AILET entrance exam Question Bank Solutions

A man rows to a place 48 km distance and come back in 14 h. He finds that he can row 4 km with the stream at the same time as 3 km against the stream. The rate of the stream is

A boat running upstream takes 8 h 48 m to cover a certain distance, while it takes 4 h to cover the same distance running downstream. What is the ratio between the speed of the boat and the speed of the water current respectively?

Mr. X drives to his office at an average speed of 48 km per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?

A car completes a certain journey in 8 h. It covers half the distance at 40 km/h and the rest at 60 km/h. The length of the journey is

A man covers half of his journey as 6 km/h and the remaining half at 3 km/h. His average speed is

A goods train is 800 meters long and it is running at a constant speed of 60 km/per hour. If it takes 120 seconds to pass a bridge, then calculate the length of the bridge?

It takes eight hours for a 600 km journey. if 120 km is done by train and the rest by car. It takes 20 min more if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is

Find the number of real solutions for the equation `(8^x + 27^x)/(12^x + 18^x) = 7/6`.

Solve the following question and mark the best possible option.
Find the maximum value of ab (72 – 3a  – 4b), for a, b > 0

Solve the following question and mark the best possible option.
Find the maximum value of (1 – x) (1 + x) (1 + x) where x ≥ 0.

Solve the following question and mark the best possible option.
Let f(a) = `(a^4 + 9)/(10a)`, then

Solve the following question and mark the best possible option.
If 0 < b < a, then find the minimum value of `a + 1/((a - b)b)`.

A box contains ₹ 56 in the form of coins of one rupee, 50 paise, and 25 paise. The number of 50 paisa coins is double the number of 25 paisa coins and four times the number of one rupee coins. The number of 50 paisa coin in the box is

The price of 7 bananas is equal to the cost of 3 kiwis. The price of 2 kiwis is equal to the cost of 1 banana and 5 chikoos. lf Rambo has just enough money to buy 30 chikoos, then how many bananas Rambo could buy with the same amount?

287 x 287 + 269 x 269-2 x 287 x 269 = ?

(112 x 54⁴) = ?

If `114/0.144 = 14.4/x`, then the value of x is

3889 + 12.952 - ? = 3854.002

(1000)⁹ ÷ (10)²⁴ =?

`((489 + 375)^2-(489 - 375)^2)/((489×375))` = ?