JEE Main 2025 (Online) 23rd January Evening Shift

The equation of a transverse wave travelling along a string is y(x,t)=4.0 [20 10-3x+600t ]mm, where x is in mm and t is in second. The velocity of the wave is :

1. -60 m/s
2. +60 m/s
3. +30 m/s
4. -30 m/s

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is Ey=9.3 V m-1. Then, the magnetic field vector of the wave at that point is

1. Bz=1.55 10-8 T
2. Bz=6.2 10-8 T
3. Bz=3.1 10-8 T
4. Bz=9.3 10-8 T

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected.

1. 3 days
2. 27 days
3. 81 days
4. 1 day

A massless spring gets elongated by amount x1 under a tension of 5 N. Its elongation is x2 under the tension of 7 N. For the elongation of (5x1-2x2), the tension in the spring will be,

1. 20 N
2. 39 N
3. 11 N
4. 15 N

Water of mass m gram is slowly heated to increase the temperature from T1 to T2. The change in entropy of the water, given specific heat of water is 1 J kg-1 K-1, is :

1. m(T2-T1)
2. zero
3. m ( T1T2 )
4. m ( T2T1 )

What is the current through the battery in the circuit shown below? [figure]

1. 1.5 A
2. 0.25 A
3. 1.0 A
4. 0.5 A

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

1. (A) is true but (R) is false
2. Both (A) and (R) are true and (R) is the correct explanation of (A)
3. (A) is false but (R) is true
4. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

A ball having kinetic energy KE, is projected at an angle of 60 from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?

1. (KE)2
2. (KE)8
3. (KE)4
4. (KE)16

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V, what is the wavelength of the em-wave? (Given hc=1242 eV nm where h is the Planck's constant and c is the speed of light in vacuum.)

1. 400 nm
2. 600 nm
3. 300 nm
4. 200 nm

Two point charges -4 and 4 , constituting an electric dipole, are placed at (-9,0,0) cm and (9,0,0) cm in a uniform electric field of strength 104 N C-1. The work done on the dipole in rotating it from the equilibrium through 180 is :

1. 18.4 mJ
2. 12.4 mJ
3. 16.4 mJ
4. 14.4 mJ

A concave mirror of focal length f in air is dipped in a liquid of refractive index . Its focal length in the liquid will be:

1. f
2. f
3. f
4. f( -1)

The width of one of the two slits in Young's double slit experiment is d while that of the other slit is x d. If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is 9:4 then what is the value of x ? (Assume that the field strength varies according to the slit width.)

1. 2
2. 3
3. 4
4. 5

The refractive index of the material of a glass prism is 3. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

1. 60
2. 50
3. 58
4. 48

Two charges 7 and -4 are placed at (-7 cm,0,0) and (7 cm,0,0) respectively. Given, 0=8.85 10-12 C2 N-1 m-2, the electrostatic potential energy of the charge configuration is :

1. -2.0 J
2. -1.5 J
3. -1.2 J
4. -1.8 J

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1. The reading of the pressure gauge falls to P2 when the valve is opened. The speed of water flowing in the pipe is proportional to

1. (P1-P2)2
2. P1-P2
3. P1-P2
4. (P1-P2)4

The energy of a system is given as E(t)= 3e- t, where t is the time and =0.3 s-1. The errors in the measurement of and t are 1.2\% and 1.6\%, respectively. At t=5 s, maximum percentage error in the energy is :

1. 6\%
2. 11.6\%
3. 4\%
4. 8.4\%

Match List - I with List - II Choose the correct answer from the options given below :

1. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
2. (A)-(I), (B)-(IV), (C)-(II), (D)-(III)
3. (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
4. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)

[figure] Using the given P-V diagram, the work done by an ideal gas along the path ABCD is :

1. 3P0 V0
2. -3P0 V0
3. -4P0 V0
4. 4P0 V0

A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that (t)=5t2-8t, where (t) is the angular position of the rotating disc as a function of time t. How much power is delivered by the applied torque, when t=2 s ?

