JEE Main 2026 (Online) 6th April Morning Shift

The density of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l and d are 97.42 0.02 g, 8.35 0.05 mm and 20.20 0.02 mm, respectively. Calculated percentage fractional error in is .

1. 0.63%
2. 0.82%
3. 0.72%
4. 0.25%

The potential energy of a particle changes with distance x from a fixed origin as V= A xx+B, where A and B are constants with appropriate dimensions. The dimensions of AB are .

1. [ M1L5/2T-2]
2. [ M3/2L5/2T-2]
3. [ M1L2T-2]
4. [ M1L7/2T-2]

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive force is J. (take g = 10 m/s2)

1. -8.75
2. -8.35
3. -9.55
4. -9.98

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in contact with side-surface, having coefficient of friction . The cube (S) moves towards the right with acceleration of g2, where g is gravitational acceleration. During this movement the block P and Q remain stationary. The value of is . (take g = 10 m/s2) [figure]

1. 0.33
2. 0.67
3. 1
4. 0.5

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 108 N/m2 and its radius is 4 mm, then maximum acceleration the lift can take is m/s2. (take g = 10 m/s2 and =3.14)

1. 2.56
2. 3.89
3. 4.32
4. 5.16

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are and respectively.

1. 0.128 Nm, 100
2. 0.0128 Nm, 50
3. 0.128 Nm, 50
4. 0.0128 Nm, 100

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height h as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height h= R. The value of is . [figure]

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

The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point (p) of normal bisector, as shown in the figure is . [figure]

1. ( 34, 1.25 )
2. ( 34, 1.0 )
3. (0, 0)
4. (1.25, 0)

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11. When the joined wire is kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is m.

1. 1.1
2. 2.22
3. 1.21
4. 4.44

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is kPa.

1. 100
2. 120
3. 90
4. 105

In interference experiment the path difference between two interfering waves at a point A on the screen is /3, where is the wavelength of these waves, and at another point B the path difference is /6. The ratio of intensities at points A and B is .

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

A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x=A to x= A 2 is sec.

1. 1/4
2. 5/4
3. 5/8
4. 3/8

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is nC. ( 0=8.85 10-12 C2/Nm2 and =3.14)

1. 2.14
2. 2.44
3. 3.25
4. 0.7

The maximum rated power of the LED is 2 mW and it is used in the circuit with input voltage of 5 V as shown in the figure below. The current through resistance RS is 0.5 mA. The minimum value of the resistance of RS, to ensure that the LED is not damaged is k . [figure]

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

A point light source emits E.M. waves in free space. A detector, placed at a distance of L m, measures the intensity as I0. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as 45°. The measured intensity at new location will be .

1. I04
2. I0
3. I0 2
4. I02

A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of 4R in front of spherical interface. The magnitude of the magnification of point source image is . [figure]

1. 1.66
2. 2.33
3. 2.66
4. 1.33

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is 10-14 J. The value of is . ( 0=4 10-7 Tm/A, =3.14)

1. 6.28
2. 6.28 10-6
3. 628
4. 6.28 10-4

An inductor of inductance 10 mH having resistance of 100 is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is . [figure]

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

The ratio of momentum of the photons of the 1st and 2nd line of Balmer series of Hydrogen atoms is / . The possible values of and are :

1. 27 and 20
2. 3 and 16
3. 5 and 36
4. 20 and 27

A LCR series circuit driven with Erms=90 V at frequency fd=30 Hz has resistance R=80 , an inductance with inductive reactance XL=20.0 and capacitance with capacitive reactance XC=80.0 . The power factor of the circuit is .

1. 0.8
2. 0.64
3. 0.9
4. 0.5

Refer to the circuit diagram given below. The heat generated across the 6 resistance in 100 second is 100 J. The value of is . (Nearest integer) [figure]

An unpolarized light of intensity I0 passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is 0° and intensity of light emerged from analyser is 38I0, the angle of rotation of the light by the solution with respect to analyser is degrees.

The energy released when 717.13 kg of 37Li is converted into 24He by proton bombardment is 1032 eV. The value of is . (Nearest integer) (Mass of 37Li=7.0183 u, mass of 24He=4.004 u, mass of proton =1.008 u and 1 u =931 MeV/c2 and Avogadro number =6.0 1023)

A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as E=2x i+3y2 j+4 k N/C. The work done in moving the charge is J.

A certain gas is isothermally compressed to ( 13 )rd of its initial volume (V0=3 litre) by applying required pressure. If the bulk modulus of the gas is 3 105 N/m2, the magnitude of work done on the gas is J.

