JEE Main Previous Year Questions (2025): Basic Mathematics for Physics | Physics for JEE Main & Advanced PDF Download

 Page 1


JEE Main Previous Year Questions 
(2025): Basic Mathematics for Physics 
 
Q1: Two particles are located at equal distance from origin. The position vectors of those 
are represented by ?? ?
= ?? ??ˆ + ?? ?? ??ˆ + ?? ?? ˆ
 and ?? ?
= ?? ??ˆ - ?? ??ˆ + ?? ?? ?? ˆ
, respectively. If both the 
vectors are at right angle to each other, the value of ?? -?? is ____ . 
Answer: (c) 
Solution: 
 A
? ? 
· B
? ? 
= 0 
  4 - 6n + 8p = 0 
 |A
? ? 
| = |B
? ? 
|
4 + 9n
2
+ 4 = 4 + 4 + 16p
2
9n
2
= 16p
2
P = +
3
4
n
4 - 6n ± 6n = 0
12n = 4
n =
1
3
 
 
Q2: For an experimental expression ?? =
???? .?? ×?????? ?? ???? .?? , where all the digits are significant. Then 
to report the value of ?? we should write 
(a) ?? = 1326.19 
(b) ?? = 1330 
(c) ?? = 1326.186 
(d) ?? = 1326.2 
Answer: (b) 
  ?? =
32.3×1125
27.4
= 1326.18 
So we need to report to three significant digit. 
So, ?? = 1330 
 
 
Page 2


JEE Main Previous Year Questions 
(2025): Basic Mathematics for Physics 
 
Q1: Two particles are located at equal distance from origin. The position vectors of those 
are represented by ?? ?
= ?? ??ˆ + ?? ?? ??ˆ + ?? ?? ˆ
 and ?? ?
= ?? ??ˆ - ?? ??ˆ + ?? ?? ?? ˆ
, respectively. If both the 
vectors are at right angle to each other, the value of ?? -?? is ____ . 
Answer: (c) 
Solution: 
 A
? ? 
· B
? ? 
= 0 
  4 - 6n + 8p = 0 
 |A
? ? 
| = |B
? ? 
|
4 + 9n
2
+ 4 = 4 + 4 + 16p
2
9n
2
= 16p
2
P = +
3
4
n
4 - 6n ± 6n = 0
12n = 4
n =
1
3
 
 
Q2: For an experimental expression ?? =
???? .?? ×?????? ?? ???? .?? , where all the digits are significant. Then 
to report the value of ?? we should write 
(a) ?? = 1326.19 
(b) ?? = 1330 
(c) ?? = 1326.186 
(d) ?? = 1326.2 
Answer: (b) 
  ?? =
32.3×1125
27.4
= 1326.18 
So we need to report to three significant digit. 
So, ?? = 1330 
 
 
Q3: The maximum percentage error in the measurement of density of a wire is [Given, 
mass of wire = (?? .???? ± ?? .?????? )?? radius of wire = (?? .???? ± ?? .???? )???? length of wire =
(???? .???? ± ?? .???? )???? ] 
(a) 8 
(b) 5 
(c) 4 
(d) 7 
 
Answer: (b) 
Solution:  
d =
m
 vol. 
=
m
?? R
2
l
?
 d?? ?? =
dm
m
+
2dR
R
+
dl
l
 
?
d?? ?? = (
0.003
0.6
+
2 × 0.01
0.5
+
0.05
10
) 100 = 5% 
 
Q4: The energy of a system is given as ?? (?? ) = ?? ?? ?? -????
, where t is the time and ?? =
?? .?? ?? -?? . The errors in the measurement of ?? and ?? are ?? .?? % and ?? .?? %, respectively. At 
?? = ?? ?? , maximum percentage error in the energy is : 
(a) 6% 
(b) 8.4% 
(c) 11.6% 
(d) 4% 
Answer: (a) 
Solution:  
E = ?? 3
e
-????
 
