JEE Main 2025 (Online) 7th April Evening Shift

The dimension of 0 0 is equal to that of: ( 0 = Vacuum permeability and 0 = Vacuum permittivity)

1. Voltage
2. Inductance
3. Resistance
4. Capacitance

A photoemissive substance is illuminated with a radiation of wavelength i so that it releases electrons with de-Broglie wavelength e. The longest wavelength of radiation that can emit photoelectron is o. Expression for de-Broglie wavelength is given by: (m: mass of the electron, h: Planck's constant and c: speed of light)

1. e = h i 2mc
2. e = h 2mc ( 1 i - 1 o )
3. e = h2mc ( 1 i - 1 o )
4. e = h o2mc

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is : (use acceleration due to gravity g = 10 m/s2 and neglect air resistance)

1. 7.2 km
2. 2 5 km
3. 2 2 km
4. 4 km

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 most appropriate answer from the options given below:

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

Which one of the following forces cannot be expressed in terms of potential energy?

1. Frictional force
2. Coulomb's force
3. Restoring force
4. Gravitational force

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

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Given: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol)

1. 1 : 10
2. 10 : 1
3. 1 : 10
4. 1 : 1

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 most appropriate answer from the options given below:

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

The unit of 2I 0 c is : (I = intensity of an electromagnetic wave, c = speed of light)

1. Vm
2. NC-1
3. NC
4. Nm

A dipole with two electric charges of 2 magnitude each, with separation distance 0.5 , is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30 from the axis, it tends to realign in the direction due to a torque. The value of torque is:

1. 2.5 10-9 Nm
2. 2.5 10-12 Nm
3. 5 10-3 Nm
4. 5 10-9 Nm

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 most appropriate answer from the options given below :

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

A mirror is used to produce an image with magnification of 14. If the distance between object and its image is 40 cm, then the focal length of the mirror is .

1. 10 cm
2. 12.7 cm
3. 10.7 cm
4. 15 cm

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 most appropriate answer from the options given below :

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

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle 0 ) with 30 inclined with the vertical. The length of water risen in the capillary is cm. (Take g = 9.8 m/s2)

1. 825
2. 685
3. 572
4. 715

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 most appropriate answer from the options given below:

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

Consider the following logic circuit. [figure] The output is Y = 0 when :

1. A = 1 and B = 0
2. A = 0 and B = 0
3. A = 1 and B = 1
4. A = 0 and B = 1

The equation of a wave travelling on a string is y = [20 x + 10 t], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

1. 10 cm
2. 2.5 cm
3. 20 cm
4. 5.0 cm

A transparent block A having refractive index = 1.25 is surrounded by another medium of refractive index = 1.0 as shown in the figure. A light ray is incident on the flat face of the block with incident angle as shown in the figure. What is the maximum value of for which light suffers total internal reflection at the top surface of the block? [figure]

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

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

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

Let M and R be the mass and radius of a disc. A small disc of radius R/3 is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis passing through the centre O and perpendicular to the plane of disc is 4xMR2. The value of x is . [figure]

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivities of these rods are: LALB = 12, rArB = 2 and KAKB = 12. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is K, when equilibrium is established.

The electric field in a region is given by E = (2 i + 4 j + 6 k) 103 N/C. The flux of the field through a rectangular surface parallel to x–z plane is 6.0 Nm2C-1. The area of the surface is cm2.

An inductor of reactance 100 , a capacitor of reactance 50 , and a resistor of resistance 50 are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is W.

A parallel plate capacitor has charge 5 10-6 C. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is 4 10-6 C then the dielectric constant of the slab is .

An object with mass 500 g moves along x-axis with speed v = 4 x m/s. The force acting on the object is :

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

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

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

The correct statements from the following are : Choose the correct answer from the options given below :

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

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

1. Statement I is incorrect but Statement II is correct
2. Both Statement I and Statement II are incorrect
3. Both Statement I and Statement II are correct
4. Statement I is correct but Statement II is incorrect

The descending order of basicity of the following amines is : Choose the correct answer from the options given below :

1. E > A > D > C > B
2. E > D > A > B > C
3. E > D > B > A > C
4. B > E > D > A > C

In SO2, NO2- and N3-, the hybridizations at the central atom are respectively :

1. sp2, sp2 and sp2
2. sp, sp2 and sp
3. sp2, sp and sp
4. sp2, sp2 and sp

The number of optically active products obtained from the complete ozonolysis of the given compound is : [figure]

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

A mixture of 1 g each of chlorobenzene, aniline, and benzoic acid is dissolved in 50 mL ethyl acetate and placed in a separating funnel. 5 M NaOH (30 mL) was added in the same funnel. The funnel was shaken vigorously and then kept aside. The ethyl acetate layer in the funnel contains :

1. chlorobenzene and aniline
2. benzoic acid and aniline
3. benzoic acid
4. benzoic acid and chlorobenzene

"P" is an optically active compound with molecular formula C6H12O. When "P" is treated with 2,4-dinitrophenylhydrazine, it gives a positive test. However, in presence of Tollens' reagent, "P" gives a negative test. Predict the structure of "P".