An oxide of iron contains 69.9% iron, its empirical formula, is: (Given : Molar mass of Fe and O are 56 and 16 g mol-1 respectively.)

1. FeO
2. Fe2O3
3. Fe3O4
4. FeO3

If shortest wavelength of hydrogen atom in Lyman series is x, then longest wavelength in Balmer series of He+ is:

1. 9x5
2. 36x5
3. x4
4. 5x9

Match the LIST-I with LIST-II

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

The pairs among A = [SO32-, CO32-], B = [O22-, F2], C = [CN-, CO], D = [NH3, H3O+] and E = [MnO42-, CrO42-] that do not have similar Lewis dot structure are

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

Arrange the following isothermal processes in order of the magnitude of the work (p − V) involved between states 1 and 2. Choose the correct option.

1. |wB| > |wA| > |wC| > |wD|
2. |wC| > |wD| > |wA| > |wB|
3. |wC| > |wD| > |wB| > |wA|
4. |wB| > |wA| > |wD| > |wC|

When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapor pressure of solution was x% of vapor pressure of pure solvent. What is x% ?

1. 50%
2. 60%
3. 70%
4. 80%

One mole each of He and A(g) are taken in a 10 L closed flask and heated to 400 K to establish the following equilibrium. A(g) B(g) Kc for this reaction at 400 K is 4.0. The partial pressures (in atm) of He and B(g) are respectively (at equilibrium) (Assume He, A(g) and B(g) behave as ideal gases) (Given : R = 0.082 L atm K-1 mol-1)

1. 3.28, 2.624
2. 2.624, 3.28
3. 3.28, 0.656
4. 0.656, 6.56

Consider the following data. arraycc Electrolyte & m ( S cm2 mol-1) \ BaCl2 & x1 \ H2SO4 & x2 \ HCl & x3 array BaSO4 is sparingly soluble in water. If the conductivity of the saturated BaSO4 solution is x S cm-1 then the solubility product of BaSO4 can be given as (Here m = m)

1. 106x2 2(x1 + x2 - 2x3)2
2. x2(x1 + x2 - 2x3)2
3. 2(x1 + x2 - 2x3)2106x2
4. x2(x1 + x2 + 2x3)2

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

Match the LIST-I with LIST-II

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

Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex? Choose the correct answer from the options given below :

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

Rf value for 2-methylpropene in a solvent system (Ethyl acetate + ether) is 0.42. 2-methylpropene is treated with dilute H2SO4 to give major organic product (X). Rf value for (X) in the same solvent system under identical condition will be:

1. 0.42
2. 0.82
3. 0.62
4. 0.12

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

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

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

Consider the following sequence of reactions [figure] The major product P is:

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

Arrange the following compounds according to increasing order of boiling points. n-C4H9OH (A), n-C4H9NH2 (B), n- C4H10 (C) and C2H5NHC2H5 (D).

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

Match the List-I with List-II

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

Match the List-I with List-II

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

First and second ionization enthalpies of lithium are 520 kJ mol-1 and 7297 kJ mol-1 respectively. Energy required to convert 3.5 mg lithium (g) into Li2+(g) [ Li(g) Li2+(g)] is kJ. (nearest integer) [Molar mass of Li = 7 g mol-1]

Consider the following sequence of reactions. [figure] The percentage of nitrogen in the yellow product (X) formed is %. (Nearest Integer) (Given Molar mass in g mol-1 H : 1, C : 12, N : 14)

4.7 g of phenol is heated with Zn to give product X. If this reaction goes to 60% completion then the number of moles of compound X formed will be 10-2. (Nearest Integer) (Given molar mass in g mol-1 : H:1, C:12, O:16)

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with t1/2 = 3 hour. The percentage of sucrose remaining after 6 hours is . (Nearest integer) (Given : log 2 = 0.3010 and log 3 = 0.4771)

Consider the reaction X Y at 300 K. If H and K are 28.40 kJ mol-1 and 1.8 10-7 at the same temperature, then the magnitude of S for the reaction in J K-1 mol-1 is . (Nearest integer) (Given : R = 8.3 J K-1 mol-1, ln 10 = 2.3, log 3 = 0.48, log 2 = 0.30)

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

1. 2
2. 5
3. 10
4. 13

Let one root of the quadratic equation in x : (k2-15k+27 )x2+9(k-1)x+18=0 be twice the other. Then the length of the latus rectum of the parabola y2=6kx is equal to :

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

Let e1 and e2 be two distinct roots of the equation x2-ax+2=0. Let the sets \a R : e1 and e2 are the eccentricities of hyperbolas\=( , ), and \a R : e1 and e2 are the eccentricities of an ellipse and a hyperbola, respectively\=( , ). Then 2+ 2+ 2 is equal to :

