Staff Selection Commission Combined Graduate Level Exam
Question : In the given figure $\mathrm{PQRS}$, a square of side $20\;\mathrm{cm}$ and $\mathrm{SR}$ is extended to point $\mathrm{T}$. If the length of $\mathrm{QT}$ is $25\;\mathrm{cm}$, then what is the distance (in $\mathrm{cm}$) between the centres, $\mathrm{O_1}$ and $\mathrm{O_2}$, of the two circles?
Option 1: $5\sqrt{10}$
Option 2: $4\sqrt{10}$
Option 3: $2\sqrt{10}$
Option 4: $16\sqrt{2}$
Correct Answer: $5\sqrt{10}$
Solution :
We have, $\mathrm{QT}=25\;\mathrm{cm}$ and $\mathrm{QR=SR}=20\;\mathrm{cm}$ Construction: Join $\mathrm{O_1B}$ and $\mathrm{O_2C}$. In $\triangle \mathrm{QRT}$, $⇒\mathrm{QT^2=QR^2+RT^2}$ $⇒\mathrm{RT=15}\;\mathrm{cm}$ Inradius of triangle QRT $=\mathrm{\frac{15+20-25}{2} = 5\;\mathrm{cm}}$ $⇒\mathrm{O_2C=5\;\mathrm{cm}}$ Since, $\mathrm{O_1B=10}\;\mathrm{cm}$ and $\mathrm{AB=5\;\mathrm{cm}}$ $⇒\mathrm{O_1A= O_1B-AB=5\;\mathrm{cm}}$ $⇒\mathrm{O_2A= O_1B+AB=15\;\mathrm{cm}}$ Use Pythagoras' theorem in $\triangle\mathrm{ AO_1O_2}$ $⇒\mathrm{(O_1O_2)^2=(O_1A)^2+(O_2A)^2=15^2+5^2=250}$ $⇒\mathrm{O_1O_2}=5\sqrt{10}\;\mathrm{cm}$ Hence, the correct answer is $5\sqrt{10}$.
Question : Directions: Select the related letter cluster from the given alternatives. DHLP : WSOK :: FJNR : ?
Option 1: UQMI
Option 2: TPLH
Option 3: SOKG
Option 4: VRNJ
Correct Answer: UQMI
Solution : Given: DHLP : WSOK :: FJNR : ?
Like, DHLP : WSOK→(DW, HS, LO, PK) are opposite pairs. Similarly, FJNR : (?)→(FU, JQ, NM, RI) are opposite pairs.
Thus, FJNR is coded as UQMI. Hence, the first option is correct.
Question : Select the most appropriate synonym of the given word. Earnestly
Option 1: Wordily
Option 2: Ambiguously
Option 3: Verbosely
Option 4: Sincerely
Correct Answer: Sincerely
Solution : The correct choice is the fourth option.
Earnestly means with deep sincerity, seriousness, and commitment and sincerely means with genuine and honest intent, truthfulness, or commitment similar in meaning to earnestly.
The meanings of the other options are as follows:
Wordily: It means an
Question : The average of 11 numbers is 7. If every number is doubled, what will be the new average of the numbers?
Option 1: 3.5
Option 2: 7
Option 3: 10.5
Option 4: 14
Correct Answer: 14
Solution : Given: The average of 11 numbers is 7. Total of 11 numbers = 11 × 7 = 77 If every number is doubled, their total will also be doubled. So, new total = 77 × 2 = 154 So, new average = $\frac{154}{11}$ = 14
Question : Directions: In the following question, find the odd number pair from the given alternatives.
Option 1: 65 – 90
Option 2: 73 – 97
Option 3: 112 – 137
Option 4: 162 – 187
Correct Answer: 73 – 97
Solution : Let's check the options – First option: 65 – 90→90 – 65 = 25 Second option: 73 – 97→97 – 73 = 24 ≠ 25 Third option: 112 – 137→137 – 112 = 25 Fourth option: 162 – 187→187 – 162 = 25
Question : Which of the following is not the function of the central bank of the country?
Option 1: It controls money supply of the country.
Option 2: It acts as a banker to the government.
Option 3: It accepts deposits from the public.
Option 4: It issues the currency of the country.
Correct Answer: It accepts deposits from the public.
Solution : The correct option is It accepts deposits from the public.
The central bank typically does not accept deposits from the public; that is usually a function of commercial banks. The central bank's functions include monetary policy formulation, issuing currency,
Question : Directions: Select the figure that will replace the question mark (?) in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : In the given figures, as we move from one box to another box – 1. The figure in the centre of each box, is rotating 90° in the anticlockwise direction. 2. The two circles are moving in an anticlockwise direction, shifting their positions in the corner.
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank. Women won their present status through (1)____ and sacrifices rather than through men's kindness. Women and their supporters have fought, and in some places continue to fight for the same rights as (2)____. Laws were made to replace local customs which denigrated and suppressed women's rights. Women have (3)_____ higher positions in the world at all levels; political, economic and social. But in reality, women still suffer from (4)____ at various levels. For example, women work more and earn less than men. In addition to that, the majority of the world's poor and illiterate are women. The road to real (5)_____ is still long. Question: Select the most appropriate option to fill in the blank number 4.
Option 1: issues
Option 2: tolerance
Option 3: equality
Option 4: discrimination
Correct Answer: discrimination
Solution : The fourth option is the correct choice.
The context indicates that despite progress, women still face challenges, and the word that best conveys these challenges is discrimination. It implies unfair treatment based on gender.
Question : Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Option 1: 8 cm
Option 2: 16 cm
Option 3: 12 cm
Option 4: 9 cm
Correct Answer: 16 cm
We have, OB = 10 cm and OD = 6 cm Radius perpendicular to the tangent. $\angle ODB$ = 90º Using Pythagoras' theorem in $\triangle ODB$ OB2 = OD2 + BD2 ⇒ 102 = 62 + BD2 ⇒
Question : A student's marks were wrongly entered as 65 instead of 45. Due to this, the average marks for the class got increased by $\frac{1}{3}$. The number of students in the class is:
Option 1: 40
Option 2: 20
Option 3: 60
Option 4: 30
Correct Answer: 60
Solution : Let $n$ be the total number of students and $x$ be the average when the mark is counted as 45. The average when the mark is counted as 65 is $x+\frac{1}{3}$ Now, $x$ = $\frac{\text{total marks of (n-1)students + 45}}{n}$ ⇒ Total marks of $(n-1)$
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