CDS Elementary Mathematics 2019 Question Paper

What is the remainder when $(17^{29}+19^{29})$ is divided by 18?

What is the largest value of $n$ such that $10^n$ divides the product $2^5\cdot 3^3\cdot 4^8\cdot 5^3\cdot 6^7\cdot 7^6\cdot 8^{12}\cdot 9^9\cdot 10^6\cdot 15^{12}\cdot 20^{14}\cdot 22^{11}\cdot 25^{15}$?

How many pairs $(A,B)$ are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd?

Consider the multiplication $999\times abc=def132$ in decimal notation, where $a,b,c,d,e$ and $f$ are digits. What are the values of $a,b,c,d,e$ and $f$ respectively?

Three cars A, B and C started from a point at 5 p.m., 6 p.m. and 7 p.m. respectively and travelled at uniform speeds of 60 km/hr, 80 km/hr and $x$ km/hr respectively in the same direction. If all the three met at another point at the same instant during their journey, then what is the value of $x$?

Priya's age was cube of an integral number (different from 1) four years ago and square of an integral number four years hence. How long should she wait so that her age becomes square of a number in the previous year and cube of a number in the next year?

Which of the following statements is not true?

For $x>0$, what is the minimum value of $x+\frac{x+2}{2x}$?

If $\frac{1+px}{1-px}\cdot \sqrt{\frac{1-qx}{1+qx}}=1$, then what are the non-zero solutions of $x$?

In a hostel the rent per room is increased by 20%. If the number of rooms in the hostel is also increased by 20% and the hostel is always full, then what is the percentage change in the total collection at the cash counter?