1. 60 MR2
2. 72 MR2
3. 8 MR2
4. 108 MR2

A galvanometer having a coil of resistance 30 need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be 30X , where X is

1. 447
2. 298
3. 149
4. 596

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5 . The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be V s-1.

In a series LCR circuit, a resistor of 300 , a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is 104 radians s-1

An air bubble of radius 1.0 mm is observed at a depth 20 cm below the free surface of a liquid having surface tension 0.095 J/m2 and density 103 kg/m3. The difference between pressure inside the bubble and atmospheric pressure is N/m2. (Take g=10 m/s2)

At steady state the charge on the capacitor, as shown in the circuit below, is . [figure]

A satellite of mass M2 is revolving around earth in a circular orbit at a height of R3 from earth surface. The angular momentum of the satellite is M GMRx. The value of x is , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

pH of water is 7 at 25 C. If water is heated to 80 C, it's pH will :

1. Decrease
2. Remains the same
3. Increase
4. H+ concentration increases, OH- concentration decreases

When a non-volatile solute is added to the solvent, the vapour pressure of the solvent decreases by 10 mm of Hg. The mole fraction of the solute in the solution is 0.2. What would be the mole fraction of the solvent if decrease in vapour pressure is 20 mm of Hg ?

1. 0.2
2. 0.4
3. 0.8
4. 0.6

Match List - I with List - II Choose the correct answer from the options given below :

1. A-IV, B-II, C-III, D-I
2. A-IV, B-III, C-I, D-II
3. A-III, B-I, C-IV, D-II
4. A-III, B-IV, C-II, D-I

Consider a binary solution of two volatile liquid components 1 and 2. x1 and y1 are the mole fractions of component 1 in liquid and vapour phase, respectively. The slope and intercept of the linear plot of 1x1 vs 1y1 are given respectively as :

1. P10P20, P10-P20P20
2. P20P10, P20-P10P10
3. P20P10, P10-P20P20
4. P10P20, P20-P10P20

Given below are the atomic numbers of some group 14 elements. The atomic number of the element with lowest melting point is :

1. 14
2. 50
3. 6
4. 82

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

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 are false

The -Helix and - Pleated sheet structures of protein are associated with its :

1. tertiary structure
2. quaternary structure
3. primary structure
4. secondary structure

The effect of temperature on spontaneity of reactions are represented as : [figure] The incorrect combinations are :

1. A and C only
2. B and D only
3. A and D only
4. B and C only

Match List - I with List - II Choose the correct answer from the options given below :

1. A-III, B-IV, C-I, D-II
2. A-I, B-IV, C-III, D-II
3. A-III, B-II, C-I, D-IV
4. A-II, B-II, C-I, D-IV

Identify the products [A] and [B], respectively in the following reaction: [figure]

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Which of the following graphs most appropriately represents a zero order reaction?

1. [figure]
2. [figure]
3. [figure]
4. [figure]

Identify the coordination complexes in which the central metal ion has d4 configuration. Choose the correct answer from the options given below :

1. B, C and D only
2. C and E only
3. A, B and E only
4. B and D only

Identify A, B and C in the given below reaction sequence [figure]

1. PbCl2, PbSO4, PbCrO4
2. PbS, PbSO4, Pb(CH3COO)2
3. PbS, PbSO4, PbCrO4
4. PbCl2, Pb(SO4)2, PbCrO4

Standard electrode potentials for a few half cells are mentioned below : E Cu2+/Cu = 0.34 V, E Zn2+/Zn = -0.76 V E Ag+/Ag = 0.80 V, E Mg2+/Mg = -2.37 V Which one of the following cells gives the most negative value of G ?