1. 18
2. 22
3. 26
4. 34

Let the set of all values of k R such that the equation z ( z+2+i )+k(2+3i)=0, z C, has at least one solution, be the interval [ , ]. Then 9( + ) is equal to :

1. -10
2. -8
3. 10 13
4. 8 13

The value of 13-23+33- +153 is :

1. 1706
2. 1856
3. 1982
4. 2403

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is :

1. 349
2. 3413
3. 329
4. 3213

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is :

1. 2670
2. 2840
3. 2920
4. 3600

If the coefficients of the middle terms in the binomial expansions of (1+ x)26 and (1- x)28, 0, are equal, then the value of is :

1. 1
2. 1413
3. 277
4. 727

A data consists of 20 observations x1, x2, , x20. If i=120 (xi+5 )2=2500 and i=120 (xi-5 )2=100, then the ratio of mean to standard deviation of this data is :

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

A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is 916, then N is equal to :

1. 5
2. 7
3. 8
4. 9

If the eccentricity e of the hyperbola x2a2- y2b2=1, passing through (6, 4 3 ), satisfies 15 (e2+1 )=34e, then the length of the latus rectum of the hyperbola x2b2- y22 (a2+1 )=1 is :

1. 10
2. 20
3. 25
4. 30

Let chord PQ of length 3 13 of the parabola y2=12x be such that the ordinates of points P and Q are in the ratio 1 : 2. If the chord PQ subtends an angle at the focus of the parabola, then is equal to :

1. 35
2. 45
3. 513
4. 1213

Let 0< <1, = 13 and -1(1- )+ -1(1- )= 4. Then 6( + ) is equal to :

1. 6
2. 7
3. 8
4. 9

Let S= \ (-2 , 2 ) : +1= 3 \. Then S is equal to :

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

Let the image of the point P(1, 6, a) in the line L : x1= y-12= z-a+1b, b>0, be ( a3, 0, a+c ). If S( , , ), >0, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is 2 14, then + + is equal to :

1. 19
2. 20
3. 21
4. 22

Let a line L be perpendicular to both the lines L1 : x+13= y+35= z+57 and L2 : x-21= y-44= z-67. If is the acute angle between the lines L and L3 : x- 872= y- 471= z2, then is equal to :

1. 32 2
2. 52 2
3. 53 2
4. 43 2

The value of x 0 ( x2 2 xx2- 2 x ) is :

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

The value of the integral - /4 /4 ( 32 4 x1+e x )dx is :

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

The area of the region \(x, y) : 0 y 6-x, . . y2 4x-3, x 0 \ is :

1. 8
2. 9
3. 12
4. 15

Let e be the base of natural logarithm and let f : \1, 2, 3, 4\ \1, e, e2, e3 \ and g : \1, e, e2, e3 \ \1, 12, 13, 14 \ be two bijective functions such that f is strictly decreasing and g is strictly increasing. If (x)= [f-1 \g-1 ( 12 ) \ ]x, then the area of the region R= \(x, y) : x2 y (x), . . 0 x 1 \ is :

1. 3- e(2)3 e(2)
2. 13 e(2)
3. 3+ e(2)
4. 3+ e(2)2+ e(3)

Let A= bmatrix-1 & 1 & -1\ 1 & 0 & 1\ 0 & 0 & 1 bmatrix satisfy A2+ (adj (adj(A) ) )+ (adj(A) (adj (adj(A) ) ) )= bmatrix2 & -2 & 2\ -2 & 0 & -1\ 0 & 0 & -1 bmatrix for some , R. Then ( - )2 is equal to .

Let the centre of the circle x2+y2+2gx+2fy+25=0 be in the first quadrant and lie on the line 2x-y=4. Let the area of an equilateral triangle inscribed in the circle be 27 3. Then the square of the length of the chord of the circle on the line x=1 is .

If a= i+ j+ k, b= j- k and c be three vectors such that a c= b and a c=3, then c ( a-2 b ) is equal to .

For the functions f( )= 2 + 2 , and g( )= 2 + 2 , > >0, let 0< < 2 f( )= 0< < g( ). If the first term of a G.P. is ( 2 ), its common ratio is ( 2 ) and the sum of its first 10 terms is mn, (m, n)=1, then m+n is equal to .

Let y=y(x) be the solution of the differential equation (x2-x x2-1 )dy + (y (x- x2-1 )-x )dx=0, x 1. If y(1)=1, then the greatest integer less than y ( 5 ) is .