{x} = 125 + 2\times x\times \frac{2}{x}$ ⇒ $(x+\frac{2}{x})^2
Question : Given: $(a-b)=2, (a^{3}-b^{3})=26$, then $(a+b)^{2}$ is:
Option 1: 9
Option 2: 4
Option 3: 16
Option 4: 12
Correct Answer: 16
Solution : $a−b = 2$ $a^3-b^3=26$ ⇒ $a^3-b^3$ = $(a−b)$$(a^2+ab+b^2)$ ⇒ $26= 2\times (a^2+ab+b^2)$ ⇒ $13 =(a^2+ab+b^2) $.........(i) ⇒ $(a−b)^2 = a^2+b^2-2ab$ ⇒ $(2)^2 = a^2+b^2+ab−3ab$ Putting the value from equation (i) ⇒ $4 = 13−3ab$ ⇒ $3ab = 9$ ⇒ $ab =3$ $(a+b)^2 = (a−b)^2+4ab =
Question : Directions: Three of the following letter clusters are alike in some manner and hence form a group. Which letter cluster does not belong to that group?
Option 1: LEB
Option 2: JZF
Option 3: TJP
Option 4: MCI
Correct Answer: LEB
Solution : Let's check each option – First option: LEB; L – 7 = E, E – 3 = B Second option: JZF; J – 10 = Z, Z + 6 = F Third option: TJP; T – 10 = J, J + 6 = P Fourth
Question : Select the most appropriate passive form of the given sentence. The king covered the hole with a huge stone.
Option 1: The hole has been covered by the king with a huge stone.
Option 2: The hole was covered by the king with a huge stone.
Option 3: The king was covered by the hole with a huge stone.
Option 4: A huge stone was covered by the king with a hole.
Correct Answer: The hole was covered by the king with a huge stone.
Solution : The second option is the correct answer.
Passive voice is a grammatical construction where the subject of the sentence undergoes the action rather than performing it. The given sentence is an example of the active
Question : Directions: Arrange the following words as per their order in the dictionary. 1. Resign 2. Repair 3. Residue 4. Research 5. Rescue
Option 1: 4, 5, 3, 1, 2
Option 2: 2, 5, 4, 3, 1
Option 3: 2, 5, 4, 1, 3
Option 4: 5, 4, 3, 1, 2
Correct Answer: 2, 5, 4, 3, 1
Solution : Given: 1. Resign 2. Repair 3. Residue 4. Research 5. Rescue
Step 1: Since all the words start with the same letter R, so move on to the next letter. Step 2: The second letter of each word is the
Question : Directions: The table given below shows information about bats manufactured by six different companies. Each company manufactures only plastic and wooden bats. Each company labels these bats as Brand A or Brand B. The table shows the number of plastic bats as a percentage of the total bats manufactured by each company. It also shows the ratio of wooden bats labelled A and B. Each company manufactured a total of 550000 bats.
X = Average of plastic bats manufactured by V, U, and T. Y = Wooden bats of Brand A manufactured by V. What is the value (X – Y)?
Option 1: 197600
Option 2: 432890
Option 3: 260000
Option 4: 293300
Correct Answer: 260000
Solution : X is the average of plastic bats manufactured by V, U, and T. For V, the percentage of plastic bats is 60%. The number of plastic bats = 0.60 × 550000 = 330000 For U, the percentage of plastic bats is 75%. The number of
Question : The slant height and radius of a right circular cone are in the ratio 29 : 20. If its volume is $4838.4 \pi ~\mathrm{cm}^3$, then its radius is:
Option 1: 28 cm
Option 2: 20 cm
Option 3: 25 cm
Option 4: 24 cm
Correct Answer: 24 cm
Solution : The ratio of slant height and radius = 29 : 20 Let slant height($l$) be $29x$ and radius($r$) be $20x$. Height, $h = \sqrt{l^2-r^2} = \sqrt{(29x)^2-(20x)^2} = \sqrt{(841-400)x^2}= \sqrt{441x^2} = 21x$ Volume of cone = $4838.4 \pi$ ⇒ $\frac{1}{3} \pi r^2 h = 4838.4
Question : Direction: In the following question, select the missing number from the given responses.
Option 1: 4
Option 2: 3
Option 3: 7
Option 4: 6
Correct Answer: 4
Solution : Given:
In the first row, 3 + 8 + 7 = 18
In the second row, 9 + 6 + 3 = 18
In the third row, 2 + 12 = 14 → 18 – 14
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