JEE Main 2023 January 25 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


SECTION - A 
1.  According to law of equipartition of energy the molar specific heat of a diatomic gas at constant 
volume where the molecule has one additional vibrational mode is:- 
(1)  (2)   (3)  (4)  
Sol. 3 
 (degree of freedom) 
 ? f = 3 + 2 + 2 = 7 
 C V = 
 
2. A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The 
magnitude of induced emf, between the ends of wire will be 
 (1) 20 V (2) 8 V (3) 12 V (4) 16 V 
Sol. 4 
 e = ?? ?? ??   
 e = 2 × 8 × 1 
 e = 16 volt 
 
3. The energy levels of an atom is shown in figure. 
 
 Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? 
 Given (h = 6.62× 10
-34
Js) 
 (1) D (2) B (3) C (4) A 
Sol. 1 
  
 
4. Given below are two statements : 
 Statement I: Stopping potential in photoelectric effect does not depend on the power of the light 
source. 
 Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the 
wavelength of the incident light. 
 In the light of above statements, choose the most appropriate answer from the options given below 
 (1) Statement I is incorrect but statement II is correct 
(2) Statement ?? is correct but statement ???? is incorrect 
(3) Both Statement ?? and statement II are correct 
(4) Both Statement I and Statement II are incorrect 
Sol. 3 
 Both statement I and statement II are correct 
 
? ? ? ?
??
?
EE
?
(ev) 10
hc 1241 1241
124.1
(nm)
fR R
? 
22
7
R
2
3
R
2
7
R
2
9
R
2
5
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
Page 2


SECTION - A 
1.  According to law of equipartition of energy the molar specific heat of a diatomic gas at constant 
volume where the molecule has one additional vibrational mode is:- 
(1)  (2)   (3)  (4)  
Sol. 3 
 (degree of freedom) 
 ? f = 3 + 2 + 2 = 7 
 C V = 
 
2. A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The 
magnitude of induced emf, between the ends of wire will be 
 (1) 20 V (2) 8 V (3) 12 V (4) 16 V 
Sol. 4 
 e = ?? ?? ??   
 e = 2 × 8 × 1 
 e = 16 volt 
 
3. The energy levels of an atom is shown in figure. 
 
 Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? 
 Given (h = 6.62× 10
-34
Js) 
 (1) D (2) B (3) C (4) A 
Sol. 1 
  
 
4. Given below are two statements : 
 Statement I: Stopping potential in photoelectric effect does not depend on the power of the light 
source. 
 Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the 
wavelength of the incident light. 
 In the light of above statements, choose the most appropriate answer from the options given below 
 (1) Statement I is incorrect but statement II is correct 
(2) Statement ?? is correct but statement ???? is incorrect 
(3) Both Statement ?? and statement II are correct 
(4) Both Statement I and Statement II are incorrect 
Sol. 3 
 Both statement I and statement II are correct 
 
? ? ? ?
??
?
EE
?
(ev) 10
hc 1241 1241
124.1
(nm)
fR R
? 
22
7
R
2
3
R
2
7
R
2
9
R
2
5
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
5. The distance travelled by a particle is related to time t as ?? = 4t
2
. The velocity of the particle at t = 5 s 
is:- 
 (1) 40 ms
-1
 (2) 20 ms
-1
 (3) 8 ms
-1
 (4) 25 ms
-1
 
Sol. 1 
 v = 8
dx
t
dt
? 
 v = 8 × 5 
 v = 40 m/s 
 
6. Match List I with List II 
 
 Choose the correct answer from the options given below: options  
 (1) A-I, B-II, C-III, D-IV (2) A-II, B-III, C-IV, D-I 
(3) A-I, B-III, C-IV, D-II (4) A-III, B-I, C-II, D-IV 
Sol. 4 
 [Y] = 
2
2
.
F L MLT
A L L
?
?
? = ML
–1
T
–2
  
 F = 6 ? ? ? ?r ? 
 [ ?] = 
2
1
F MLT
6 r L LT
?
?
?
??
 