  ln E = 3ln ?? - ?? t 
(
dE
E
)
max
=
3 d?? ?? + ?? dt
t
× t
 = 3 × 1.2% + (0.3 × 1.6 × 5)%
 = 6%
 
 
Q5: A physical quantity ?? is related to four observables ?? ,?? ,?? ,?? as follows : 
?? =
????
?? ????
 
where, ?? = (???? ± ?? )???? ;?? = (???? ± ?? .?? )?? ;?? = (???? ± ?? .?? )?????? -?? and ?? = (???? ± ?? .?? )?? , then 
the percentage error in Q is 
?? ????????
, where ?? = ____ . 
Page 3


JEE Main Previous Year Questions 
(2025): Basic Mathematics for Physics 
 
Q1: Two particles are located at equal distance from origin. The position vectors of those 
are represented by ?? ?
= ?? ??ˆ + ?? ?? ??ˆ + ?? ?? ˆ
 and ?? ?
= ?? ??ˆ - ?? ??ˆ + ?? ?? ?? ˆ
, respectively. If both the 
vectors are at right angle to each other, the value of ?? -?? is ____ . 
Answer: (c) 
Solution: 
 A
? ? 
· B
? ? 
= 0 
  4 - 6n + 8p = 0 
 |A
? ? 
| = |B
? ? 
|
4 + 9n
2
+ 4 = 4 + 4 + 16p
2
9n
2
= 16p
2
P = +
3
4
n
4 - 6n ± 6n = 0
12n = 4
n =
1
3
 
 
Q2: For an experimental expression ?? =
???? .?? ×?????? ?? ???? .?? , where all the digits are significant. Then 
to report the value of ?? we should write 
(a) ?? = 1326.19 
(b) ?? = 1330 
(c) ?? = 1326.186 
(d) ?? = 1326.2 
Answer: (b) 
  ?? =
32.3×1125
27.4
= 1326.18 
So we need to report to three significant digit. 
So, ?? = 1330 
 
 
Q3: The maximum percentage error in the measurement of density of a wire is [Given, 
mass of wire = (?? .???? ± ?? .?????? )?? radius of wire = (?? .???? ± ?? .???? )???? length of wire =
(???? .???? ± ?? .???? )???? ] 
(a) 8 
(b) 5 
(c) 4 
(d) 7 
 
Answer: (b) 
Solution:  
d =
m
 vol. 
=
m
?? R
2
l
?
 d?? ?? =
dm
m
+
2dR
R
+
dl
l
 
?
d?? ?? = (
0.003
0.6
+
2 × 0.01
0.5
+
0.05
10
) 100 = 5% 
 
Q4: The energy of a system is given as ?? (?? ) = ?? ?? ?? -????
, where t is the time and ?? =
?? .?? ?? -?? . The errors in the measurement of ?? and ?? are ?? .?? % and ?? .?? %, respectively. At 
?? = ?? ?? , maximum percentage error in the energy is : 
(a) 6% 
(b) 8.4% 
(c) 11.6% 
(d) 4% 
Answer: (a) 
Solution:  
E = ?? 3
e
-????
 
  ln E = 3ln ?? - ?? t 
(
dE
E
)
max
=
3 d?? ?? + ?? dt
t
× t
 = 3 × 1.2% + (0.3 × 1.6 × 5)%
 = 6%
 
 
Q5: A physical quantity ?? is related to four observables ?? ,?? ,?? ,?? as follows : 
?? =
????
?? ????
 
where, ?? = (???? ± ?? )???? ;?? = (???? ± ?? .?? )?? ;?? = (???? ± ?? .?? )?????? -?? and ?? = (???? ± ?? .?? )?? , then 
the percentage error in Q is 
?? ????????
, where ?? = ____ . 
Answer: 7700 
Solution:  
Q =
ab
4
 cd
 
 ?
?Q
Q
× 100 = [
?a
a
+ 4
? b
 b
+
?c
c
+
?d
 d
] × 100
 ?
x
1000
= [
3
60
+ 4(
0.1
20
) + (
0.2
40
) +
0.1
50
] × 100
 ? x = 7700