AILET entrance exam Question Bank Solutions for Mathematics

The differential of coefficient of x^x is: 

The value of sin^h-1x: 

If f(y) = log y, then f(y) + f(1/y) is equal to:

sec x dx is equal to:

The value of Cos h^-1 x is: 

The value of cos h (π π i) is :

The position vectors of the two points A and B are a and b respectively then the position vector of the point C which divides AB in the ration 2 : 1 will be :

In a University, for each f 200 spent by the Cultural Committee, Debating Committee spends f 20 and for every Rs. 400 spent by the Debating Committee, the Student Welfare Committee spends f 150. The triple ratio of the money spent by the Cultural Committee to the money spent by the Debating Committee to the money spent by the Student Welfare Committee can be expressed as

₹324 is divided among three friends Sonu, Monu, and Hari in the ratio 5:6:7. What is Monu's share of the money?

The ratio in which Aman and Bimal have contributed to the capital of a company is 3: 4. Bimal has invested his capital for only 3 months and has received half as much profit as Aman, at the end of the year. Find out for how much time has Aman invested his capital in the company.

Two whole numbers whose sum is 64 can be in the ratio of?

Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes?

In a bag, there are coins of 25 paise, 10 paise, and 5 paise in the ratio of 1 : 2 : 3. If there is ₹30 in all, how many 5 paise coins are there?

The ratio between two numbers is 2 : 3. If the consequent is 24, the antecedent is

The fourth proportional to 5, 8, 15 is

Seats for Mathematics, Physics, and Biology in a school are in the ratio 5 : 7: 8. There is a proposal to increase these seats by 40%, 50% and 75%, respectively. What will be the ratio of increased seats?

The ratio of ages of Ram and Gopal is 2 : 5 and the ratio of the ages of Gopal and Vishnu is 3 : 4. What would be the ratio of the ages of Ram, Gopal, and Vishnu?

The sum of the three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is

A sum of money is to be distributed among A, B, C and D in the proportion of 5 : 2 : 4 : 3. If C gets ₹1000 more than D, what is B's share?

A, B and C enter into a partnership in the ratio `7/2:4/3:6/5`. After 4 months, A increase in his share 50%. If the total profit at the end of one year be ₹21600, then B's share in the profit is