Staff Selection Commission Combined Graduate Level Exam
Question : Which of the following statements is correct? I. If $x = 12, y = -2$ and $z = -10$, then $x^3+y^3+z^3=720$ II. If $x + y = 48$ and $4xy =128$, then the value of $4x^2+4y^2$ is 8960
Option 1: Neither I nor II
Option 2: Only I
Option 3: Both I and II
Option 4: Only II
Correct Answer: Both I and II
Solution : I. $x = 12, y = -2, z = -10$ $x^3+y^3+z^3$ $= 12^3 + (-2)^3 + (-10)^3$ $=1728-8-1000$ $=720$ So, $x^3+y^3+z^3=720$ II. $x + y = 48$ ⇒ $4xy =128$ ⇒ $xy = 32$ ⇒ $4x^2+4y^2=4(x^2+y^2)$ $=4[(x+y)^2-2xy]$ $=4[48^2-2×32]$ $=9216-256$ $=8960$ S0, $4x^2+4y^2=8960$
Question : The ratio of monthly incomes of A and B is 4 : 5 respectively. The ratio of monthly savings of A and B is 14 : 19 respectively. If the monthly expenditure of A and B is INR 1200 each, then what is the difference between the monthly incomes of A and B?
Option 1: INR 2000
Option 2: INR 4000
Option 3: INR 1000
Option 4: INR 5000
Correct Answer: INR 1000
Solution : Given: The ratio of monthly incomes of A and B is 4: 5 respectively. The ratio of monthly savings of A and B is 14: 19 respectively. Let the ratio of monthly incomes of A and B be $4x: 5x$ respectively. Let the ratio
Question : Select the most appropriate option to fill in the blank. Which _______ do you usually take to reach your office?
Option 1: route
Option 2: root
Option 3: rout
Option 4: rude
Correct Answer: route
Solution : The correct choice is the first option.
A route is a path or way to get from one place to another. In this context, it makes sense to ask about the route someone takes to reach their office.
The meanings of the other options
Question : Comprehension: Read the following passage and answer the questions given after it. In the late 18th century the Industrial Revolution began to transform life in Britain. Until then, most people lived in the countryside and made their living from farming. By the mid-19th century, most people in Britain lived in towns and made their living from mining or manufacturing industries. In 1712 a man named Thomas Newcomen (1663-1729) made primitive steam engines for pumping water from mines. In 1769 James Watt (1736-1819) patented a more efficient steam engine. In 1785 his engine was adapted to driving machinery in a cotton factory. The use of steam engines to drive machines slowly transformed the industry. Meanwhile, during the 1700s Britain built up a great overseas empire. The North American colonies were lost after the War of Independence 1776-1783. On the other hand, after the Seven Years' War 1756-1763, Britain captured Canada and India. Britain also took Dominica, Grenada, St. Vincent and Tobago in the West Indies. In 1707 the Act of Union was passed. Scotland was united with England and Wales. England became part of Great Britain. Owning land was the main form of wealth in the 18th century. Political power and influence were in the hands of rich landowners. At the top were the nobility. Below them were a class of nearly rich landowners called the gentry. In the early 18th century there were another class of landowners called yeomen who were small landowners, described as farmers of the middle class. However, during the century this class became less and less numerous. However other middle class people such as merchants and professional men became richer and more numerous, especially in the towns. Below them were the great mass of the population, craftsmen and labourers. In the 18th century, probably half the population lived at subsistence or bare survival levels. In the early 18th century England suffered from gin drinking. It was cheap and it was sold everywhere as you did not need a license to sell it. Many people ruined their health by drinking gin. Sadly, for many poor people drinking gin was their only comfort. The situation improved after 1751 when a tax was imposed on gin. At the end of the 17th century, it was estimated the population of England and Wales was about 5 1/2 million. The population of Scotland was about 1 million. The population of London was about 600,000. In the mid-18th century, the population of Britain was about 6 1/2 million. In the late 18th century it grew rapidly and by 1801 it was over 9 million. The population of London was almost 1 million. During the 18th century, towns in Britain grew larger. Nevertheless, most towns still had populations of less than 10,000. However, in the late 18th century new industrial towns in the Midland and the North of England mushroomed. Meanwhile, the population of London grew to nearly 1 million by the end of the century. Other towns were much smaller. The population of Liverpool was about 77,000 in 1800. Birmingham had about 73,000 people and Manchester had about 70,000. Bristol had a population of about 68,000. Sheffield was smaller with 31,000 people and Leeds had about 30,000 people. Question: Which of the following statements is NOT true according to the passage?
