JEE Main 2025 (Online) 28th January Evening Shift

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is -3, then the magnitude of the radius of curvature of the mirror is :

1. 3.75 cm
2. 15 cm
3. 7.5 cm
4. 30 cm

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

1. 290 g
2. 200 g
3. 190 g
4. 300 g

[figure] In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage VAB is correctly represented by:

1. [figure]
2. [figure]
3. VAB would be zero at all times.
4. [figure]

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10 rad s-1 about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? ( = 3.14)

1. 0.5024 V
2. 0.0628 V
3. 0.2512 V
4. 0.1256 V

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between t = 0 to t = 4 s? [figure]

1. 11 m
2. 30 m
3. 13 m
4. 10 m

The magnetic field of an E.M. wave is given by B = ( 32 i + 12 j )30 [ (t - zc ) ] (S.I. Units). The corresponding electric field in S.I. units is:

1. E = ( 12 i + 32 j )30c [ (t + zc ) ]
2. E = ( 12 i - 32 j )30c [ (t - zc ) ]
3. E = ( 32 i - 12 j )30c [ (t + zc ) ]
4. E = ( 34 i + 14 j )30c [ (t - zc ) ]

A balloon and its content having mass M is moving up with an acceleration ‘a’. The mass that must be released from the content so that the balloon starts moving up with an acceleration ‘3a’ will be (Take ‘g’ as acceleration due to gravity)

1. 3Ma2a + g
2. 2Ma3a + g
3. 3Ma2a - g
4. 2Ma3a - g

The ratio of vapour densities of two gases at the same temperature is 425, then the ratio of r.m.s. velocities will be :

1. 52
2. 254
3. 425
4. 25

[figure] An infinite wire has a circular bend of radius a, and carrying a current I as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:

1. 02 Ia [ 2+2 ]
2. 04 Ia [ 3 2+1 ]
3. 04 Ia [ 2+1 ]
4. 04 Ia [ 3 2+2 ]

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as:

1. 1n4
2. 1n2
3. 1n3
4. 1n

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

1. 8.4
2. 11.2
3. 5.6
4. 2.8

Which of the following phenomena cannot be explained by wave theory of light?

1. Refraction of light
2. Reflection of light
3. Diffraction of light
4. Compton effect

A body of mass 4 kg is placed on a plane at a point P having coordinates (3, 4) m. Under the action of force F = (2 i + 3 j) N, it moves to a new point Q having coordinates (6, 10) m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of :

1. 4 : 3
2. 13 : 6
3. 1 : 2
4. 6 : 13

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

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

[figure] A bar magnet has total length 2l = 20 units and the field point P is at a distance d = 10 units from the centre of the magnet. If the relative uncertainty of length measurement is 1\%, then uncertainty of the magnetic field at point P is :

1. 10%
2. 5%
3. 3%
4. 4%

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A. If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of -2, then the radius of curvature of meniscus is :

1. 23 cm
2. 43 cm
3. 13 cm
4. 1 cm

The kinetic energy of translation of the molecules in 50 g of CO2 gas at 17 is :

1. 4205.5 J
2. 3582.7 J
3. 3986.3 J
4. 4102.8 J

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg m-3)

1. 400 cm3
2. 600 cm3
3. 1400 cm3
4. 4000 cm3

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

A parallel plate capacitor of capacitance 1 μF is charged to a potential difference of 20 V. The distance between plates is 1 μm. The energy density between plates of capacitor is :

1. 1.8 103 J/m3
2. 2 102 J/m3
3. 2 10-4 J/m3
4. 1.8 105 J/m3

A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm. The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is 10-13 m3/s.

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of 7 106 Pa, would be mm3. (Given bulk modulus of copper = 1.4 1011 N m-2)

An electric dipole of dipole moment 6 10-6 C m is placed in uniform electric field of magnitude 106 V/m. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be J.

The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be A. [figure]

[figure] A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E tn, then value of n is .