1. Zn | Zn2+(1M) || Ag+(1M) | Ag
2. Ag | Ag+(1M) || Mg2+(1M) | Mg
3. Zn | Zn2+(1M) || Mg2+(1M) | Mg
4. Cu | Cu2+(1M) || Ag+(1M) | Ag

Consider the reaction X2Y(g) X2(g) + 12Y2(g) The equation representing correct relationship between the degree of dissociation (x) of X2Y(g) with its equilibrium constant Kp is . Assume x to be very very small.

1. x = [3] KpP
2. x = [3] Kp2P
3. x = [3] 2 Kp2P
4. x = [3] 2KpP

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

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

The ascending order of relative rate of solvolysis of following compounds is : [figure]

1. (C) < (D) < (B) < (A)
2. (D) < (A) < (B) < (C)
3. (D) < (B) < (A) < (C)
4. (C) < (B) < (A) < (D)

Given below are two statements about X-ray spectra of elements : In the light of the above statements, choose the correct answer from the options given below :

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 are false

Consider the following reactions K2Cr2O7 [-H2O]KOH [A] [-H2O]H2SO4 [B] + K2SO4 The products [A] and [B], respectively are :

1. K2Cr(OH)6 and Cr2O3
2. K2CrO4 and Cr2O3
3. K2CrO4 and K2Cr2O7
4. K2CrO4 and CrO

Given below are two statements: Consider the following reaction [figure] In the light of the above statements, choose the correct answer from the options given below :

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

0.01 mole of an organic compound (X) containing 10\% hydrogen, on complete combustion produced 0.9 g H2O. Molar mass of (X) is g mol-1.

The bond dissociation enthalpy of X2 H bond calculated from the given data is kJ mol-1. (Nearest integer) M+X-(s) M+(g)+X-(g) H lattice=800 kJ mol-1 M(s) M(g) H sub=100 kJ mol-1 M(g) M+(g)+e-(g) H i=500 kJ mol-1 X(g)+e-(g) X-(g) H eg=-300 kJ mol-1 M(s)+ 12X2(g) M+X-(s) H f=-400 kJ mol-1 [Given : M+X- is a pure ionic compound and X forms a diatomic molecule X2 in gaseous state]

When 81.0 g of aluminium is allowed to react with 128.0 g of oxygen gas, the mass of aluminium oxide produced in grams is . (Nearest integer) Given : Molar mass of Al is 27.0 g mol-1 Molar mass of O is 16.0 g mol-1

Consider the following sequence of reactions. [figure] Total number of sp3 hybridised carbon atoms in the major product C formed is .

A compound ' X ' absorbs 2 moles of hydrogen and ' X ' upon oxidation with KMnO4 | H+ gives [figure] The total number of bonds present in the compound ' X ' is .

If I= 0 2 32x 32x+ 32x dx, then 02I x x x 4x+ 4x dx equals :

1. 212
2. 24
3. 216
4. 28

The number of complex numbers z, satisfying |z|=1 and | z z+ zz |=1, is :

1. 8
2. 10
3. 4
4. 6

The length of the chord of the ellipse x24+ y22=1, whose mid-point is (1, 12 ), is :

1. 23 15
2. 13 15
3. 15
4. 53 15

Let the point A divide the line segment joining the points P(-1,-1,2) and Q(5,5,10) internally in the ratio r:1 (r>0). If O is the origin and ( OQ OA )- 15 | OP OA |2=10, then the value of r is :

1. 7
2. 14
3. 7
4. 3

A board has 16 squares as shown in the figure : [figure] Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

1. 35
2. 45
3. 2330
4. 710

If the square of the shortest distance between the lines x-21= y-12= z+3-3 and x+12= y+34= z+5-5 is mn, where m, n are coprime numbers, then m+n is equal to :

1. 14
2. 6
3. 21
4. 9

Let X=R . Define a relation R on X as : (a1,b1)R(a2,b2) b1=b2 In the light of the above statements, choose the correct answer from the options given below :

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

If the area of the region \(x,y):-1 x 1, 0 y a+e|x|-e-x, a>0 \ is e2+8e+1e, then the value of a is :

