Home · JEE Main & Advanced · IOQM · Functions

Functions — JEE Main & Advanced IOQM PYQs

20 previous year questions from Functions with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

20 questionsIOQMSolutions on every page

Let n be a positive integer such that 1 n 1000 . Let M_n be the number of integers in the set X_n= 4 n+1 , 4 n+2 , ., 4 n+1000 . Let a= M_n: 1 n 1000 and b= M_n: 1 n 1000 . Find a-

Olympiad workbook Solution View → 2

Positive integers x, y, z satisfy x y+z=160 . Compute the smallest possible value of x+y z .

Olympiad workbook Solution View → 3

Consider the sequence of number [n+ 2 n + 1 2 ] for n 1 , where [x] denotes the greatest integer not exceeding x . If the missing integers in the sequence are n₁ < n₂ < n₃ < then f

Olympiad workbook Solution View → 4

Let x₁ be a positive real number and for every integer n 1 let x_ n+1 =1+x₁ x₂ x_ n-1 x_n . If x₅=43 , what is the sum of digits of the largest prime factor of x₆ ?

Olympiad workbook Solution View → 5

Let f: R R be a function satisfying the relation 4 f(3-x)+3 f(x)=x^2 for any real x . Find the value of f(27)-f(25) to the nearest integer. (Here R denotes the set of real numbers.

Olympiad workbook Solution View → 6

Let f(x)= x 3 + 3 x 10 for all real x . Find the least natural number n such that f(n +x)=f(x) for all real x .

Olympiad workbook Solution View → 7

Find the largest value of a^b such that the positive integers a, b>1 satisfy a^b b^a+a^b+b^a=5329 .

Olympiad workbook Solution View → 8

The sum of [x] for all real numbers x satisfying the equation 16+15 x+15 x^2=[x]^3 is:

Olympiad workbook Solution View → 9

Let P(x)=a₀+a₁ x+a₂ x^2+ .+a_n x^n be a polynomial in which a_i is non-negative integer for each i 0,1,2,3, , n . If P(1)=4 and P(5)=136 , what is the value of P(3) ?

Olympiad workbook Solution View → 10

For any real number x , let [x] denotes the integer part of x ; x be the fractional part of x ( x =x-|x|) . Let A denote the set of all real numbers x satisfying x = x+[x]+[x+(1 /

Olympiad workbook Solution View → 11

Let f: R R be a function satisfying the relation 4 f(3-x)+3 f(x)=x^2 for any real x . Find the value of f(27)-f(25) to the nearest integer. (Here R denotes the set of real numbers.

Olympiad workbook Solution View → 12

The sum of [x] for all real numbers x satisfying the equation 16+15 x+15 x^2=[x]^3 is:

Olympiad workbook Solution View → 13

Let f(x)= x 3 + 3 x 10 for all real x . Find the least natural number n such that f(n +x)=f(x) for all real x .

Olympiad workbook Solution View → 14

Let n be a positive integer such that 1 n 1000 . Let M_n be the number of integers in the set X_n= 4 n+1 , 4 n+2 , ., 4 n+1000 . Let a= M_n: 1 n 1000 and b= M_n: 1 n 1000 . Find a-

Olympiad workbook Solution View → 15

Let x₁ be a positive real number and for every integer n 1 let x_ n+1 =1+x₁ x₂ x_ n-1 x_n . If x₅=43 , what is the sum of digits of the largest prime factor of x₆ ?

Olympiad workbook Solution View → 16

Positive integers x, y, z satisfy x y+z=160 . Compute the smallest possible value of x+y z .

Olympiad workbook Solution View → 17

Find the largest value of a^b such that the positive integers a, b>1 satisfy a^b b^a+a^b+b^a=5329 .

Olympiad workbook Solution View → 18

For any real number x , let [x] denotes the integer part of x ; x be the fractional part of x ( x =x-|x|) . Let A denote the set of all real numbers x satisfying x = x+[x]+[x+(1 /

Olympiad workbook Solution View → 19

Consider the sequence of number [n+ 2 n + 1 2 ] for n 1 , where [x] denotes the greatest integer not exceeding x . If the missing integers in the sequence are n₁ < n₂ < n₃ < then f

Olympiad workbook Solution View → 20

Let P(x)=a₀+a₁ x+a₂ x^2+ .+a_n x^n be a polynomial in which a_i is non-negative integer for each i 0,1,2,3, , n . If P(1)=4 and P(5)=136 , what is the value of P(3) ?

Olympiad workbook Solution View →

Practice all Functions questions in the app →