JEE-ADVANCED SERIES Mathematics
Relations And Functions
11 previous year questions.
Volume: 11 Ques
Yield: Medium
High-Yield Trend
3
2023 3
2021 2
2020 1
2000 2
1983 Chapter Questions 11 MCQs
01
PYQ 1983
medium
mathematics ID: jee-adva
The domain of definition of the function is
1
(-3, -2) excluding - 2.5
2
[0, 1] excluding 0.5
3
[-2, 1) excluding 0
4
none of these
02
PYQ 1983
medium
mathematics ID: jee-adva
Which of the following functions is periodic?
1
f(x) = x - [x] where [x] denotes the largest integer less than or equal to the real number x
2
for
3
4
none of these
03
PYQ 2000
medium
mathematics ID: jee-adva
Let f : R R be any function. Define g : R R by g(x) = |f(x)| for all x. Then g is
1
onto if f is onto
2
one-one if f is one-one
3
continuous if f is continuous
4
differentiable if f is differentiable
04
PYQ 2020
medium
mathematics ID: jee-adva
Let the function be defined by
.
Suppose the function f has a local minimum at precisely when , where Then the value of is ______
.
Suppose the function f has a local minimum at precisely when , where Then the value of is ______
05
PYQ 2020
medium
mathematics ID: jee-adva
Let the function be defined by and let be an arbitrary function. Let be the product function defined by . Then which of the following statements is/are TRUE?
1
If is continuous at , then is differentiable at
2
If is differentiable at , then is continuous at
3
If is differentiable at , then is differentiable at
4
If is differentiable at , then is differentiable at
06
PYQ 2021
medium
mathematics ID: jee-adva
Which of the following statements is TRUE ?
1
2
For every , there exists and such that
3
For every , there exists a such that
4
is an increasing function on the interval
07
PYQ 2021
medium
mathematics ID: jee-adva
Which of the following statements is TRUE?
1
, for all
2
, for all
3
, for all
4
, for all
08
PYQ 2021
easy
mathematics ID: jee-adva
Let and be functions such that ,
,
and .
,
and .
09
PYQ 2023
medium
mathematics ID: jee-adva
Let f :[0,1] → [0,1] be the function defined by Consider the square region S = [0,1] x [0,1]. Let G = {(x,y) ∈ S: y > f(s)} be called the green region and R = {(x,y) ∈ S: y < f(s)} be called the red region. Let Lh = {(x,h) ∈ S: x ∈ [0,1] be the horizontal line drawn at a height h ∈ [0,1]. Then which of the following statements is(are) true?
1
There exists an h ∈ [ ] such that the area of the green region above the line Lh equals the area of the green region below the line Lh
2
There exists an h ∈ [ ] such that the area of the red region above the line Lh equals the area of the red region below the line Lh
3
There exists an h ∈ [ ] such that the area of the green region above the line Lh equals the area of the red region below the line Lh
4
There exists an h ∈ [ ] such that the area of the red region above the line Lh equals the area of the green region below the line Lh
10
PYQ 2023
medium
mathematics ID: jee-adva
Let tan-1 x ∈( ) for x ∈ R Then the number of real solutions of the equation √1 + cos (2x) = √2 tan -1 (tan x) in the set (- 3π/2, - π/2) ∪ (- π/2, π/2) ∪ (π/2, 3π/2) is equal to
11
PYQ 2023
hard
mathematics ID: jee-adva
Let tan-1 x ∈( ) for x ∈ R. Then the number of real solutions of the equation in the set is equal to