1. 7
2. 5
3. 6
4. 8

Let the range of the function f(x)=6+16 x ( 3-x ) ( 3+x ) 3x 6x, x be [ , ]. Then the distance of the point ( , ) from the line 3x+4y+12=0 is :

1. 11
2. 10
3. 8
4. 9

The system of equations x+y+z=6, x+2y+5z=9, x+5y+ z= , has no solution if

1. =17, =18
2. =17, 18
3. =15, 17
4. 17, 18

The distance of the line x-22= y-63= z-34 from the point (1,4,0) along the line x1= y-22= z+33 is :

1. 17
2. 13
3. 15
4. 14

x (2x2-3x+5 )(3x-1) x2 (3x2+5x+4 ) (3x+2)x is equal to :

1. 2e3
2. 23 e
3. 2e 3
4. 2 3e

Let A=[aij] be a 3 3 matrix such that A bmatrix0\\1\\0 bmatrix= bmatrix0\\0\\1 bmatrix, A bmatrix4\\1\\3 bmatrix= bmatrix0\\1\\0 bmatrix and A bmatrix2\\1\\2 bmatrix= bmatrix1\\0\\0 bmatrix, then a23 equals :

1. 2
2. -1
3. 1
4. 0

Let A=\(x,y) :|x+y| 3\ and B=\(x,y) :|x|+|y| 3\. If C=\(x,y) :x=0 or y=0\, then (x,y) |x+y| is :

1. 18
2. 24
3. 15
4. 12

If in the expansion of (1+x)p(1-x)q, the coefficients of x and x2 are 1 and -2, respectively, then p2+q2 is equal to :

1. 8
2. 20
3. 13
4. 18

A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2=0 and y+2=0, respectively. If the locus of the point P, that divides the rod AB internally in the ratio 2:1 is 9 (x2+ y2+ xy+ x+28y )-76=0, then - - is equal to :

1. 24
2. 22
3. 21
4. 23

Let x3 x dx=g(x)+C, where C is the constant of integration. If 8 (g ( 2 )+g' ( 2 ) )= 3+ 2+ , , , Z, then + - equals :

1. 47
2. 55
3. 62
4. 48

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm, the ice-cream melts at the rate of 81 cm3/min and the thickness of the ice-cream layer decreases at the rate of 14 cm/min. The surface area (in cm2) of the chocolate ball (without the ice-cream layer) is :

1. 128
2. 196
3. 225
4. 256

Let the shortest distance from (a,0), a>0, to the parabola y2=4x be 4. Then the equation of the circle passing through the point (a,0) and the focus of the parabola, and having its centre on the axis of the parabola is :

1. x2+y2-8x+7=0
2. x2+y2-6x+5=0
3. x2+y2-4x+3=0
4. x2+y2-10x+9=0

Let x=x(y) be the solution of the differential equation y= (x-y dxdy ) ( xy ), y>0 and x(1)= 2. Then (x(2)) is equal to :

1. 2 ( e 2 )-1
2. 1-2 ( e 2 )2
3. 1-2 ( e 2 )
4. 2 ( e 2 )2-1

Let , be the roots of the equation x2-ax-b=0 with Im( )<Im( ). Let Pn= n- n. If P3=-5 7 i, P4=-3 7 i, P5=11 7 i and P6=45 7 i, then | 4+ 4 | is equal to .

The focus of the parabola y2=4x+16 is the centre of the circle C of radius 5. If the values of , for which C passes through the point of intersection of the lines 3x-y=0 and x+ y=4, are 1 and 2, 1< 2, then 12 1+29 2 is equal to .

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is .

The roots of the quadratic equation 3x2-px+q=0 are 10th and 11th terms of an arithmetic progression with common difference 32. If the sum of the first 11 terms of this arithmetic progression is 88, then q-2p is equal to .

The variance of the numbers 8, 21, 34, 47, , 320 is .