Very helpful

JEE


JEE MAIN 2026 (PYQ)
Mathematics
Relations and Functions

Q1 If the domain of the function Q7 If g (x) = 3x
2
+ 2x − 3, f (0) = −3 and
f (x) = sin
−1
(
1
) is 4g (f (x)) = 3x
2
− 32x + 72 , then f (g (2)) is
2
x −2x−2
equal to:
(−∞, α ]∪[β, γ ]∪[δ, ∞) , then α + β + γ + δ
(1) 25
(2) − 7
is equal to 6 2

(3) 7
(4) − 25
(1) 3 (2) 5 2 6



(3) 4 (4) 2 Q8 If the domain of the function
is
5−x
Q2 Let f be a function such that
−1 1
f (x) = sin ( ) +
3+2x loge (10−x)

3f (x) + 2f (
m

19x
) = 5x , x ≠ 0, where (−∞, α ]∪[β, γ) − {δ} , then
. Then f (5) – f (2) is equal to
9 2
m = ∑
i=1
(i) 6 (α + β + γ + δ) is equal to
(1) 18 (2) 36 (1) 68 (2) 70
(3) 9 (4) –9 (3) 66 (4) 67

Q3 Let R be a relation defined on the set Q9 Let the relation R on the set
{1, 2, 3, 4} × {1, 2, 3, 4} by M = {1, 2, 3, … , 16} be given by
R = {((a, b), (c, d)) : 2a + 3b = 3c + 4d} . R = {(x, y) : 4y = 5x − 3, x, y ∈ M} .
Then the number of elements in R is Then the minimum number of elements required
(1) 18 (2) 15 to be added in R, in order to make the relation
(3) 6 (4) 12 symmetric, is equal to
(1) 3 (2) 2
Q4 The number of relations, defined on the set {a, b,
(3) 1 (4) 4
c, d}, which are both reflexive and symmetric, is
equal to: Q10 The number of elements in the relation
(1) 64 (2) 256 R = {(x, y) : 4x
2
+ y
2
< 52, x, y ∈ Z}

(3) 16 (4) 1024 is
(1) 86 (2) 67
Q5 The number of strictly increasing functions f from
(3) 77 (4) 89
the set {1, 2, 3, 4, 5, 6} to the set {1, 2, 3, ….., 9}
such that f (i) ≠ i for 1 ≤ i ≤ 6, is equal to : Q11 Let the domain of the function
(1) 21 (2) 22 f (x) = log
3
log
5

(3) 27 (4) 28 (7 − log (x
2
− 10x + 85)) be
2



Q6 Let A = {2, 3, 5, 7, 9}. Let R be the relation on A −1 3x−7
+ sin (∣
∣
∣)
∣
defined by xRy if and only if 2x ≤ 3y. Let l be the
17−x


(α, β]. Then α + β is equal to:
number of elements in R, and m be the minimum
number of elements required to be added in R to (1) 12 (2) 9
(3) 10 (4) 8
make it a symmetric relation. Then l + m is equal
to : Q12 Given below are two statements:
(1) 23 (2) 25 Statement-I: The function f : R → R defined
(3) 21 (4) 27 by f (x) =
x
in one-one.
1+ |x|




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Statement-II: The function f : R → R defined Then the number of onto functions f:A→B is
equal to
2

by f (x) is many-one.
x +4x−30
=
2
x −8x+18

In the light of the above statements, choose the (1) 62 (2) 32

correct answer from the options given below: (3) 81 (4) 79

(1) Statement I is false but Statement II is true
(2) Both Statement I and Statement II are true
(3) Statement I is true but Statement II is false
(4) Both Statement I and Statement II is false

Q13 The sum of all the elements in the range of
f (x) = Sgn(sinx) + Sgn(cosx) + Sgn(tanx) + Sgn
(cotx), x where
nπ
≠ , n ∈ Z,
2

1, if t > 0
Sgn(t) = { , is:
−1 if t < 0

(1) –2 (2) 2
(3) 4 (4) 0

Q14 Let A = -2,-1,0,1,2,3,4. Let R be a relation on A
defined by xRy if and only if 2x + y ≤ 2 . Let l
be the number of elements in R. Let m and n be
the minimum number of elements required to be
added in R to make it reflexive and symmetric
relations respectively. Then l + m + n is equal to:
(1) 35 (2) 34
(3) 33 (4) 32

Q15 Let A = {0, 1, 2,…9}. Let R be a relation on A
defined by (x, y) ∈R if and only if |x–y| is a
multiple of 3. Given below are two statements:
Statement I: n(R) = 36.
Statement II: R is an equivalence relation.
In the light of the above statements, choose the
correct answer from the given below
(1) Both Statement I and Statement II are correct
(2) Statement I is incorrect but Statement II is
correct
(3) Statement I is correct but Statement II is
incorrect
(4) Both Statement I and Statement II are
incorrect

Q16 Consider two sets
A = {x ∈ Z : |(|x − 3| − 3)| ≤ 1} and
B
(x−2)(x−4)
= {x ∈ R − {1, 2} : log (|x − 2|) = 0}
x−1 e

.




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