JEE Main 2026 (Online) 4th April Morning Shift

In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If the circular scale has 100 divisions, the least count of screw gauge is mm.

1. 1 10-2
2. 1 10-3
3. 5 10-2
4. 5 10-3

The increase in the pressure required to decrease the volume ( V) of water is 6.3 107 N/m2. The percentage decrease in the volume is . (Bulk modulus of water =2.1 109 N/m2.)

1. 2 %
2. 3 %
3. 6 %
4. 4 %

The time taken by a block of mass m to slide down from the highest point to the lowest point on a rough inclined plane is 50 % more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at 45° with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is .

1. 3/4
2. 2/3
3. 5/9
4. 4/9

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, Mc2= MeV.

1. 6.9
2. 7.9
3. 2.2
4. 4.3

A solid sphere of mass M and radius R is divided into two unequal parts. The smaller part having mass M/8 is converted into a sphere of radius r and the larger part is converted into a circular disc of thickness t and radius 2R. If I1 is moment of inertia of a sphere having radius r about an axis through its centre and I2 is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia I2/I1= .

1. 35
2. 70
3. 140
4. 210

The two projectiles are projected with the same initial velocities at the 15° and 30° with respect to the horizontal. The ratio of their ranges is 1:x. The value of x is

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

The graph shows variation of stopping potential V0 with the frequency of the incident radiation for three photosensitive metals X1, X2 and X3. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation? [figure]

1. X1
2. X2
3. X3
4. All the metals will give out photoelectrons with same kinetic energies.

A slit of width a is illuminated by light of wavelength . The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance D from the slit system is .

1. D a
2. 1.5 D a
3. 2 D a
4. 3 D a

A string A of length 0.314 m and Young's modulus 2 1010 N/m2 is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is mm. (radius of both the strings is 0.2 mm and acceleration due to gravity = 10 m/s2) (Mass of both strings is to be neglected as compared to the mass of load)

1. 3
2. 2
3. 1.9
4. 1

One gas of n1 mole of molecules at temperature T1, volume V1, and pressure P1, and another gas of n2 mole of molecules at temperature T2, volume V2, and pressure P2, are mixed resulting in pressure P and volume V of the mixture. The temperature of the mixture is .

1. (T1+T2)2
2. T1T2PVT2P1V1+T1P2V2
3. (T2P1V1+T1P2V2)T1T2PV
4. |T1-T2|2

An ideal gas undergoes a process maintaining relation between pressure (P) and volume (V) as P=P0 (1+ ( V0V )2 )-1, where P0 and V0 are constants. If two samples A and B (two moles each) with initial volumes V0 and 3V0 respectively undergo above mentioned process and attain same pressure, then the difference in the temperatures of these samples, TB-TA is . (R = gas constant)

1. 9P0V08R
2. 11P0V010R
3. 7P0V06R
4. 13P0V011R

A voltmeter with internal resistance of x Ω can be used to measure up to 20 V. In order to increase its measuring range to 30 V, the required modification is to .

1. connect resistor of x2 Ω, in series with voltmeter.
2. connect resistor of x2 Ω, in parallel to voltmeter.
3. connect a resistor of x Ω in series with voltmeter.
4. connect resistor of 2x Ω in parallel to voltmeter.

Two 4 bits binary numbers, A = 1101 and B = 1010 are given in the inputs of a logic circuit shown in figure below. The output (Y) will be : [figure]

1. Y = 1101
2. Y = 0010
3. Y = 0111
4. Y = 1000

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is cm. [figure]

1. 2.5
2. 5
3. 7.5
4. 7

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed v. If x is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to x , where is .

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

An insulated wire is wound so that it forms a flat coil with N=200 turns. The radius of the innermost turn is r1=3 cm, and of the outermost turn r2=6 cm. If 20 mA current flows in it then the magnetic moment will be 10-2 A m2. The value of is .

1. 4.4
2. 2.64
3. 3.25
4. 1.2

Consider a circuit consisting of a capacitor (20 μF), resistor (100 Ω) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is 10 Ω. The time constant of the circuit is 10-3 s. The value of is . [figure]

1. 2.2
2. 2.0
3. 2.1
4. 2.4

The voltage and the current between A and B points shown in the circuit are . [figure]

1. 24 V, 12 A
2. 24 V, 4 A
3. 18 V, 12 A
4. 27 V, 4 A

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of 5 10-7 radian. The value of R is cm.

1. 61
2. 122
3. 244
4. 305

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave. [figure]

1. (Ex i+Ey j) (kx-kz- t)
2. (Ex i+Ez k) (kx+ky- t)
3. (Ex j+Ey k) (ky+kz- t)
4. (Ex i+Ey j+Ez k) (kx+ky-kz- t)

A 1 kg block subjected to two simultaneous forces (2 i+3 j+4 k ) N and (3 i- j-2 k ) N is moved a distance of 25 m along (3 i-4 j ) direction. The work done in this process is J.

