Staff Selection Commission Combined Graduate Level Exam
Question : If $a \cot \theta=b$, what will be the value of $\frac{b \cos \theta–a \sin \theta}{b \cos \theta+a \sin \theta}$?
Option 1: $\frac{b^2+a^2}{b^2–a^2}$
Option 2: $b^2+a^2$
Option 3: $\frac{b^2–a^2}{b^2+a^2}$
Option 4: $0$
Correct Answer: $\frac{b^2–a^2}{b^2+a^2}$
Solution : Given: $a \cot \theta=b$ $⇒\cot \theta=\frac{b}{a}$ $⇒\frac{\cos \theta}{\sin \theta}=\frac{b}{a}$ Let $\cos a = bk $ and $\sin a =ak$ (where $k$ is a constant) Putting these values in the expression, we get, $\frac{b \cos \theta–a \sin \theta}{b \cos \theta+a \sin \theta}$ $=\frac{b×bk-a×ak}{b×bk+a×ak}$ $=\frac{k(b^2–a^2)}{k(b^2+a^2)}$ $=\frac{b^2–a^2}{b^2+a^2}$ Hence, the correct answer is $\frac{b^2–a^2}{b^2+a^2}$.
Question : Comprehension: Read the given passage and answer the questions that follow. Plato is the earliest important educational thinker, and education is an essential element in 'The Republic' (his most important work on philosophy and political theory, written around 360 B.C.). In it, he advocates some rather extreme methods: removing children from their mothers' care and raising them as wards of the state, and differentiating children suitable to the various castes, the highest receiving the most education, so that they could act as guardians of the city and care for the less able. He believed that education should be holistic, including facts, skills, physical discipline, music, and art. Plato believed that talent and intelligence are not distributed genetically and thus can be found in children born to all classes, although his proposed system of selective public education for an educated minority of the population does not really follow a democratic model.
Aristotle considered human nature, habit, and reason to be equally important forces to be cultivated in education, the ultimate aim of which should be to produce good and virtuous citizens. He proposed that teachers lead their students systematically, and that repetition be used as a key tool to develop good habits, unlike Socrates' emphasis on questioning his listeners to bring out their own ideas. He emphasized the balancing of the theoretical and practical aspects of subjects taught, among which he explicitly mentions reading, writing, mathematics, music, physical education, literature, history, and a wide range of sciences, as well as play, which he also considered important.
Question: Which of these statements is NOT true?
Option 1: Socrates encouraged the listeners to come up with original ideas.
Option 2: The Republic was written around 360 A.D.
Option 3: Socrates considered music and physical education as important aspects of learning.
Option 4: Plato's methods of education can be called 'extreme'.
Correct Answer: The Republic was written around 360 A.D.
Solution : The second option is the correct choice.
The statement the Republic was written around 360 A.D. is not true.
Explanation: The Republic, Plato's most important work on philosophy and political theory, was written around 360 B.C., not 360 A.D. The use of B.C. (Before Christ) and A.D. (Anno Domini) helps specify the historical period. Plato lived in ancient Greece, and his influential work was composed in the 4th century B.C., making the correct time reference.
Question : Directions: In the following question, which one is the wrong number in the given series? 7, 56, 447, 3584, 28672
Option 1: 3584
Option 2: 56
Option 3: 7
Option 4: 447
Correct Answer: 447
Solution : Given: 7, 56, 447, 3584, 28672
In the above-given series, multiply the previous number by 8 to get the next number. 7 × 8 = 56; 56 × 8 = 448 ≠ 447; 448 × 8 = 3584; 3584 × 8 = 28672
So, 447 is the wrong number as it doesn't follow the pattern. Hence, the fourth option is correct.
Question : When a magnesium ribbon is burnt in oxygen, it gets converted to ______.
Option 1: magnesium peroxide
Option 2: magnesium hydroxide
Option 3: magnesium carbonate
Option 4: magnesium oxide
Correct Answer: magnesium oxide
Solution : The correct option is magnesium oxide.