Option 1: After the War of Independence, Britain had colonies in North America.
Option 2: In the mid-19th century the towns grew and most people were engaged in mining and manufacturing.
Option 3: In 18th century England almost half the population consisted of poor people.
Option 4: Before the Industrial Revolution, most of the people in England lived in villages and were engaged in agriculture.
Correct Answer: After the War of Independence, Britain had colonies in North America.
Solution : The right choice is the first option.
Explanation: The passage mentions that during the 1700s, Britain built a great overseas empire but lost the North American colonies after the War of Independence, which occurred
Question : Directions: Arrange the following words as per their order in the dictionary. 1. Eyelid 2. Eyeless 3. Eyesore 4. Eyesight
Option 1: 2, 1, 4, 3
Option 2: 2, 1, 3, 4
Option 3: 4, 3, 1, 2
Option 4: 4, 2, 3, 1
Correct Answer: 2, 1, 4, 3
Solution : Given: 1. Eyelid 2. Eyeless 3. Eyesore 4. Eyesight
Step 1: Since all the words start with the same letter E, so move on to the next letter. Step 2: The second and third letters of each word are the same,
Question : Which of the following is called the 'Land of the Golden Pagoda'?
Option 1: Myanmar
Option 2: China
Option 3: Japan
Option 4: North Korea
Correct Answer: Myanmar
Solution : The correct answer is Myanmar.
In Mon State, Myanmar, there is a well-known Buddhist pilgrimage site called the Kyaiktiyo Pagoda, also called the Golden Rock. After the pilgrimage, devotees cover the holy rock, also known as the "golden rock", with gold leaves pasted on as
Question : Directions: Select the figure from among the given options that can replace the question mark (?) in the following series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Here the pattern is as follows – 1. In the given figure, consecutive odd numbers are present diagonally. 2. The star gets shaded and non-shaded alternatively. So, following the above pattern, the required figure will be as follows –
Hence, the third option is correct.
Question : A dishonest dealer sells a product at an 11% loss on cost price but uses 22% less weight. What is his percentage profit or loss?
Option 1: 14.1% loss
Option 2: 14.1% gain
Option 3: 11.4% gain
Option 4: 11.4 % loss
Correct Answer: 14.1% gain
Solution : Here cost price is denoted by CP, and the selling price is denoted by SP. Let his good contains 1 kg. Its actual weight is 22% of 1000 g = 780 g Let the CP of each gm be Re. 1. Then CP of
Question : Direction: In the given question, select the related letter from the given alternatives.
$\sqrt{A F I}=M: \sqrt{A D D}=L:: \sqrt{A B A}=?$
Option 1: I
Option 2: N
Option 3: O
Option 4: K
Correct Answer: K
Solution : Given:
The place value of A is 1, F is 6, I is 9.
So, the value of $\sqrt{A F I}$ is $\sqrt{169}$ = 13 = M.
Likewise, the place value of A is 1, D
Question : A can of water and milk mixture contains 60% milk. A part of this mixture is replaced by another mixture containing 50% milk and the percentage of milk was found to be 52%. The quantity of mixture replaced is:
Option 1: $\frac{1}{5}$
Option 2: $\frac{3}{5}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{2}{5}$
Correct Answer: $\frac{4}{5}$
Solution : Given, a can of mixture of water and milk containing 60% milk. Then, a part of this mixture is replaced by another mixture containing 50% milk. The percentage of milk is found to be 52%. ⇒ The ratio of the original solution that has 60%
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