Functions: Challenging Problems for JEE Mains and Advanced скачать в хорошем качестве

Functions: Challenging Problems for JEE Mains and Advanced

In this LIVE session, we are challenging problems for JEE Mains and Advanced challenging problem series Problems Discussed: Functions Problem 1. Let f : A → R,f(x) = (2 −2|x−1|)logx (x2 − 1), then (where set A denotes domain and R denotes set of all real numbers) (A) number of integers in domain of f(x) is 1 (B) f(x) is many-one function (C) domain of function is (1,2] (D) f(x) is into function Problem 2. Let m be the number of real solutions for the equation 7|x|(15 − |x|) = 1 and n be number of different real solution of the equation f(f(x)) = 0 where f(x) = x3 −3x+1. Then find the value of m+n Problem 3.(Multi Correct Option) Let N bethe number of functions f : {1,2,3,.........,2018} → {1,2,3,.......2018} satisfying f(j) f(i) +j −i ∀ integers i,j such that 1 i j 2018. Then correct option(s) is/are (A) N ∈ 2 2017 i=0 (2017Ci)2 ,3 2017 =0 (2017Ci)2 (B) N ∈ 2017 i=0 (2017Ci)2 ,2 2012 i=0 (2017Ci)2 (C) N =2018C2018 +2019C2018 + ···...... + 4034C2018 (D) N =2017C2017 +2018C2017 + ......... + 4034C2017 Problem 4. Given that f(x) +f 1 1−x = 2(1−2x) x(1−x) , x ∈ R,x = 0, 1 then the given f(x) is (A) one-one (B) f(0) = 1 (C) many one (D) f(3) = 3 Problem 5. Let the function f(x) = √ ex +x−a for a ∈R. If there exists x0 ∈ [−1,1] such that f (f (xo)) = x0, then the range of ’a’ is: (A) [1,e +1] (B) [1,e] (C) 1 HWProblems HW1. If the domain of the function f(x) = log10(x2 −3x−4) + sin−1 2x−7 5 +cos−1 x−2 3 is the interval (α,β], then the value of α + β is: HW2. If a function satisfies (x−y)f(x+y)−(x+y)f(x−y) = 2(x2y −y3) ∀ x,y ∈ R and f(1) = 2, then (A) f(x) must be polynomial function (B) f(3) = 12 (C) f(0) = 0 (D) f(3) = 2 HW3. Find minimum value of (x1 −x2)2 + HW4. Let f(x) = ln x2+e 8 −x2 1 − 16 x2 2 x2+1 then the range of g(x) = sinf(x)+ cosf(x) is (A) 1,23/4 (B) 1,21/2 (C) [1,22] (D) (1,2) HW5. f(x) is monic polynomial of degree 4 such that, f(1) = 1,f(2) = 4,f(3) = 9,f(4) = 16, then find f(5) HW6. Match List-I with List-II and select the correct answer using the code given below the list. List I P f :R→(−1,1),f(x) = 10x−10−x 10x+10−x Codes : P Q R S (A) 1 3 2 4 (B) 1 4 3 2 (C) 3 2 4 1 (D) 1 3 4 2 Tags: jee challenging questions jee advanced level problems jee mains tough questions hard maths problems for jee jee problem solving series advanced problem solving maths jee high level questions iit jee tough problems concept based jee questions jee mains 2026 January attempt solutions jee mains 2026 paper jee mains 2026 live jee mains 2026 january attempt jee mains 2026 jee 2026 jee mains preparation jee mains maths jee mains physics jee mains chemistry jee aspirants 2026 jee strategy 2026 jee mains tips jee mains motivation jee mains exam jee mains syllabus jee mains important questions jee mains revision jee mains mock test jee mains analysis jee mains expected questions jee mains rank boost