Consider the following statements in respect of the sum $S = x + y + z$, where $x$, $y$ and $z$ are distinct prime numbers each less than 10:

1. The unit digit of $S$ can be 0.
2. The unit digit of $S$ can be 9.
3. The unit digit of $S$ can be 5.

Which of the statements given above are correct?

On January 1st, 2023, a person saved Rs $1$. On January 2nd, 2023, he saved Rs. $2$ more than that on the previous day. On January 3rd, 2023, he saved Rs. $2$ more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well a perfect cube?

How many consecutive zeros are there at the end of the integer obtained in the product $1^2 \times 2^4 \times 3^6 \times 4^8 \times.... \times 25^{50}$?

Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements:

1. $(p-r)^{2^{qs}}$ is even.
2. $(q-s)^{q^{2s}}$ is even.
3. $(q + r)^{2^{p + s}}$ is odd.

Which of the statements given above are correct?

If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

Three numbers $x$, $y$, $z$ are selected from the set of the first seven natural numbers such that $x > 2y > 3z$. How many such distinct triplets $(x, y, z)$ are possible?

What is the number of fives used in numbering a 260-page book?

A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?

What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey ?

A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?

Two persons P and Q enter into a business. P puts ₹ $14,000$ more than Q, but P has invested for $8$ months and Q has invested for $10$ months. If P's share is ₹ $400$ more than Q's share out of the total profit of ₹ $2,000$, what is the capital contributed by P?

X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work.

P’s salary is 20% lower than Q’s salary which is 20% lower than R’s salary. By how much percent is R’s salary more than P’s salary?

Let $p$ and $q$ be positive integers satisfying $p<q$ and $p+q=k$. What is the smallest value of $k$ that does not determine $p$ and $q$ uniquely?

Consider the following :

1. 1000 litres = $1m^3$
2. 1 metric ton = 1000 kg
3. 1 hectare = $10000 m^2$

Which of the above are correct?

In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If $(X + Y)$ is the greatest two-digit number, then what is the number of possible values of X?

A Question is given followed by two Statements I and II. Consider the Question and the Statements. A certain amount was distributed among X, Y and Z. Question: Who received the least amount?

Statement-I: X received $\frac{4}{5}$ of what Y and Z together received. Statement-II: Y received $\frac{2}{7}$ of what X and Z together received.

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

A certain number of men can complete a piece of work in $6k$ days, where $k$ is a natural number. By what percent should the number of men be increased so that the work can be completed in $5k$ days?

421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1 ?

$32^5 + 2^{27}$ is divisible by

What is the sum of the first 28 terms in the following sequence? 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2,......

What is the rightmost digit preceding the zeros in the value of $30^{30}$?

A father said to his son, “$n$ years back I was as old as you are now. My present age is four times your age $n$ years back”. If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?

Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women

If the average weight of the women is 63 kg, then what is the average weight of the boys?

$222^{333} + 333^{222}$ is divisible by which of the following numbers ?

A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?