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

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

1. Both Statement I and Statement II are correct
2. Statement I is incorrect but Statement II is correct
3. Both Statement I and Statement II are incorrect
4. Statement I is correct but Statement II is incorrect

Choose the incorrect trend in the atomic radii (r) of the elements.

1. rRb < rCs
2. rAt < rCs
3. rBr < rK
4. rMg < rAl

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

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

Liquid A and B form an ideal solution. The vapour pressures of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If xA and xB are the mole fraction of A and B in solution while yA and yB are the mole fraction of A and B in vapour phase, then,

1. (xA - yA) < (xB - yB)
2. xAxB = yAyB
3. xAxB < yAyB
4. xAxB > yAyB

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

The hydration energies of K+ and Cl- are -x and -y kJ/mol respectively. If the lattice energy of KCl is -z kJ/mol, then the heat of solution of KCl is :

1. x + y + z
2. z - (x + y)
3. -z - (x + y)
4. x - y - z

The number of unpaired electrons responsible for the paramagnetic nature of the following complex species are respectively : [Fe(CN)6]3-, [FeF6]3-, [CoF6]3-, [Mn(CN)6]3-

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

A(g) B(g) + C(g) is a first order reaction. array|l|c|c| Time & t & \ Psystem & Pt & P \ array The reaction was started with reactant A only. Which of the following expressions is correct for rate constant k?

1. k = 1t P Pt
2. k = 1t P 2(P - Pt)
3. k = 1t 2(P - Pt)Pt
4. k = 1t P (P - Pt)

Given below are two statements : 1 M aqueous solutions of each of Cu(NO3)2, AgNO3, Hg2(NO3)2, Mg(NO3)2 are electrolysed using inert electrodes. Given: E0Ag+/Ag = 0.80 V, E0Hg22+/Hg = 0.79 V, E0Cu2+/Cu = 0.34 V and E0Mg2+/Mg = -2.37 V. In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both Statement I and Statement II are incorrect
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 correct

The extra stability of half-filled subshell is due to : Identify the correct statements :

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

'X' is the number of acidic oxides among VO2, V2O3, CrO3, V2O5 and Mn2O7. The primary valency of cobalt in [Co(H2NCH2CH2NH2)3]2(SO4)3 is Y. The value of X + Y is .

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

The correct statement amongst the following is :

1. The standard state of a pure gas is the pure gas at a pressure of 1 bar and temperature 273 K.
2. f H 500 is zero for O2(g).
3. f H 298 is zero for O(g).
4. The term 'standard state' implies that the temperature is 0°C.

In Dumas' method 292 mg of an organic compound released 50 mL of nitrogen gas (N2) at 300 K temperature and 715 mm Hg pressure. The percentage composition of 'N' in the organic compound is % (Nearest integer) (Aqueous tension at 300 K = 15 mm Hg)

Butane reacts with oxygen to produce carbon dioxide and water following the equation given below. C4H10(g) + 132O2(g) 4CO2(g) + 5H2O(l) If 174.0 kg of butane is mixed with 320.0 kg of O2, the volume of water formed in liters is . (Nearest integer) [Given : (a) Molar mass of C, H, O are 12, 1, 16 g mol-1 respectively, (b) Density of water = 1 g mL-1]

The number of paramagnetic metal complex species among [Co(NH3)6]3+, [Co(C2O4)3]3-, [MnCl6]3-, [Mn(CN)6]3-, [CoF6]3-, [Fe(CN)6]3- and [FeF6]3- with same number of unpaired electrons is .

One litre buffer solution was prepared by adding 0.10 mol each of NH3 and NH4Cl in deionised water. The change in pH on addition of 0.05 mol of HCl to the above solution is 10-2. (Nearest integer) Given : pKb of NH3 = 4.745 and 10 3 = 0.477

Identify the structure of the final product (D) in the following sequence of the reactions : [figure] Total number of sp2 hybridised carbon atoms in product D is .