 [ ?] = M L
–1
 T
–1
 
 [h] = 
E
f
 = 
22
1
ML T
T
?
?
 = ML
2
T
–1
 
 Work function ( ?) = ML
2
T
–2
 
 
 
7. Match List I with List II  
LIST I LIST II 
A. Troposphere I. Approximate 65- 75 km over Earth's surface 
B. E- Part of Stratosphere II. Approximate 300 km over Earth's surface 
C. F2- Part of Thermosphere III. Approximate 10 km over Earth's surface 
D. D- Part of Stratosphere IV. Approximate 100 km over Earth's surface 
 
 Choose the correct answer from the options given below: 
 (1) A-III, B-IV, C-II, D-I (2) A-III, B-II, C-I, D-IV 
 (3) A-I, B-IV, C-III, D-II (4) A-I, B-II, C-IV, D-III 
Sol. 1 
 By theory 
Page 3


SECTION - A 
1.  According to law of equipartition of energy the molar specific heat of a diatomic gas at constant 
volume where the molecule has one additional vibrational mode is:- 
(1)  (2)   (3)  (4)  
Sol. 3 
 (degree of freedom) 
 ? f = 3 + 2 + 2 = 7 
 C V = 
 
2. A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The 
magnitude of induced emf, between the ends of wire will be 
 (1) 20 V (2) 8 V (3) 12 V (4) 16 V 
Sol. 4 
 e = ?? ?? ??   
 e = 2 × 8 × 1 
 e = 16 volt 
 
3. The energy levels of an atom is shown in figure. 
 
 Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? 
 Given (h = 6.62× 10
-34
Js) 
 (1) D (2) B (3) C (4) A 
Sol. 1 
  
 
4. Given below are two statements : 
 Statement I: Stopping potential in photoelectric effect does not depend on the power of the light 
source. 
 Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the 
wavelength of the incident light. 
 In the light of above statements, choose the most appropriate answer from the options given below 
 (1) Statement I is incorrect but statement II is correct 
(2) Statement ?? is correct but statement ???? is incorrect 
(3) Both Statement ?? and statement II are correct 
(4) Both Statement I and Statement II are incorrect 
Sol. 3 
 Both statement I and statement II are correct 
 
? ? ? ?
??
?
EE
?
(ev) 10
hc 1241 1241
124.1
(nm)
fR R
? 
22
7
R
2
3
R
2
7
R
2
9
R
2
5
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
5. The distance travelled by a particle is related to time t as ?? = 4t
2
. The velocity of the particle at t = 5 s 
is:- 
 (1) 40 ms
-1
 (2) 20 ms
-1
 (3) 8 ms
-1
 (4) 25 ms
-1
 
Sol. 1 
 v = 8
dx
t
dt
? 
 v = 8 × 5 
 v = 40 m/s 
 
6. Match List I with List II 
 
 Choose the correct answer from the options given below: options  
 (1) A-I, B-II, C-III, D-IV (2) A-II, B-III, C-IV, D-I 
(3) A-I, B-III, C-IV, D-II (4) A-III, B-I, C-II, D-IV 
Sol. 4 
 [Y] = 
2
2
.
F L MLT
A L L
?
?
? = ML
–1
T
–2
  
 F = 6 ? ? ? ?r ? 
 [ ?] = 
2
1
F MLT
6 r L LT
?
?
?
??
 
