Prepare for Civil Services Aptitude Test (Paper-II) with step-by-step solutions for Quantitative Aptitude, Logical Reasoning, Analytical Ability, Data Interpretation, and Reading Comprehension.
Marking pattern: +2.50 positive, -0.83 negative (Official UPSC CSAT Pattern).
If n is a natural number, then what is the number of distinct remainders of (1n + 2n) when divided by 4?
Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
What is the 489th digit in the number 123456789101112...?
A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows:
P: I did not steal. Q stole it.
Q: R did not steal. I did not steal.
R: I did not steal. I do not know who did it.
Who stole the mobile phone?
Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point.
Which of the following statements is/are correct?
I. The result of the match between P and Q is a draw with the score 0-0.
II. The number of goals scored by R against Q is 1.
Which of the statements given above is/are correct?
Directions for the following item: Read the following passage and answer the item that follows. Your answer to this item should be based on the passage only.
Passage - 1
It is hard to predict how changes in the climate and the atmosphere's chemistry will affect the prevalence and virulence of agricultural diseases. But there is a risk that such changes will make some plant infections more common in all climatic zones, perhaps catastrophically so. Part of the problem is that centuries of selective breeding have refined the genomes of most high-value crops. They are spectacular at growing in today's conditions but genetic variations that are not immediately useful to them have been bred out. This is good for yields but bad for coping with changes. A minor disease or even an unknown one could suddenly rampage through a genetically honed crop.
Which one of the following statements best reflects the central idea conveyed by the passage?
Directions for the following item: Refer to Passage - 1 given above and answer the item based on the passage only.
With reference to the above passage, the following assumptions have been made:
I. Global climate change can result in the migration of several plant diseases to new areas.
II. Scientific understanding of the wild relatives of our present crops would enable us to strengthen food security.
Which of the above assumptions is/are valid?
Directions for the following item: Read the following passage and answer the item that follows. Your answer to this item should be based on the passage only.
Passage - 2
"A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents show him where the dangers are. So if he is wise he will often pray to be delivered from his friends, because they will ruin him. But, though it hurts, he ought also to pray never to be left without opponents; for they keep him on the path of reason and good sense. The national unity of free people depends upon a sufficiently even balance of political power to make it impracticable for the administration to be arbitrary and for opposition to be revolutionary and irreconcilable."
Which one of the following statements best reflects the critical message conveyed by the author of the passage?
Directions for the following item: Refer to Passage - 2 given above and answer the item based on the passage only.
With reference to the above passage, the following assumptions have been made:
I. In a democracy, a strong opposition is required only if the Head of Government is indifferent.
II. The more aggressive the opposition, the better is the governance in a democracy.
Which of the above assumptions is/are valid?
P is the brother of Q and R. S is R's mother. T is P's father. How many of the following statements are definitely true?
I. S and T are a couple.
II. Q is T's son.
III. T is Q's father.
IV. S is P's mother.
V. R is T's daughter.
VI. P is S's son.
Select the correct answer using the code given below:
If NO is coded as 210, NOT is coded as 4200 and NOTE is coded as 21000, then how is NOTES coded?
If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded?
The 5-digit number PQRST (all distinct digits) is such that $T \ne 0$. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?
X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in $8\frac{2}{3}$ days. What is n equal to?
What is X in the sequence 1, 3, 6, 11, 18, X, 42?
Directions for the following item: Read the following passage and answer the item that follows. Your answer to this item should be based on the passage only.
Passage - 1
There has been no democracy that has grown economically without corporate capitalism. It helps in modernizing the economy and enabling the transition from rural to urban, and agriculture to industry and services, which are inevitable with growth. It generates jobs — and there is no other way to fix a country's unemployment challenge without a further impetus to private business. Big companies can operate on a large scale and become competitive both domestically and externally. A vibrant corporate capitalist base also leads to additional revenues for the State — which in turn, can be used for greater welfare for the marginalized and creating a more level playing field in terms of opportunities.
Which one of the following statements best reflects the critical message conveyed by the author of the passage?
Directions for the following item: Refer to Passage - 1 given above and answer the item based on the passage only.
With reference to the above passage, the following assumptions have been made:
I. Corporate capitalism promotes the growth of labour force and provides more employment opportunities.
II. Poor and marginalized sections of population are benefited by corporate capitalism due to trickle-down effect.
Which of the above assumptions is/are valid?
Directions for the following item: Read the following passage and answer the item that follows. Your answer to this item should be based on the passage only.
Passage - 2
"A network of voluntary associations stands as a 'buffer' between the relatively powerless individual and the potentially powerful State."
Which one of the following statements reflects the best explanation of the above passage?
Consider the following statements:
I. There exists a natural number which when increased by 50% can have its number of factors unchanged.
II. There exists a natural number which when increased by 150% can have its number of factors unchanged.
Which of the statements given above is/are correct?
There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person?
In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code?
What is the remainder when $9^3 + 9^4 + 9^5 + 9^6 + \dots + 9^{100}$ is divided by 6?
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: What is the smallest 1-digit number having exactly 4 distinct factors?
Statement I: 2 is one of the factors.
Statement II: 3 is one of the factors.
Which one of the following is correct in respect of the above Question and the Statements?
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: Let P, Q, R, S be distinct non-zero digits. If $PP \times PQ = RRSS$, where $P \le 3$ and $Q \le 4$, then what is Q equal to?
Statement I: $R = 1$.
Statement II: $S = 2$.
Which one of the following is correct in respect of the above Question and the Statements?
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: How is Q related to P?
Statement I: P has two sisters, R and S.
Statement II: R's father is the brother of Q.
Which one of the following is correct in respect of the above Question and the Statements?