The surface tension of a soap solution is 3.5 10-2 N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is 10-6 J. The value of is . ( =22/7)

The velocity of a particle executing simple harmonic motion along x-axis is described as v2=50-x2, where x represents displacement. If the time period of motion is x7 s, the value of x is .

A body of mass 2 kg begins to move under the influence of time dependent force F= (2t i+6t2 j ) N, where i and j are unit vectors along x and y-axis respectively. The power produced by the force at t=2 s is W.

An inductor of 10 mH, capacitor of 0.1 μF and a resistor of 100 Ω are connected in series across an a.c. power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitive reactance is 3 Ω. The value of is .

Number of moles and number of molecules in 1.4187 L of SO2 at STP respectively are

1. 0.1266; 3.812 1022
2. 0.0633; 3.812 1022
3. 0.1266; 7.6238 1022
4. 0.0633; 7.6238 1022

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

1. 5 : 1
2. 5 : 0.81
3. 5 : 1.75
4. 5 : 27

Which of the following is correct set of 4 quantum numbers of 19th electron in Chromium (Atomic number = 24) in accordance with Aufbau principle?

1. n = 3, l = 2, m = +2, s = + 12
2. n = 3, l = 2, m = -2, s = + 12
3. n = 4, l = 1, m = 0, s = + 12
4. n = 4, l = 0, m = 0, s = + 12

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 true but Statement II is false
4. Statement I is false but Statement II is true

At T(K), the equilibrium constant of A2(g) + B2(g) C(g) is 2.7 10-5. What is the equilibrium constant for 13A2(g) + 13B2(g) 13C(g) at the same temperature?

1. (2.7 10-5)3
2. 6 10-2
3. 2.7 10-5
4. 3 10-2

In order to oxidise a mixture of 1 mole each of FeC2O4, Fe2(C2O4)3, FeSO4 and Fe2(SO4)3 in acidic medium, the number of moles of KMnO4 required is

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

Consider the first order reaction R P. The fraction of molecules decomposed in the given first order reaction can be expressed as

1. 1 - ek1t
2. 1 + ek1t
3. 1 + e-k1t
4. 1 - e-k1t

A monoatomic anion (A-) has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element (A) respectively are

1. 80, 17, liquid
2. 81, 16, solid
3. 80, 16, gas
4. 81, 15, gas

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 true but Statement II is false
4. Statement I is false but Statement II is true

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

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

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

1. A, B and C Only
2. A, C and D Only
3. A and C Only
4. B and D Only

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

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

Increasing order of electron withdrawing power of following functional groups is : a. -CN b. -COOH c. -NO2 d. -I

1. c < b < d < a
2. c < a < b < d
3. d < b < a < c
4. a < b < c < d

An alkene (X) on ozonolysis followed by reduction gives following products. H- O \|C-H (2 moles), H- O \|C- O \|C- O \|C-H, CH3- O \|C- O \|C- O \|C-CH3 The alkene (X) is :

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

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

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

Amongst the following, the total number of compounds soluble in aqueous NaOH at room temperature is: [figure]

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

Product C of the following reaction sequence will be [figure]

1. 1-Bromo-4-nitrobenzene
2. 1, 3, 5-Tribromo-2-nitrobenzene
3. 4-Bromo-1-nitrobenzene
4. 1, 3, 5-Tribromobenzene

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 true but Statement II is false
4. Statement I is false but Statement II is true

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

Identify the colour of compound 'X' in the sequence of the reaction. [figure]

1. Violet
2. Green
3. Red
4. Colourless

According to Lewis theory, the total number of bond-pairs and lone pair of electrons around the central atom of XeO64- ion is .

Consider the following sequence of reactions to give the major product (X) [figure] P g of the major product (X) formed is reacted with NaHCO3 solution to liberate a gas which occupied 11.2 dm3 at STP. P = g. (Given molar mass in g mol-1 H : 1, C : 12, O : 16, Cl : 35.5)

2.0 g of a bromo hydrocarbon (X) was subjected to Carius analysis, gave 3.36 g of AgBr. The percentage of carbon in the compound (X) is 26.7%. Total number of carbon atoms in the empirical formula for compound (X) is . (Given molar mass in g mol-1 H : 1, C : 12, Br : 80, Ag : 108)

The pH of a solution obtained by mixing 5 mL of 0.1 M NH4OH solution with 250 mL of 0.1 M NH4Cl solution is 10-2. (Nearest integer) Given: pKb(NH4OH) = 4.74 2 = 0.30 3 = 0.48 5 = 0.70

A non-volatile, non-electrolyte solid solute when dissolved in 40 g of a solvent, the vapour pressure of the solvent decreased from 760 mm Hg to 750 mm Hg. If the same solution boils at 320 K, then the number of moles of the solvent present in the solution is . (Nearest integer) [Given: boiling point of the pure solvent = 319.5 K, Kb of the solvent = 0.3 K kg mol-1]

