Staff Selection Commission Combined Graduate Level Exam
Question : Identify the correct statement
Option 1: The resistance of a wire depends on the length and density of the wire.
Option 2: Specific resistance is the same for all conductors.
Option 3: The resistance of a wire depends on the length and cross-section of the wire.
Option 4: Specific resistance is dependent on the cross-sectional area of the wire.
Correct Answer: The resistance of a wire depends on the length and cross-section of the wire.
Solution : The correct answer is The resistance of a wire depends on the length and cross-section of the wire.
The resistance of a conductor is determined by the following characteristics.
Question : If $x^2+\frac{1}{x^2}=2$, then the value of $x-\frac{1}{x}$ is:
Option 1: –2
Option 2: 0
Option 3: 1
Option 4: –1
Correct Answer: 0
Solution : Given: $x^2+\frac{1}{x^2}=2$ We know that the algebraic identity is $(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$ Substitute the value of $x^2+\frac{1}{x^2}=2$ in the above expression, we get, $(x-\frac{1}{x})^2=2-2$ ⇒ $(x-\frac{1}{x})^2=0$ ⇒ $(x-\frac{1}{x})=0$ Hence, the correct answer is 0.
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 - operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (168, 35, 143) (182, 65, 127)
Option 1: (142, 83, 69)
Option 2: (253, 99, 154)
Option 3: (203, 89, 117)
Option 4: (159, 62, 87)
Correct Answer: (142, 83, 69)
Solution : Given: (168, 35, 143); (182, 65, 127)
In the given sets, subtract the third number from the first number and then add 10. (168, 35, 143)→168 – 143 = 25; 25 + 10 = 35 (182, 65, 127)→182 – 127 = 55; 55
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
The climate (1) / of Mumbai (2) / is better than Hyderabad. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The error lies in the third part of the sentence.
The comparative degree "better" is employed to compare two things. In this particular sentence, it compares the climates of two places. When comparing one thing to another, it's appropriate to use "that of" for singular
Question : Directions: Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 7 : 25 :: 4 : 4 :: 3 : ?
Option 1: 5
Option 2: 4
Option 4: 7
Correct Answer: 1
Solution : Given: 7 : 25 :: 4 : 4 :: 3 : ?
Like, 7 : 25→(7 – 2)2 = (5)2 = 25 And, 4 : 4→(4 – 2)2 = (2)2 = 4 Similarly, for 3 : ?→(3 – 2)2 =
Do you know (1) / whom the (2) next speaker is? (3) / No Error (4)
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The error lies in the second part of the sentence.
Explanation: The relative pronoun "whom" is used for the object of a verb or preposition, while "who" is used for the subject. In this case, "who" is the correct choice because it is the subject
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,
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.
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
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
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