AILET entrance exam Question Bank Solutions

If x - a is a factor of P(x), then P(a) should be

A polynomial of degree ‘2’ is called

A polynomial of degree ‘1’ is called

A rational fraction `("N"("x"))/("D"("x"))`, with D(x) not equal to zero and degree of N(x) is less than degree of D(x) is known as

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is

The number of natural numbers of two or more than two digits in which digits from left to right are in increasing order is

Find the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7.

Find the least number that when divided by 16, 18, and 20 leaves a remainder 4 in each case, but is completely divisible by 7.

If `"x"/"y"=4/5`, then the value of `(4/7+(2"y"-"x")/(2"y"+"x"))` is

In a family, the father took one-fourth of the cake and he had three times more than the others had. The total number of family members is

A purse contains some coins consisting of rupees, fifty paise coins, and twenty-five paise coins. If coins are in the ratio of 2: 3: 10 and their total value is ₹72, the number of twenty-five paise coins will be

The difference between the number of numbers from 2 to 100 which are not divisible by any other number except 1 and itself and the numbers which are divisible by at least one more number along with one and itself.

The average of three prime numbers lying between 47 and 74 is 191/3. The greatest possible sum between any two out of the 3 prime numbers is

Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2, the third number is

Ten years ago, Sunil was half of Sudip's age. If the age of both at present is in the ratio of 3:4, what will be the total of their present age?

P, Q, and R are three consecutive odd numbers in ascending order. If the value of three times P is 3 less than two times R. Find the value of R.

A piece of string is 40 centimeters long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized and the shortest piece is 23 centimeters shorter than the longest piece. Find the length of the shortest piece (in cm).

Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is ₹700 when there are 25 boarders and ₹600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

You can collect rubies and emeralds as many as you can. Each ruby is worth ₹4 crore and each emerald is worth ₹5 crore. Each ruby weights 0.3 kg and each emerald weights 0.4 kg. Your bag can carry at the most 12 kg. What you should collect to get the maximum wealth?