Test (elaborations) mathematics on functions for Jee Mains and Advance
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Course
Mathematics
Institution
Certainly! Let’s dive into the topic of functions, which is crucial for JEE preparation. . This document provides 20 questions of very tough level on functions, If you think that you are pro in mathematics, the solve this document and prove us wrong!!!!!!!!!!!
1. If f(x) = x3+3x2 + 12x 2 sinx, where f: R→R, then
(a) f(x) is many-one and onto (b) f(x) is one-one and onto
(c) f(x) is one-one and into (d) f(x) is many-one and into
2. Let function f: R→ R be defined by f(x) =2x+sin x for x ∈R. Then, f is
(a) One-one and onto (b) One-one but not onto
(c) Onto but not one-one (d) Neither one-one nor onto
3. If f:[0, ∞) →[0, ∞) and f(x)= then f is:
+
,-+
(a) One-one and onto (b) One-one but not onto
(c) Onto but not one- one (d) Neither one-one nor onto
4. The function f: [0, 3] →[1, 29], defined by f(x)=2x3 15x2+36x+1, is
(a) One-one and onto (b) Onto but not one-one
(c) One-one but not onto (d) Neither one-one nor onto
5. For real x, let f(x)= x3+5x+1, then
(a) f is onto R but not one-one (b) f is one-one and onto R
(c) f is neither one-one nor onto R (d) f is one-one but not onto R
6. A function f from the set of natural numbers to integers defined by
7 1
, when n is odd
6(7) = 8 27
– , when n is even
2
(a) neither one-one nor onto (b) one-one but not onto
(c) onto but not one-one (d) one-one and onto both
7. Let f: N → ; be a function defined as f(x)=4x+3 where y= {y ∈ >: y=4x+3 for some x ∈N}. f is
invertible and its inverse is
@A-B AC@ A-@ AC@
(a) g(y)= (b)g(y)=4+ (c) g(y)= (d) g(y)=
@ B B B
8. If the function f(x) and g(x) are defined on R →R such that
0, x ∈ rational 0, x ∈ irrational
f(x)= D ; g(x) = D
x, x ∈ irrational x, x ∈ rational
Then (f g) (x) is
(a) one-one and onto (b) neither one-one nor onto
(c) one-one but not onto (d) onto but not one-one
9. Let F = {1, 2, 3, 4} and G = {1,2}. Then, the number of onto functions from E to F is
(a) 14 (b) 16 (c) 12 (d) 8
10. If the function 6: R→ R is deJined by 6(K) = |K|(K MN7 K), then which of the following statements
is TRUE? (2020 Adv.)
(a) 6 is one-one, but NOT onto (b) 6 is onto, but NOT one-one
(c) 6 is BOTH one-one and onto (d) 6 is NEITHER one-one NOR onto
11. Let a function 6: (0, ∞) → (0, ∞) be defined by 6(K) = S1 +S. Then, 6 is
,
(a) injective only (b) both injective as well as surjective
(c) not injective but it is surjective (d) neither injective nor surjective
E2C Maths Forum
By: ER. Ashok Kumar
Trained from Renowned Institute, KOTA (RAJ.)
Address : Beside Siliguri Child Welfare Society, Baghajatin Park, Siliguri, Contact No : 9046278670
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