Let f : R R be a polynomial function of degree four having extreme values at x = 4 and x = 5. If x 0 f(x)x2 = 5, then f(2) is equal to :

1. 8
2. 10
3. 12
4. 14

Let y = y(x) be the solution of the differential equation (x2 + 1)y' - 2xy = (x4 + 2x2 + 1) x, y(0) = 1. Then -33 y(x) dx is :

1. 36
2. 24
3. 18
4. 30

If the locus of z C, such that Re ( z-12z+i ) + Re ( z-12 z-i ) = 2, is a circle of radius r and center (a, b), then 15abr2 is equal to :

1. 16
2. 24
3. 12
4. 18

Let an be the nth term of an A.P. If Sn = a1 + a2 + a3 + + an = 700, a6 = 7 and S7 = 7, then an is equal to :

1. 65
2. 56
3. 70
4. 64

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is mn, (m, n) = 1, then n2 - m2 is equal to :

1. 64
2. 80
3. 60
4. 72

If the range of the function f(x) = 5-xx2-3x+2, x 1, 2, is (- , ] [ , ), then 2 + 2 is equal to :

1. 188
2. 192
3. 190
4. 194

The number of real roots of the equation x|x-2| + 3|x-3| + 1 = 0 is :

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

Let the length of a latus rectum of an ellipse x2a2 + y2b2 = 1 be 10. If its eccentricity is the minimum value of the function f(t) = t2 + t + 1112, t R, then a2 + b2 is equal to :

1. 115
2. 120
3. 125
4. 126

Let e1 and e2 be the eccentricities of the ellipse x2b2 + y225 = 1 and the hyperbola x216 - y2b2 = 1, respectively. If b < 5 and e1 e2 = 1, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is :

1. 45
2. 35
3. 74
4. 32

If the equation of the line passing through the point (0, - 12, 0 ) and perpendicular to the lines r = ( i + a j + b k ) and r = ( i - j - 6 k ) + (-b i + a j + 5 k ) is x-1-2 = y+4d = z-c-4, then a + b + c + d is equal to :

1. 13
2. 14
3. 12
4. 10

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is :

1. 757
2. 755
3. 750
4. 760

If the area of the region \(x, y) : 1 + x2 y \x + 7, 11 - 3x\\ is A, then 3A is equal to :

1. 50
2. 46
3. 49
4. 47

The number of solutions of the equation 2 2 + 5 2 = 2 3 5 2 in [- 2, 2 ] is :

1. 5
2. 7
3. 6
4. 9

Consider the lines L1: x - 1 = y - 2 = z and L2: x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5, 1, -3) on the lines L1 and L2 be Q and R respectively. If the area of the triangle PQR is A, then 4A2 is equal to :

1. 151
2. 147
3. 139
4. 143

Let A = \( , ) R R : | - 1| 4 and | - 5| 6\ and B = \( , ) R R : 16( - 2)2 + 9( - 6)2 144\. Then

1. A B
2. B A
3. neither A B nor B A
4. A B = \(x, y) : -4 x 4, -1 y 11\

Let a and b be the vectors of the same magnitude such that | a + b| + | a - b|| a + b| - | a - b| = 2 + 1. Then | a + b|2| a|2 is :

1. 2 + 2
2. 2 + 4 2
3. 4 + 2 2
4. 1 + 2

Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by joining the vertices of P. If p + q = 126, then the eccentricity of the ellipse x216 + y2n = 1 is :

1. 1 2
2. 12
3. 74
4. 34

Let a random variable X take values 0, 1, 2, 3 with P(X = 0) = P(X = 1) = p, P(X = 2) = P(X = 3) and E(X2) = 2E(X). Then the value of 8p - 1 is :

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

Let the system of equations x + 5y - z = 1 4x + 3y - 3z = 7 24x + y + z = , R, have infinitely many solutions. Then the number of the solutions of this system, if x, y, z are integers and satisfy 7 x + y + z 77, is :

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

If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = mx + c is at (3, -1), then m - c is :

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

The sum of the series 2 1 20C4 - 3 2 20C5 + 4 3 20C6 - 5 4 20C7 + + 18 17 20C20, is equal to .

If the function f(x) = ( x) - ( x) x - x is continuous at x = 0, then f(0) is equal to .

If ( 1x + 1x3 ) ( [23]3x-24 + x-26 ) dx = - 3( + 1) (3x + x ) + 1 + C, x > 0, ( , , Z), where C is the constant of integration, then + + is equal to .

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corresponding directrix of this hyperbola be (-5, 0) and 5x + 9 = 0, respectively. If the product of the focal distances of a point ( , 2 5) on the hyperbola is p, then 4p is equal to .

For t > -1, let t and t be the roots of the equation ((t + 2)1/7 - 1 )x2 + ((t + 2)1/6 - 1 )x + ((t + 2)1/21 - 1 ) = 0 If t -1+ t = a and t -1+ t = b, then 72(a + b)2 is equal to .