Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE PYQs · IOQM · Functions

JEE Functions PYQs with Solutions

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

20 questionsIOQMAnswers + solutions

About Functions PYQs

Functions has 20 previous year questions in the Quantrex Academy JEE Main & Advanced IOQM bank. The 20 questions in this list come from Olympiad workbook (20). Each question opens on its own page with the options, the correct answer and the worked solution where available.

Functions questions with solutions

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

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 n_1 < n_2 < n_3

Olympiad workbook Solution View → 4

Let x_1 be a positive real number and for every integer n ≥ 1 let x_ n+1 =1+x_1 x_2 … … x_ n-1 x_n . If x_5=43 , what is the sum of digits of the largest prime factor of x_6 ?

Olympiad workbook Solution View → 5

Let f: ℝ arrow 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

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 π+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)=a_0+a_1 x+a_2 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\

Olympiad workbook Solution View → 11

Let f: ℝ arrow 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

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 π+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

Olympiad workbook Solution View → 15

Let x_1 be a positive real number and for every integer n ≥ 1 let x_ n+1 =1+x_1 x_2 … … x_ n-1 x_n . If x_5=43 , what is the sum of digits of the largest prime factor of x_6 ?

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\

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 n_1 < n_2 < n_3

Olympiad workbook Solution View → 20

Let P(x)=a_0+a_1 x+a_2 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 →

Main Functions list

The larger JEE Functions list is under Mathematics (700 questions).

Related JEE IOQM chapters

Permutation and Combination (112)Basics of Mathematics (88)Properties of Triangles (64)Sequences and Series (38)Quadratic Equation (38)Circle (30)Straight Lines (24)Binary Numbers (8)Vector Algebra (6)Binomial Theorem (6)

Functions in other exams

NDA Functions (129)BITSAT Functions (39)