A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

Question: Is $(p + q)^2 - 4pq$, where $p$, $q$ are natural numbers, positive? Statement I: $p < q$. Statement II: $p > q$.

Which one of the following is correct in respect of the above Question and the Statements?

A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills $\frac{3}{8}$th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?

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?

The price (p) of a commodity is first increased by k%, then decreased by k%; again increased by k%, and again decreased by k%. If the new price is q, then what is the relation between p and q?

What is the unit digit in the multiplication of $1 \times 3 \times 5 \times 7 \times 9 \times \dots \times 999$?

The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?

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 ?

What is the 489th digit in the number $123456789101112...?$

How many possible values of $(p + q + r)$ are there satisfying $\frac{1}{p} + \frac{1}{q} + \frac{1}{r} = 1$, where p, q, and r are natural numbers (not necessarily distinct)?

What is the maximum value of n such that $7 \times 343 \times 385 \times 1000 \times 2401 \times 77777$ is divisible by $35^n$?

What is the remainder when $9^3 + 9^4 + 9^5 + \dots + 9^{100}$ is divided by 6?

There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?

Consider the first 100 natural numbers. How many of them are not divisible by any one of $2$, $3$, $5$, $7$, and $9$?

A 4-digit number N is such that when divided by 3, 5, 6, and 9 it leaves a remainder of 1, 3, 4, and 7 respectively. What is the smallest value of N?

The average of three numbers p, q, and r is k. $p$ is as much more than the average as $q$ is less than the average. What is the value of $r$?

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 ?

Consider a set of 11 numbers:

Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers $\ge$ –5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers.

Which one of the following is correct?

Three prime numbers p, q, and r, each less than 20, are such that $p - q = q - r$. How many distinct possible values can we get for $(p + q + r)$?

P and Q walk along a circular track. They start at 5:00 am. from the same point in opposite directions. P walks at an average speed of $5$ rounds per hour and Q walks at an average speed of $3$ rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?

Team X scored a total of $N$ runs in 20 overs. Team Y tied the score in $10\%$ less overs. Had Team Y's average run rate (runs per over) been $50\%$ higher, the scores would have been tied in 12 overs. How many runs were scored by Team X?

A natural number N is such that it can be expressed as $N = p + q + r$, where p, q, and r are distinct factors of N. How many numbers below 50 have this property?

If $4 \leq x \leq 8$ and $2 \leq y \leq 7$, then what is the ratio of the maximum value of $(x + y)$ to the minimum value of $(x - y)$?

If N² = 12345678987654321, then how many digits does the number N have?

If n is a natural number, then what is the number of distinct remainders of $(1^n + 2^n)$ when divided by 4?

A tram overtakes 2 persons X and Y walking at 3 km/h and 4 km/h in the same direction and completely passes them in 8 s and 9 s respectively. What is the length of the tram?

Let x be a real number between 0 and 1. Which of the following statements is/are correct?

I. $x^2 > x^3$ II. $x > \sqrt{x}$

Select the correct answer using the code given below:

A question is given followed by two Statements 1 and 2. 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-1: $2$ is one of the factors. Statement-2: $3$ is one of the factors.

Which one of the following is correct in respect of the above Question and the Statements?

Let $P = QQQ$ be a 3-digit number. What is the HCF of $P$ and $481$?

Let both $p$ and $k$ be prime numbers such that $(p^2 + k)$ is also a prime number less than 30. What is the number of possible values of $k$?

Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, $PQR - PS = PPT$. If $Q = 3$ and $T < 6$, then what is the number of possible values of $(R, S)$?

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of runs scored by X to runs scored by Y equals the ratio of runs scored by Y to runs scored by Z.

Value-I = Runs scored by X Value-II = Runs scored by Y Value-III = Runs scored by Z

Which one of the following is correct?

A question is given followed by two Statements 1 and 2. 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-1: $R = 1$. Statement-2: $S = 2$.

Which one of the following is correct in respect of the above Question and the Statements?

The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?

Let $p + q = 10$, where $p$ and $q$ are integers.

Value-I = Maximum value of $p \times q$ when $p$, $q$ are positive integers. Value-II = Maximum value of $p \times q$ when $p \ge -6$, $q \ge -4$.

Which one of the following is correct?

A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct?

I. The minimum number of cuts is $9$. II. The number of smaller pieces which are not painted on any face is $6$.

Select the correct answer using the code below: