Staff Selection Commission Combined Graduate Level Exam
Question : Directions: Select the missing number from the given responses.
Option 1: 172
Option 2: 75
Option 3: 77
Option 4: 170
Correct Answer: 77
Solution : Given:
In each column, the third number is the difference of the first two numbers. Column 2: 314 – 39 = 275 Column 3: 205 – 102 = 103 Similarly, Column 1: 111 – 34 = 77
So, 77 is the missing number. Hence, the third option is correct.
Question : Comprehension: Read the given passage and answer the questions that follow.
Santiniketan embodies Rabindranath Tagore's vision of a place of learning that is unfettered by religious and regional barriers. Established in 1863 with the aim of helping education go beyond the confines of the classroom, Santiniketan grew into the Visva Bharati University in 1921, attracting some of the most creative minds in the country.
He developed a curriculum that was a unique blend of art, human values, and cultural interchange. Even today, in every step, in every brick, and in every tree at Santiniketan, one can still feel his presence, his passion, his dedication, and his pride in the institution.
In 1862, Maharishi Debendranath Tagore, father of Rabindranath, was taking a boat ride through Birbhum, the westernmost corner of Bengal, when he came across a landscape that struck him as the perfect place for meditation. He bought the large tract of land built a small house and planted some saplings around it. Debendranath Tagore decided to call the place Santiniketan, or the 'abode of peace', because of the serenity it brought to his soul. In 1863, he turned it into a spiritual center where people from all religions, castes, and creeds came and participated in meditation.
In the years that followed, Debendranath's son Rabindranath went on to become one of the most formidable literary forces India has ever produced. He wrote in all literary genres but he was first and foremost a poet. As one of the earliest educators to think in terms of the global village, he envisioned an education that was deeply rooted in one's immediate surroundings but connected to the cultures of the wider world.
Located in the heart of nature, the school aimed to combine education with a sense of obligation towards the larger civic community. Blending the best of Western and traditional Eastern systems of education, the curriculum revolved organically around nature with classes being held in the open air. Tagore wanted his students to feel free despite being in the formal learning environment of a school because he himself had dropped out of school when he found himself unable to think and felt claustrophobic within the four walls of a classroom. Nature walks and excursions were a part of the curriculum, special attention was paid to natural phenomena and students were encouraged to follow the life cycles of insects, birds, and plants.
The rural paradise of Santiniketan, Tagore's erstwhile home, has become a thriving center of art, education, and internationalism over the years.
Question Tagore's 'erstwhile' home means:
Option 1: former home
Option 2: rural retreat
Option 3: serene abode
Option 4: magnificent house
Correct Answer: former home
Solution : The first option is the correct choice.
In the given context, "erstwhile" means "former".
So, when the passage mentions Tagore's erstwhile home, it is referring to Rabindranath Tagore's former home or the home he used to live in at Santiniketan.
Question : A man walks from his house at an average speed of 5 km/h and reaches his office 6 minutes late. If he walks at an average speed of 6 km/h, he reaches 2 minutes early. The distance of the office from his house is:
Option 1: 6 km
Option 2: 9 km
Option 3: 12 km
Option 4: 4 km
Correct Answer: 4 km
Solution : $\text{Distance}=\frac{(S_1 \times S_2)(t_1+ t_2)}{S_2– S_1}$ where $S_1$ and $S_2$ are two speeds for the same distance and $t_1$ is the time by which man reaches late than the actual time and $t_2$ is the time by which man reaches early than actual time. $S_1$ = 5 km/h and $t_1$ = 6 minutes. $S_2$ = 6 km/h and $t_2$ = 2 minutes. The formula used here is, $\text{Distance}=\frac{(S_1\times S_2)\frac{(t_1+t_2)}{60}}{S_2–S_1}$. $=\frac{(5 \times 6)(6+2)}{6–5}\times \frac{1}{60}$ $=30\times \frac{8}{60}=4$ km Hence, the correct answer is 4 km.
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error He went / to the bed / with a / slight fever.
Option 1: slight fever
Option 2: to the bed
Option 3: with a
Option 4: He went
Correct Answer: to the bed
Solution : The error lies in the second option.
The correct preposition to use in this context is to bed rather than to the bed.
The expression to bed is idiomatic when referring to going to sleep or lying down, and it doesn't require the article the.
Therefore, the correct sentence is," He went to bed with a slight fever".
Question : The height of an equilateral triangle is $7 \sqrt{3}$ cm. What is the area of this equilateral triangle?
Option 1: $36 \sqrt{3}$ cm2
Option 2: $25 \sqrt{3}$ cm2
Option 3: $49 \sqrt{3}$ cm2
Option 4: $32 \sqrt{3}$ cm2
Correct Answer: $49 \sqrt{3}$ cm2
Solution : Height of an equilateral triangle = $\frac{\sqrt{3}}{2} \times Side$ Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times Side^2$ So, each side of the triangle = $\frac{7\sqrt{3}}{\frac{\sqrt{3}}{2}}$ = 14 cm Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times 14^2$ = $49\sqrt{3}$ cm2 ∴ The area of this equilateral triangle is $49\sqrt{3}$ cm2. Hence, the correct answer is $49\sqrt{3}$ cm2.