 [ ?] = M L
–1
 T
–1
 
 [h] = 
E
f
 = 
22
1
ML T
T
?
?
 = ML
2
T
–1
 
 Work function ( ?) = ML
2
T
–2
 
 
 
7. Match List I with List II  
LIST I LIST II 
A. Troposphere I. Approximate 65- 75 km over Earth's surface 
B. E- Part of Stratosphere II. Approximate 300 km over Earth's surface 
C. F2- Part of Thermosphere III. Approximate 10 km over Earth's surface 
D. D- Part of Stratosphere IV. Approximate 100 km over Earth's surface 
 
 Choose the correct answer from the options given below: 
 (1) A-III, B-IV, C-II, D-I (2) A-III, B-II, C-I, D-IV 
 (3) A-I, B-IV, C-III, D-II (4) A-I, B-II, C-IV, D-III 
Sol. 1 
 By theory 
 
8. The light rays from an object have been reflected towards an observer from a standard flat mirror, 
the image observed by the observer are:- 
 A. Real 
B. Erect 
C. Smaller in size then object 
D. Laterally inverted 
 Choose the most appropriate answer from the options given below: 
 (1) A, C, and D Only  (2) B and D Only 
 (3) A and D Only  (4) B and C Only 
Sol. 2 
 By theory 
 
9. The graph between two temperature scales ?? and ?? is shown in the figure. Between upper fixed point 
and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The 
relationship for conversion between the two scales is given by:- 
 
 (1) 
?? ?? 100
=
?? ?? -180
150
 (2) 
?? ?? 150
=
?? ?? -180
100
 (3) 
?? ?? 180
-
?? ?? -40
100
 (4) 
?? ?? 100
=
?? ?? -30
150
 
Sol. 4 
  
 
Q
P
t0
t 30
180 30 100 0
?
?
?
??
 
 
Q
P
t
t 30
150 100
?
? 
 
Q
P
t
t 30
100 150
?
? 
 
 
 
100 
t Q 100 equals 
division 
0 
180 
t
P
 
150 equals 
division 
30 
Page 4


SECTION - A 
1.  According to law of equipartition of energy the molar specific heat of a diatomic gas at constant 
volume where the molecule has one additional vibrational mode is:- 
(1)  (2)   (3)  (4)  
Sol. 3 
 (degree of freedom) 
 ? f = 3 + 2 + 2 = 7 
 C V = 
 
2. A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The 
magnitude of induced emf, between the ends of wire will be 
 (1) 20 V (2) 8 V (3) 12 V (4) 16 V 
Sol. 4 
 e = ?? ?? ??   
 e = 2 × 8 × 1 
 e = 16 volt 
 
3. The energy levels of an atom is shown in figure. 
 
 Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? 
 Given (h = 6.62× 10
-34
Js) 
 (1) D (2) B (3) C (4) A 
Sol. 1 
  
 
4. Given below are two statements : 
 Statement I: Stopping potential in photoelectric effect does not depend on the power of the light 
source. 
 Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the 
wavelength of the incident light. 
 In the light of above statements, choose the most appropriate answer from the options given below 
 (1) Statement I is incorrect but statement II is correct 
(2) Statement ?? is correct but statement ???? is incorrect 
(3) Both Statement ?? and statement II are correct 
(4) Both Statement I and Statement II are incorrect 
Sol. 3 
 Both statement I and statement II are correct 
 
? ? ? ?
??
?
EE
?
(ev) 10
hc 1241 1241
124.1
(nm)
fR R
? 
22
7
R
2
3
R
2
7
R
2
9
R
2
5
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
5. The distance travelled by a particle is related to time t as ?? = 4t
2
. The velocity of the particle at t = 5 s 
is:- 
 (1) 40 ms
-1
 (2) 20 ms
-1
 (3) 8 ms
-1
 (4) 25 ms
-1
 
Sol. 1 
 v = 8
dx
t
dt
? 
 v = 8 × 5 
 v = 40 m/s 
 
6. Match List I with List II 
 
 Choose the correct answer from the options given below: options  
 (1) A-I, B-II, C-III, D-IV (2) A-II, B-III, C-IV, D-I 
(3) A-I, B-III, C-IV, D-II (4) A-III, B-I, C-II, D-IV 
Sol. 4 
 [Y] = 
2
2
.
F L MLT
A L L
?
?
? = ML
–1
T
–2
  
 F = 6 ? ? ? ?r ? 
 [ ?] = 
2
1
F MLT
6 r L LT
?
?
?
??
 
