Staff Selection Commission Combined Graduate Level Exam
Question : Find the total surface area of a cube whose volume is 343 m³.
Option 1: 186 m²
Option 2: 294 m²
Option 3: 196 m²
Option 4: 210 m²
Correct Answer: 294 m²
Solution : Given: Volume of a cube = 343 m³ Let $a$ be the side of the cube. So, $a^3$ = 343 m³ ⇒ $a$ = $\sqrt[3]{343}$ = 7 m Now, the total surface area of a cube = $6a^2$ = $6×7^2$ = 294 m2
Question : The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at a speed of 12 km/hr completes one round in 8 minutes, then the area of the park is:
Option 1: 1,53,650 sq. metres
Option 2: 1,35,600 sq. metres
Option 3: 1,53,600 sq. metres
Option 4: 1,56,300 sq. metres
Correct Answer: 1,53,600 sq. metres
Solution : Given: The ratio between the length and the breadth of a rectangular park is 3 : 2. Let length be $3x$, breadth be $2x$. A man cycling along the boundary of the park at a speed of 12 km/hr completes one round in
Question : Which article of the Constitution of India deals with the recognition of the right to education as a fundamental right?
Option 1: Article 300A
Option 2: Article 20
Option 3: Article 33
Option 4: Article 21A
Correct Answer: Article 21A
Solution : The correct answer is Article 21A.
The right to education in India is recognised as a fundamental right under Article 21A of the Indian Constitution. This article was inserted by the 86th Amendment Act of 2002 and states that the state shall provide
Question : Study the given pie charts and answer the question that follows. Which institute has the second highest percentage of students who passed to the students who appeared from that institute?
Option 1: C
Option 2: E
Option 3: D
Option 4: B
Correct Answer: D
Solution : Number of students who appeared in the examination from institutes B = 54^\circ = $\frac{54^\circ}{360^\circ} × 1200$ = 180 Number of students who appeared in the examination from institutes C = 90^\circ = $\frac{90^\circ}{360^\circ} × 1200$ = 300 Number of students who appeared in the
Question : The value of $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ is:
Option 1: $\sec\theta+\tan \theta$
Option 2: $\operatorname{cosec} \theta-\cot \theta$
Option 3: $\operatorname{cosec} \theta+\cot \theta$
Option 4: $\sec\theta-\tan \theta$
Correct Answer: $\operatorname{cosec} \theta+\cot \theta$
Solution : Given: $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ = $\sqrt{\frac{(1+\cos \theta)(1+\cos \theta)}{(1-\cos \theta)(1+\cos \theta)}}$ = $\sqrt{\frac{(1+\cos \theta)^2}{1-\cos^2\theta}}$ = $\sqrt{\frac{(1+\cos \theta)^2}{\sin^2\theta}}$ = $\frac{(1+\cos \theta)}{\sin\theta}$ = $\operatorname{cosec} \theta+\cot \theta$ Hence, the correct answer is $\operatorname{cosec}\theta+\cot\theta$.
Question : Comprehension:
Read the passage and answer the questions that follow.
The drainage systems of India are mainly controlled by the broad relief features of the subcontinent. Accordingly, the Indian rivers are divided into two major groups: the Himalayan rivers; and the Peninsular rivers.
Apart from originating from the two major physiographic regions of India, the Himalayan and the Peninsular rivers are different from each other in many ways. Most of the Himalayan rivers are perennial. It means that they have water throughout the year. These rivers receive water from rain as well as from melted snow from the lofty mountains. The major Himalayan rivers are the Indus, the Ganga, and the Brahmaputra. These rivers are long and are joined by many large and important tributaries. A river along with its tributaries may be called a river system. The two major Himalayan rivers, the Indus and the Brahmaputra originate from the north of the mountain ranges. They cut through the mountains making gorges in the upper course. The perennial Himalayan rivers have long courses from their source to the sea. They perform intensive erosional activity in their upper courses and carry huge loads of silt and sand with their swift current. In the middle and the lower courses, these rivers form meanders, oxbow lakes, levees, and many other depositional features in their floodplains as their speed slackens. They also have well-developed deltas.
A large number of the Peninsular rivers like the Godavari, Kaveri, and Krishna are seasonal, as their flow is dependent on rainfall. During the dry season when it doesn’t rain, even the large rivers have reduced flow of water in their channels. The Peninsular rivers have shorter and shallower courses as compared to their Himalayan counterparts. However, some of them originate in the central highlands and flow towards the west. Most of the rivers of peninsular India originate in the Western Ghats and flow towards the Bay of Bengal.
Question:
A river along with its tributaries may be called a:
Option 1: highland
Option 2: river system
Option 3: peninsula
Option 4: flood plain
Correct Answer: river system
Solution : The correct choice is the second option.
Explanation: In the passage, it is mentioned that "a river along with its tributaries may be called a river system." This term is used to describe the combination of a main river and all its tributaries. The
Question : The expenditure on the cost of living of a man and his family is 60% of his salary. He gets two increments of 30% and 60% of his salary. If his savings increase by 250% of his initial savings, then the new cost of living expenditure is what percentage (rounded off to the one digit after decimal) of the increased salary?
Option 1: 32.7%
Option 2: 43.6%
Option 3: 29.5%
Option 4: 36.6%
Correct Answer: 32.7%
Solution : Let the salary of the man be 100a So, expenditure = 100a $\times$ 60% = 60a Savings = 100a – 60a = 40a Now, his new salary = 100a $\times \frac{130}{100} \times \frac{160}{100}$ = 208a His new savings = 40a + 40a $\times$ 250% =
Question : Who was the Viceroy at the time of quit India Movement ?
Option 1: Lord Mountbatten
Option 2: Lord Wavell
Option 3: Lord Lin Lithgow
Option 4: Lord Irwin
Correct Answer: Lord Lin Lithgow
Solution : The Correct Answer is Lord Lin Lithgow
The longest viceroyal tenure in India's history was eight years, which Lord Linlithgow held from 1936 to 1944. Mahatma Gandhi started the August Movement, also known as the Quit India Movement, on August 8, 1942, in
Question : Direction: One day, Nita left home and cycled 10 km towards the south, turned right and cycled 5 km, turned right and cycled 10 km, and turned left and cycled 10 km. How many kilometers will she have to cycle to reach her destination (starting point)?
Option 1: 10 km
Option 2: 15 km
Option 3: 20 km
Option 4: 25 km
Correct Answer: 15 km
Solution : As per the given information, the movement of Nita will look as follows –
According to the properties of a rectangle, opposite sides of the rectangle are equal, i.e., BC = AD = 5 km.
The distance that Nita has to travel to reach
Question : A dishonest shopkeeper professes to sell goods at its cost price but uses a false weight of 950 gm for each kilogram. His gain percentage is:
Option 1: $6\frac{1}{4}\%$
Option 2: $5\frac{5}{19}\%$
Option 3: $5\frac{3}{17}\%$
Option 4: $6\frac{2}{7}\%$
Correct Answer: $5\frac{5}{19}\%$
Solution : The shopkeeper sells 950 gm instead of 1000 gm. Let the cost price of 1 gm be Re. 1. Selling price of 950 gm = Cost price of 1000 gm = Rs. 1000 The cost price of 950 gm = Rs. 950 Profit = Rs.
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