The product B formed in the following reaction sequence is: [figure]

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

The major product of the following reaction is: [figure]

1. 6-Phenylhepta-3,5-diene
2. 6-Phenylhepta-2,4-diene
3. 2-Phenylhepta-2,4-diene
4. 2-Phenylhepta-2,5-diene

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

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

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

Arrange the following in increasing order of solubility product : Ca(OH)2, AgBr, PbS, HgS

1. PbS < HgS < Ca(OH)2 < AgBr
2. HgS < AgBr < PbS < Ca(OH)2
3. HgS < PbS < AgBr < Ca(OH)2
4. Ca(OH)2 < AgBr < HgS < PbS

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

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

[figure] An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A→B→C→D→A as shown in the three cases above. Choose the correct option regarding U :

1. U(Case-III) > U(Case-II) > U(Case-I)
2. U(Case-I) > U(Case-II) > U(Case-III)
3. U(Case-I) = U(Case-II) = U(Case-III)
4. U(Case-I) > U(Case-III) > U(Case-II)

Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom? Choose the correct answer from the options given below :

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

The amphoteric oxide among V2O3, V2O4 and V2O5, upon reaction with alkali leads to formation of an oxide anion. The oxidation state of V in the oxide anion is :

1. + 4
2. + 5
3. + 3
4. + 7

Identify product [A], [B] and [C] in the following reaction sequence. CH3-C CH [H2]Pd/C [A] [(ii) Zn, H2O](i) O3 [B] + [C]

1. [A]: CH3-CH=CH2, [B]: CH3CHO, [C]: CH3CH2OH
2. [A]: CH3-CH=CH2, [B]: CH3CHO, [C]: HCHO
3. [A]: CH3CH2CH3, [B]: CH3CHO, [C]: HCHO
4. [A]: CH2=CH2, [B]: H3C- O \|C-CH3, [C]: HCHO

Identify correct conversion during acidic hydrolysis from the following : Choose the correct answer from the options given below :

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

The total number of compounds from below when treated with hot KMnO4, giving benzoic acid is: [figure] , [figure] , [figure] , [figure] , [figure] , [figure] , [figure] , [figure]

1. 4
2. 3
3. 5
4. 6

Assume a living cell with 0.9% (w/w) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data upto first decimal place only) The cell will :

1. shrink since solution is 0.45% (w/w) as a result of association of glucose molecules (due to hydrogen bonding)
2. shrink since solution is 0.5% (w/w)
3. show no change in volume since solution is 0.9% (w/w)
4. swell up since solution is 1% (w/w)

The purification method based on the following physical transformation is : (X)Solid Heat (X)Vapour Cool (X)Solid

1. Extraction
2. Crystallization
3. Distillation
4. Sublimation

Identify correct statements : Choose the correct answer from the options given below :

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

Identify the inorganic sulphides that are yellow in colour : Choose the correct answer from the options given below :

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

Consider an elementary reaction A(g) + B(g) C(g) + D(g) If the volume of reaction mixture is suddenly reduced to 13 of its initial volume, the reaction rate will become 'x' times of the original reaction rate. The value of x is :

1. 3
2. 9
3. 13
4. 19

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

Concentrated nitric acid is labelled as 75% by mass. The volume in mL of the solution which contains 30 g of nitric acid is . Given : Density of nitric acid solution is 1.25 g/mL.

1. 32
2. 40
3. 55
4. 45

For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth? Where N - Number of bacteria at any time, N0 - Initial number of bacteria.

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

The spin only magnetic moment ( ) value (B.M.) of the compound with the strongest oxidising power among Mn2O3, TiO and VO is B.M. (Nearest integer).

Total number of molecules/species from the following which will be paramagnetic is . O2, O2+, O2-, NO, NO2, CO, K2[NiCl4], [Co(NH3)6]Cl3, K2[Ni(CN)4]

Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12. The current in Amperes used for the given electrolysis is . (Nearest integer).

Consider the following data: Heat of formation of CO2(g) = -393.5 kJ mol-1 Heat of formation of H2O(l) = -286.0 kJ mol-1 Heat of combustion of benzene = -3267.0 kJ mol-1 The heat of formation of benzene is kJ mol-1. (Nearest integer)

A group 15 element forms d - d bond with transition metals. It also forms a hydride, which is the strongest base among the hydrides of other group members that form d - d bond. The atomic number of the element is .

The area of the region bounded by the curves x(1 + y2) = 1 and y2 = 2x is:

1. 4 - 13
2. 2 - 13
3. 2 ( 2 - 13 )
4. 12 ( 2 - 13 )

Bag B1 contains 6 white and 4 blue balls, Bag B2 contains 4 white and 6 blue balls, and Bag B3 contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag B2 is:

1. 25
2. 415
3. 13
4. 23

Let f: R R be a twice differentiable function such that f(2) = 1. If F(x) = x f(x) for all x R, 02 x F'(x) dx = 6 and 02 x2 F''(x) dx = 40, then F'(2) + 02 F(x) dx is equal to:

1. 13
2. 11
3. 9
4. 15

If the midpoint of a chord of the ellipse x29 + y24 = 1 is ( 2, 4/3), and the length of the chord is 2 3, then is:

