CAT 2024

Slot 2

QA

All Questions

The sum of the infinite series $\cfrac{1}{5}\left(\cfrac{1}{5} - \cfrac{1}{7}\right) + \left(\cfrac{1}{5}\right)^2 \left(\left(\cfrac{1}{5}\right)^2 - \left(\cfrac{1}{7}\right)^2\right) + \left(\cfrac{1}{5}\right)^3 \left(\left(\cfrac{1}{5}\right)^3 - \left(\cfrac{1}{7}\right)^3\right) + ......$ is equal to

If $m$ and $n$ are natural numbers such that $n > 1$, and $m^n = 2^{25} \times 3^{40}$, then $m - n$ equals

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year ...

If $(x + 6\sqrt{2})^{\cfrac{1}{2}} - (x - 6\sqrt{2})^{\cfrac{1}{2}} = 2\sqrt{2}$, then x equals

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

A bus starts at 9 am and follows a fixed route every day. One day, it traveled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it traveled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is

Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is

When $3^{333}$ is divided by 11, the remainder is

A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

The roots $\alpha, \beta$ of the equation $3x^2 + \lambda x - 1 = 0$, satisfy $\cfrac{1}{\alpha^2} + \cfrac{1}{\beta^2} = 15$.
The value of $(\alpha^3 + \beta^3)^2$, is

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would...

All the values of x satisfying the inequality $\cfrac{1}{x + 5} \leq \cfrac{1}{2x - 3}$ are

If x and y satisfy the equations $\mid x \mid + x + y = 15$ and $x + \mid y \mid - y = 20$, then $(x - y)$ equals