Question : A mask manufacturing company manufactured an ‘$x$’ number of masks in 2018. It increased its manufacturing capacity by 30% in 2019 and further increased its manufacturing by 15% in 2020. In 2021, due to the machinery breakdown, its manufacturing declined by 40%. What is the value of ‘X’ if it manufactured 179400 masks in 2021?
Option 1: 180000
Option 2: 230000
Option 3: 200000
Option 4: 210000
Correct Answer: 200000
Solution : Given: A mask manufacturing company manufactured an ‘$x$’ number of masks in 2018. It increased its manufacturing capacity by 30% in 2019 and further increased its manufacturing by 15% in 2020. Mask manufactured in 2019 = $x × \frac{130}{100}$ = $\frac{13x}{10}$ Mask manufactured in 2020 = $\frac{13x}{10} × \frac{115}{100}$ Mask manufactured in 2021 = $\frac{13x}{10}×\frac{115}{100}×\frac{100-40}{100}$ = $\frac{13x}{10}×\frac{23}{20}×\frac{3}{5}$ According to the question, ⇒ $\frac{13x}{10}×\frac{23}{20}×\frac{3}{5} = 179400$ ⇒ $x = \frac{179400×10×20×5}{13×23×3}$ $\therefore x = 200000$ Hence, the correct answer is 200000.
Question : If $xy = -6$ and $x^3+ y^3= 19$ ($x$ and $y$ are integers), then what is the value of $\frac{1}{x^{–1}}+\frac{1}{y^{–1}}$?
Option 1: –1
Option 2: –2
Option 3: 1
Option 4: 2
Correct Answer: 1
Solution : Given: $xy = -6$ and $x^3+ y^3= 19$ ($x$ and $y$ are integers) We know the algebraic identity, $(x+y)^3=x^3 + y^3+3xy(x+y)$. Substitute the given values in the above formula, ⇒ $(x+y)^3=19+3\times(-6)\times(x+y)$ ⇒ $(x+y)^3=19-18\times(x+y)$ Let $(x+y)=u$. ⇒ $u^3+18u–19=0$ ⇒ $u^3–u^2+u^2–u+19u–19=0$ ⇒ $u^2(u–1)+u(u–1)+19(u–1)=0$ ⇒ $(u–1)(u^2+u+19)=0$ ⇒ $u-1=0$ ⇒ $u=1$ ⇒ $\frac{1}{x^{–1}}+\frac{1}{y^{–1}}=x+y=1$ Hence, the correct answer is 1.
Question : Select the option that can be used as a one-word substitute for the underlined group of words. While I was travelling in Europe, I met a man who drew maps.
Option 1: Cartographer
Option 2: Geographer
Option 3: Arbitrator
Option 4: Anthropologist
Correct Answer: Cartographer
Solution : The correct choice is the first option.
A cartographer is an individual who engages in the practice or art of making maps. Therefore, "cartographer" is the appropriate one-word substitute for the underlined group of words.
Question : Which of the following is used in photography?
Option 1: Sodium bicarbonate
Option 2: Sodium thiosulphate
Option 3: Sodium hydroxide
Option 4: Sodium sulphate
Correct Answer: Sodium thiosulphate
Solution : The correct option is Sodium thiosulphate.
Sodium thiosulfate is used in photography as a fixing agent, especially in traditional film and darkroom processes. It is used to fix or stabilise the developed image on photographic paper by removing unexposed silver halide.
Question : Directions: Which of the following letter clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of ::? # : CLQ :: NDK : %
Option 1: # = AJS, % = MAM
Option 2: # = AOO, % = PAM
Option 3: # = EIT, % = QBN
Option 4: # = DIS, % = PBN
Correct Answer: # = AOO, % = PAM
Solution : Given: # : CLQ :: NDK : %
Let's check the options – First option: # = AJS, % = MAM AJS : CLQ→A + 2 = C; J + 2 = L; S – 2 = Q NDK : MAM→N – 1 = M; D – 3 = A; K + 2 = M Second option: # = AOO, % = PAM AOO : CLQ→A + 2 = C; O – 3 = L; O + 2 = Q NDK : PAM→N + 2 = P; D – 3 = A; K + 2 = M Third option: # = EIT, % = QBN EIT : CLQ→E – 2 = C; I + 3 = L; T – 3 = Q NDK : QBN→N + 3 = Q; D – 2 = B; K + 3 = N Fourth option: # = DIS, % = PBN DIS : CLQ→D – 1 = C; I + 3 = L; S – 2 = Q NDK : PBN→N + 2 = P; D – 2 = B; K + 3 = N
So, a similar pattern in both pairs can be observed only in the second option. Hence, the second option is correct.
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