Cengage Experts Team (CET) Solutions for Exercise 1: Practice Exercise

While adding the first few consecutive natural numbers, a candidate missed one of the numbers and wrote the answer as 177. Which number did the candidate miss?

If the sum of the first $11$ terms of AP is equal to the sum of the first $19$ terms, then what is the sum of the first $30$ terms?

Two cars start together in the same direction from the same place. The first one travels at a uniform speed at $10 \mathrm{km}/\mathrm{hr}$. The second one travels at the speed $8 \mathrm{km}/\mathrm{hr}$ in the first hour and increases the speed by $\frac{1}{2}$ km in each succeeding hour. After how many hours will the second car overtake the first car if both the cars travel non-stop?

A man repays a loan of Rs. $3250$ by paying Rs. $20$ in the first month and then increases the payment by Rs.$15$ every month. How long will it take him to clear the loan?

A man arranges to pay off a debt of $₹3600$ by $40$ annual instalments which form an arithmetic series. When $30$ of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment?

There are 240 balls and 'n' number of boxes B1, B2, B3, •••••, Bn. The balls are to be placed in the boxes such that B1 contains four balls more than B2, B2 contains four balls more than B3, and so on. Which one of the following cannot be the possible value of 'n'?

About $150$ workers were engaged to finish a piece of work in a certain number of days. If four workers were dropped on the second day, another four workers were dropped on the third day and so on, it takes eight more days to finish the work. Find the number of days in which the work will be finished?

Certain cells divide into two cells, every hour. What will be the total number of cells in a span of $5$ hours, if we start with a single cell?