 [ ?] = M L
–1
 T
–1
 
 [h] = 
E
f
 = 
22
1
ML T
T
?
?
 = ML
2
T
–1
 
 Work function ( ?) = ML
2
T
–2
 
 
 
7. Match List I with List II  
LIST I LIST II 
A. Troposphere I. Approximate 65- 75 km over Earth's surface 
B. E- Part of Stratosphere II. Approximate 300 km over Earth's surface 
C. F2- Part of Thermosphere III. Approximate 10 km over Earth's surface 
D. D- Part of Stratosphere IV. Approximate 100 km over Earth's surface 
 
 Choose the correct answer from the options given below: 
 (1) A-III, B-IV, C-II, D-I (2) A-III, B-II, C-I, D-IV 
 (3) A-I, B-IV, C-III, D-II (4) A-I, B-II, C-IV, D-III 
Sol. 1 
 By theory 
 
8. The light rays from an object have been reflected towards an observer from a standard flat mirror, 
the image observed by the observer are:- 
 A. Real 
B. Erect 
C. Smaller in size then object 
D. Laterally inverted 
 Choose the most appropriate answer from the options given below: 
 (1) A, C, and D Only  (2) B and D Only 
 (3) A and D Only  (4) B and C Only 
Sol. 2 
 By theory 
 
9. The graph between two temperature scales ?? and ?? is shown in the figure. Between upper fixed point 
and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The 
relationship for conversion between the two scales is given by:- 
 
 (1) 
?? ?? 100
=
?? ?? -180
150
 (2) 
?? ?? 150
=
?? ?? -180
100
 (3) 
?? ?? 180
-
?? ?? -40
100
 (4) 
?? ?? 100
=
?? ?? -30
150
 
Sol. 4 
  
 
Q
P
t0
t 30
180 30 100 0
?
?
?
??
 
 
Q
P
t
t 30
150 100
?
? 
 
Q
P
t
t 30
100 150
?
? 
 
 
 
100 
t Q 100 equals 
division 
0 
180 
t
P
 
150 equals 
division 
30 
 
10. Consider a block kept on an inclined plane (inclined at 45
°
 ) as shown in the figure. If the force 
required to just push it up the incline is 2 times the force required to just prevent it from sliding down, 
the coefficient of friction between the block and inclined plane (?? ) is equal to : 
 
 (1) 0.25 (2) 0.50 (3) 0.60 (4) 0.33 
Sol. 4 
 
  
 F 1 = mg sin ? + ?mg cos ? 
 F 1 = mg sin45 + ?mg cos45 
 F 2 = mg sin45 – ?mg cos45 
 
 F 1 = 2F 2 
 
11
mg 2mg
2 2 2 2
?? ? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
 
 1 + ? = 2 – 2 ? 
 3 ? = 1 
 ? = 
1
3
 = 0.33 
 
11. Every planet revolves around the sun in an elliptical orbit:- 
 A. The force acting on a planet is inversely proportional to square of distance from sun. 
 B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun. 
 C. The Centripetal force acting on the planet is directed away from the sun. 
 D. The square of time period of revolution of planet around sun is directly proportional to cube of 
semi-major axis of elliptical orbit. 
 Choose the correct answer from the options given below: 
 (1) B and C only (2) A and C Only (3) A and D only (4) C and D only 
Sol. 3 
 By Newton’s law  F = 
12
2
Gm m
r
 
 By kepler’s law  T
2
 ? a
3
 
 
45° 
mg  sin ? 
F 1 
?? 
45° 
m 
mg  sin ? 
F
2
 
?? 
45° 
m 
Page 5


SECTION - A 
1.  According to law of equipartition of energy the molar specific heat of a diatomic gas at constant 
volume where the molecule has one additional vibrational mode is:- 
(1)  (2)   (3)  (4)  
Sol. 3 
 (degree of freedom) 
 ? f = 3 + 2 + 2 = 7 
 C V = 
 