When a magnesium ribbon is burned in oxygen, it is converted into magnesium oxide (MgO). The chemical reaction can be represented as follows: 2Mg + O2 → 2MgO. This reaction is an example of a combustion reaction, where magnesium reacts with oxygen to form magnesium oxide, releasing energy in the form of light and heat.
Question : Direction: In the following series, how many HIG occur in such a way that I is in the middle and H and G are adjacent to it on both sides?
GGHIHIIGGJKLMGIHIG
Option 1: 3
Option 2: 2
Option 3: 5
Option 4: 4
Correct Answer: 2
Solution : Given:
By checking the number of HIG, such that I is in the middle and H and G are adjacent to it on both sides -
GGHIHIIGGJKLMGIHIG = GIH and HIG
So, there are two HIG's that follow the pattern.
hence, second option is correct.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
(Bacteria is) the most common form of life
(1) Bacteria are
(2) Bacterium are
(3) Bacteria was
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
Explanation:
"Bacteria are" is the correct form because "bacteria" is a plural noun, and the verb should agree in number, so it should be "are" whereas "bacterium are" is incorrect because "bacterium" is a singular form and cannot agree with the plural verb.
So, the correct sentence would be: "Bacteria are the most common form of life."
Question : Which of the following states in India, from October to December, receive rainfall due to northeast monsoon?
Option 1: Tamil Nadu, Kerala and Andhra Pradesh
Option 2: Punjab, Haryana and Madhya Pradesh
Option 3: Andhra Pradesh, Madhya Pradesh and Karnataka
Option 4: Uttar Pradesh, Bihar and West Bengal
Correct Answer: Tamil Nadu, Kerala and Andhra Pradesh
Solution : The correct option is Tamil Nadu, Kerala and Andhra Pradesh.
The rainy season for Tamil Nadu, Kerala, and Andhra Pradesh is the northeast monsoon. Usually, starting across southern India between October and December of each year, this monsoon system is seasonal. The northeast monsoon is characterised by winds that liberally deposit moisture across the southern states of Tamil Nadu, Andhra Pradesh, Kerala, and even the southern parts of Telangana and Karnataka after sweeping it up from the Bay of Bengal.
Question : Select the correct indirect form of the given sentence. The blind man said to me, “Can you help me cross the road?”
Option 1: The blind man asked me if I could help him cross the road.
Option 2: The blind man asked me if I will help him cross the road.
Option 3: The blind man asked me if I could help him crossed the road.
Option 4: The blind man asked me if I can help him cross the road.
Correct Answer: The blind man asked me if I could help him cross the road.
Solution : The first option is the correct choice.
The steps of conversion are as follows:
Therefore, the correct answer is: "The blind man asked me if I could help him cross the road."
Question : The number of mobile sim cards in 4 states UT is given in the bar diagram. Study the diagram and answer the question. In which State UT is there the smallest number of owners of the BSNL Sim-card?
Option 1: Punjab
Option 2: UP
Option 3: Delhi
Option 4: Bihar
Correct Answer: Delhi
Solution : It is clearly visible from the bar graph given that Delhi has the least number of BSNL-sim card users. Hence, the correct answer is Delhi.
Question : Directions: In the following question, find the odd letter cluster from the given alternatives.
Option 1: AG
Option 2: WA
Option 3: ET
Option 4: IQ
Correct Answer: ET
Solution : Let's check the options – First option: AG; A (1) + G (7) = 7 + 1 = 8 (This is an even number.) Second option: WA; W (23) + A (1) = 23 + 1 = 24 (This is an even number.) Third option: ET; E (5) + T (20) = 20 + 5 = 25 (This is an odd number.) Fourth option: IQ; I (9) + Q (17) = 9 + 17 = 26 (This is an even number.)
So, the third option is different from the other options as the resultant is an odd number. Hence, the third option is correct.
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