Let [ ] denote the greatest integer function. If the domain of the function f(x)= -1 ( 4x+2[x]3 ) is [ , ], then 12( + ) is equal to :

1. 6
2. 8
3. 9
4. 4

If the set of all solutions of |x2+x-9|=|x|+|x2-9| is [ , ] [ , ), then ( 2+ 2+ 2 ) is equal to:

1. 9
2. 18
3. 36
4. 72

Let z be a complex number such that |z+2|=|z-2| and ( z+3z-i )= 4. Then |z|2 is equal to:

1. 9
2. 4
3. 5
4. 1

The number of functions f : \1, 2, 3, 4\ \a, b, c\, which are not onto, is :

1. 48
2. 45
3. 51
4. 35

Let S= \A= bmatrixa & b\ c & d bmatrix : a, b, c, d \0, 1, 2, 3, 4\ and A2-4 A+3I=0 \ be a set of 2 2 matrices. Then the number of matrices in S, for which the sum of the diagonal elements is equal to 4, is :

1. 20
2. 17
3. 21
4. 19

Let A= bmatrix1 & 1 & 2\ -2 & 0 & 1\ 1 & 3 & 5 bmatrix. Then the sum of all elements of the matrix adj (adj (2(adj A)-1 ) ) is equal to:

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

The first term of an A.P. of 30 non-negative terms is 103. If the sum of this A.P. is the cube of its last term, then its common difference is:

1. 587
2. 2583
3. 1529
4. 529

The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

1. 5040
2. 3050
3. 3410
4. 4320

Let the smallest value of k N, for which the coefficient of x3 in (1+x)3+(1+x)4+(1+x)5+ +(1+x)99+(1+kx)100, x 0, is (43n+ 1014 ) (100C3 ) for some n N, be p. Then the value of p+n is :

1. 10
2. 11
3. 12
4. 13

Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b, 13, 67, (a>b), are 40 and 21, respectively. If the mean deviation about the median is 26, then 2a is equal to :

1. 109
2. 117
3. 161
4. 131

Let the line L1 : x+3=0 intersect the lines L2 : x-y=0 and L3 : 3x+y=0 at the points A and B, respectively. Let the bisector of the obtuse angle between the lines L2 and L3 intersect the line L1 at the point C. Then BC2 : AC2 is equal to:

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

Let the vertex A of a triangle ABC be (1, 2), and the mid-point of the side AB be (5, -1). If the centroid of this triangle is (3, 4) and its circumcenter is ( , ), then 21( + ) is equal to :

1. 309
2. 403
3. 497
4. 524

Suppose that two chords, drawn from the point (1, 2) on the circle x2+y2+x-3y=0 are bisected by the y-axis. If the other ends of these chords are R and S, and the mid point of the line segment RS is ( , ), then 6( + ) is equal to :

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

A line with direction ratios 1, -1, 2 intersects the lines x2= y3= z+13 and x+1-1= y-21= z4 at the points P and Q, respectively. If the length of the line segment PQ is , then 225 2 is equal to:

1. 1024
2. 1014
3. 1104
4. 1204

The square of the distance of the point (-2, -8, 6) from the line x-11= y-12= z-1 along the line x+51= y+5-1= z2 is equal to:

1. 3
2. 6
3. 8
4. 12

If y= -1 ( 3 x-4 x4 x+3 x )+2 -1 ( x1+ 1-x2 ), then dydx at x= 32 is equal to :

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

Let f be a real polynomial of degree n such that f(x)=f'(x)f''(x), for all x R. If f(0)=0, then 36 (f'(2)+f''(2)+ 02 f(x) dx ) is equal to:

1. 42
2. 46
3. 56
4. 66

The area of the region \(x, y) : y -|x|, y |x x|, y 0\ is:

1. 1+ 28
2. 2+ 24
3. 28-1
4. 4+ 22

Let -22 (| x|+[x x] )dx=2(3- 2)+ , where [ ] is the greatest integer function. Then ( 2 ) equals:

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

Let y=y(x) be the solution of the differential equation dydx= (1+x+x2 ) (1-y+y2 ), y(0)= 12. Then (2y(1)-1) is equal to :

1. 3 ( 11 36 )
2. 32 ( 11 312 )
3. 3 ( 11 312 )
4. 32 ( 11 36 )

A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p, then 96p is equal to .

Consider the parabola P : y2=4kx and the ellipse E : x2a2+ y2b2=1. Let the line segment joining the points of intersection of P and E, be their latus rectums. If the eccentricity of E is e, then e2+2 2 is equal to .

If A= 3 9 + 9 27 + 27 81 and B= 81 - 3 , then BA is equal to .

Let ak=( k) i+ j and bk= i-( k) j, where k= 2k-1 2n+1, for some n N, n>5. Then the value of k=1n | ak |2 k=1n | bk |2 is

The number of points, at which the function f(x)= \6x, 2+3x2 \+|x-1| |x2- 14 |, x (- , ), is not differentiable, is .