2. A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The 
magnitude of induced emf, between the ends of wire will be 
 (1) 20 V (2) 8 V (3) 12 V (4) 16 V 
Sol. 4 
 e = ?? ?? ??   
 e = 2 × 8 × 1 
 e = 16 volt 
 
3. The energy levels of an atom is shown in figure. 
 
 Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm ? 
 Given (h = 6.62× 10
-34
Js) 
 (1) D (2) B (3) C (4) A 
Sol. 1 
  
 
4. Given below are two statements : 
 Statement I: Stopping potential in photoelectric effect does not depend on the power of the light 
source. 
 Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the 
wavelength of the incident light. 
 In the light of above statements, choose the most appropriate answer from the options given below 
 (1) Statement I is incorrect but statement II is correct 
(2) Statement ?? is correct but statement ???? is incorrect 
(3) Both Statement ?? and statement II are correct 
(4) Both Statement I and Statement II are incorrect 
Sol. 3 
 Both statement I and statement II are correct 
 
? ? ? ?
??
?
EE
?
(ev) 10
hc 1241 1241
124.1
(nm)
fR R
? 
22
7
R
2
3
R
2
7
R
2
9
R
2
5
JEE –MAIN EXAMINATION – JANUARY, 2023 
(Held On Thursday 25th January, 2023) TIME : 3 : 00 PM to 6 : 00 PM 
 
 
5. The distance travelled by a particle is related to time t as ?? = 4t
2
. The velocity of the particle at t = 5 s 
is:- 
 (1) 40 ms
-1
 (2) 20 ms
-1
 (3) 8 ms
-1
 (4) 25 ms
-1
 
Sol. 1 
 v = 8
dx
t
dt
? 
 v = 8 × 5 
 v = 40 m/s 
 
6. Match List I with List II 
 
 Choose the correct answer from the options given below: options  
 (1) A-I, B-II, C-III, D-IV (2) A-II, B-III, C-IV, D-I 
(3) A-I, B-III, C-IV, D-II (4) A-III, B-I, C-II, D-IV 
Sol. 4 
 [Y] = 
2
2
.
F L MLT
A L L
?
?
? = ML
–1
T
–2
  
 F = 6 ? ? ? ?r ? 
 [ ?] = 
2
1
F MLT
6 r L LT
?
?
?
??
 
 [ ?] = M L
–1
 T
–1
 
 [h] = 
E
f
 = 
22
1
ML T
T
?
?
 = ML
2
T
–1
 
 Work function ( ?) = ML
2
T
–2
 
 
 
7. Match List I with List II  
LIST I LIST II 
A. Troposphere I. Approximate 65- 75 km over Earth's surface 
B. E- Part of Stratosphere II. Approximate 300 km over Earth's surface 
C. F2- Part of Thermosphere III. Approximate 10 km over Earth's surface 
D. D- Part of Stratosphere IV. Approximate 100 km over Earth's surface 
 
 Choose the correct answer from the options given below: 
 (1) A-III, B-IV, C-II, D-I (2) A-III, B-II, C-I, D-IV 
 (3) A-I, B-IV, C-III, D-II (4) A-I, B-II, C-IV, D-III 
Sol. 1 
 By theory 
 
8. The light rays from an object have been reflected towards an observer from a standard flat mirror, 
the image observed by the observer are:- 
 A. Real 
B. Erect 
C. Smaller in size then object 
D. Laterally inverted 
 Choose the most appropriate answer from the options given below: 
 (1) A, C, and D Only  (2) B and D Only 
 (3) A and D Only  (4) B and C Only 
Sol. 2 
 By theory 
 
9. The graph between two temperature scales ?? and ?? is shown in the figure. Between upper fixed point 
and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The 
relationship for conversion between the two scales is given by:- 
 
 (1) 
?? ?? 100
=
?? ?? -180
150
 (2) 
?? ?? 150
=
?? ?? -180
100
 (3) 
?? ?? 180
-
?? ?? -40
100
 (4) 
?? ?? 100
=
?? ?? -30
150
 
Sol. 4 
  
 
Q
P
t0
t 30
180 30 100 0
?
?
?
??
 
