CDS Elementary Mathematics 2023 Question Paper

What is the largest number which divides both $2^{35}-1$ and $2^{91}-1$?

What is the largest power of 10 that divides the product $29\times 28\times 27\times dots\times 2\times 1$?

What is the remainder when $65^{99}$ is divided by 11?

If the roots of the equation $x^2-bx+c=5$ differ by 5, then which one of the following is correct?

In a party of 150 persons, 75 persons take tea, 60 persons take coffee and 50 persons take milk. 15 of them take both tea and coffee, but no one taking milk takes tea. If each person in the party takes at least one drink, then what is the number of persons taking milk only?

A, B, C, D and E enter into a business. They invest money in the ratio 2 : 3 : 4 : 5 : 6. However, the time invested by them is in the ratio 6 : 5 : 4 : 3 : 2. If the profit distributed is directly proportional to time and money invested, then who receives the highest amount of profit?

Consider the following numbers:

1. 437
2. 797
3. 1073
   How many of the above numbers are prime?

A can do a certain work at twice the speed of B. Further, B can do the same work at 1.5 times the speed of C. All of them together can finish the work in 12 days. In how many days can C alone finish the work?

The sum of digits of a 2-digit number is 12. When the digits are reversed, the number becomes greater by eighteen. What is the difference between the digits in the number?

The time taken by a train to cross a man travelling in another train is 10 seconds, when the other train is travelling in the opposite direction. However, it takes 20 seconds, if both the trains are travelling in the same direction. The length of the first train is 200 m and that of the second train is 150 m. What is the speed of the first train?