1. 26
2. 18
3. 22
4. 20

The square of the distance of the point ( 157, 327, 7 ) from the line x+13 = y+35 = z+57 in the direction of the vector i + 4 j + 7 k is:

1. 66
2. 54
3. 41
4. 44

Two equal sides of an isosceles triangle are along -x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum of all possible distinct values of m is:

1. -2 10
2. 12
3. -6
4. 6

Let the coefficients of three consecutive terms Tr, Tr+1 and Tr+2 in the binomial expansion of (a + b)12 be in a G.P. and let p be the number of all possible values of r. Let q be the sum of all rational terms in the binomial expansion of ( [4]3 + [3]4)12. Then p + q is equal to:

1. 295
2. 283
3. 299
4. 287

If the components of a = i + j + k along and perpendicular to b = 3 i + j - k respectively, are 1611(3 i + j - k) and 111(-4 i - 5 j - 17 k), then 2 + 2 + 2 is equal to:

1. 16
2. 23
3. 26
4. 18

Let f: R - \0\ (- , 1) be a polynomial of degree 2, satisfying f(x)f ( 1x ) = f(x) + f ( 1x ). If f(K) = -2K, then the sum of squares of all possible values of K is:

1. 9
2. 1
3. 6
4. 7

Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = -1(2[x] + 1) is:

1. (- , )
2. (- , ) - \0\
3. (- , -1] [0, )
4. (- , -1] [1, )

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

1. 14
2. 12
3. 13
4. 23

If A and B are the points of intersection of the circle x2 + y2 - 8x = 0 and the hyperbola x29 - y24 = 1 and a point P moves on the line 2x - 3y + 4 = 0, then the centroid of PAB lies on the line:

1. x + 9y = 36
2. 9x - 9y = 32
3. 4x - 9y = 12
4. 6x - 9y = 20

Let A, B, C be three points in xy-plane, whose position vectors are given by 3 i + j, i + 3 j and a i + (1 - a) j respectively with respect to the origin O. If the distance of the point C from the line bisecting the angle between the vectors OA and OB is 9 2, then the sum of all the possible values of a is:

1. 2
2. 0
3. 92
4. 1

If + i and + i are the roots of x2 - (3 - 2i)x - (2i - 2) = 0, i = -1, then + is equal to:

1. 2
2. -6
3. 6
4. -2

If r=113 \ 1 ( 4 + (r - 1) 6 ) ( 4 + r 6 ) \ = a 3 + b, a, b Z, then a2 + b2 is equal to :

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

If f(x) = 1x1/4 (1 + x1/4 )dx, f(0) = -6, then f(1) is equal to :

1. 4 ( e 2 - 2 )
2. e2 2 + 2
3. 2 - e2
4. 4 ( e 2 + 2 )

Let A = bmatrix 1 2 & -2 \ 0 & 1 bmatrix and P = bmatrix & - \ & bmatrix, > 0. If B = PAP , C = P B10P and the sum of the diagonal elements of C is mn, where (m, n) = 1, then m + n is :

1. 127
2. 2049
3. 258
4. 65

Let f be a real valued continuous function defined on the positive real axis such that g(x) = 0x t f(t) dt. If g (x3 ) = x6 + x7, then value of r=115 f (r3 ) is :

1. 270
2. 340
3. 310
4. 320

Let f : [0, 3] A be defined by f(x) = 2x3 - 15x2 + 36x + 7 and g : [0, ) B be defined by g(x) = x2025x2025 + 1. If both the functions are onto and S = \x Z; x A or x B\, then n(S) is equal to :

1. 29
2. 31
3. 30
4. 36

For positive integers n, if 4an = (n2 + 5n + 6 ) and Sn = k=1n ( 1ak ), then the value of 507S2025 is :

1. 540
2. 675
3. 1350
4. 135

Let f(x) = n r=0n ( (x/2r+1 ) + 3 (x/2r+1 )1 - 2 (x/2r+1 ) ). Then x 0 ex - ef(x)(x - f(x)) is equal to .

Let A and B be the two points of intersection of the line y + 5 = 0 and the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If d denotes the distance between A and B, and a denotes the area of SAB, where S is the focus of the parabola y2 = 4x, then the value of (a + d) is .

If y = y(x) is the solution of the differential equation, 4 - x2 dydx = ( ( -1 ( x2 ) )2 - y ) -1 ( x2 ), -2 x 2, y(2) = 2 - 84, then y2(0) is equal to .

The interior angles of a polygon with n sides are in an A.P. with common difference 6 . If the largest interior angle of the polygon is 219 , then n is equal to .

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is .