 
Q
P
t
t 30
150 100
?
? 
 
Q
P
t
t 30
100 150
?
? 
 
 
 
100 
t Q 100 equals 
division 
0 
180 
t
P
 
150 equals 
division 
30 
 
10. Consider a block kept on an inclined plane (inclined at 45
°
 ) as shown in the figure. If the force 
required to just push it up the incline is 2 times the force required to just prevent it from sliding down, 
the coefficient of friction between the block and inclined plane (?? ) is equal to : 
 
 (1) 0.25 (2) 0.50 (3) 0.60 (4) 0.33 
Sol. 4 
 
  
 F 1 = mg sin ? + ?mg cos ? 
 F 1 = mg sin45 + ?mg cos45 
 F 2 = mg sin45 – ?mg cos45 
 
 F 1 = 2F 2 
 
11
mg 2mg
2 2 2 2
?? ? ? ? ?
? ? ?
? ? ? ?
? ? ? ?
 
 1 + ? = 2 – 2 ? 
 3 ? = 1 
 ? = 
1
3
 = 0.33 
 
11. Every planet revolves around the sun in an elliptical orbit:- 
 A. The force acting on a planet is inversely proportional to square of distance from sun. 
 B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun. 
 C. The Centripetal force acting on the planet is directed away from the sun. 
 D. The square of time period of revolution of planet around sun is directly proportional to cube of 
semi-major axis of elliptical orbit. 
 Choose the correct answer from the options given below: 
 (1) B and C only (2) A and C Only (3) A and D only (4) C and D only 
Sol. 3 
 By Newton’s law  F = 
12
2
Gm m
r
 
 By kepler’s law  T
2
 ? a
3
 
 
45° 
mg  sin ? 
F 1 
?? 
45° 
m 
mg  sin ? 
F
2
 
?? 
45° 
m 
 
12. For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passed 
through it. If the torsional constant of suspension wire is 4.0 × 10
-5
 N m rad 
-1
, the magnetic field is 
0.01 T and the number of turns in the coil is 200 , the area of each turn (in cm
2
 ) is : 
 (1) 1.0 (2) 2.0 (3) 1.5 (4) 0.5 
Sol. 1 
 
NBA
I
C
?? 
 
C
A
IBN
?
? 
 
5
3
4 10 .05
10 10 0.01 200
?
?
??
?
? ? ?
 
 A = 10
–4
 m
2
 
 = 1 cm
2
 
 
13. Match List I with List II 
LIST I LIST II 
A. Gauss's Law in Electrostatics I. 
? ?? ? 
· ?? ?? 
= -
?? ?? ?? ????
 
B. Faraday's Law II. 
? ?? ? 
· ?? ?? 
= 0 
C. Gauss's Law in Magnetism III. 
? ?? ? 
· ?? ?? 
= ?? 0
?? ?? + ?? 0
?
0
?? ?? ?? ????
 
D. Ampere-Maxwell Law IV. 
? ?? ? 
· ?? ?? =
?? ?? 0
 
 
 Choose the correct answer from the options given below:  
 (1) A-IV, B-I, C-II, D-III (2) A-II, B-III, C-IV, D-I 
 (3) A-III, B-IV, C-I, D-II (4) A-I, B-II, C-III, D-IV 
Sol. 1 
 
14. Two objects are projected with same velocity 'u' however at different angles ?? and ?? with the 
horizontal. If ?? + ?? = 90
°
, the ratio of horizontal range of the first object to the 2 nd object will be: 
 (1) 2:1 (2) 1:2 (3) 1:1 (4) 4:1 
Sol. 3 
  
 R 1 = 
2
u sin 2
g
?
 
 R 2 =  
22
u sin 2 u sin 2(90 )
gg
? ? ?
? 
 R 2 = 
2
u sin 2
g
?
 = R 1  
? ?
? ?