JEE Main 2026 (Online) 5th April Morning Shift

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and 7th Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

1. 0.07 cm negative zero error
2. 0.7 cm negative zero error
3. 0.07 cm positive zero error
4. 0.7 cm positive zero error

L, C and R represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula M L2 T-4 A-2 corresponds to .

1. R LC
2. RLC
3. C LR
4. 1R LC

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface, the change in g is approximately %. The value of is . (Take radius of the earth = 6400 km.)

1. 0.12
2. 0.25
3. 0.50
4. 0.75

Three masses m1=4 kg, m2=4 kg and m3=6 kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of T1/T2 is . (take g=10 m/s2) [figure]

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

A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making 37° with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At t=0 wedge (Y) is pulled toward right with constant force (f) of 24 N. Taking the block X at rest at t=0, the time taken by it to slide down 8.8 m on the slope, while Y is on the move, is s. (take tan (37°) = 3/4 and g = 10 m/s2) [figure]

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

The Young's modulus of steel wire of radius r and length L is Y. If the radius r and length L of the wire are doubled then the value of Y

1. increases by two times
2. reduces by half
3. remains unchanged
4. becomes one fourth

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Choose the correct answer from the options given below :

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

Consider the following statements: Choose the correct combination of statements from the options given below:

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

Refer to the figure given below. The values of I1, I2 and I3 are . [figure]

1. I1=2.5 A, I2=1.875 A, I3=1.875 A
2. I1=1.875 A, I2=2.5 A, I3=1.875 A
3. I1=1.875 A, I2=1.875 A, I3=2.5 A
4. I1=2.5 A, I2=2.5 A, I3=1.875 A

An electron of mass m is moving in an electric field E=-2E0 i (E0 = constant > 0), with an initial velocity V=v0 i (v0 = constant > 0). If 0= h4mv0, its de Broglie wavelength at time t is . (e = charge of electron)

1. 4 0 [1- E0e2m tv0 ]
2. 4 0 [1+ E0e2m tv0 ]
3. 4 0 [1+ 2E0em tv0 ]
4. 4 0 [1- 2E0em tv0 ]

In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit (f). The ratio of the radius of the orbits is given by ri:rf=16:4. The wavelength of photon emitted due to this transition is nm. (Given Rydberg constant = 1.0973 107 /m)

1. 121
2. 242
3. 486
4. 974

A displacement current of 4.0 A can be set up in the space between two parallel plates of 6 μF capacitor. The rate of change of potential difference across the plates of the capacitor is nearly 106 V/s. The value of is .

1. 0.58
2. 0.67
3. 0.82
4. 0.75

Refer to the figure given below, current between terminals A and B is A. [figure]

1. 12.5
2. 1.25
3. 7.5
4. 5

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is 2.4 μm. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be μm.

1. 1.2
2. 2
3. 2.4
4. 2.88

A ray of light passing through an equilateral prism is having velocity 2.12 108 m/s in the prism material, then the minimum angle of deviation is degrees.

1. 45
2. 30
3. 28
4. 58

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is 10-19 J. The value of is . (h=6.62 10-34 J s, e=1.6 10-19 C and c=3 108 m/s)

1. 3.68
2. 4.68
3. 5.68
4. 2.68

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

1. increased two times
2. increased 32 times
3. decreased two times
4. decreased 32 times

Two wires as shown in the figure below, made of steel and have breaking stress of 12 108 N/m2. Area of cross-section of upper wire is 0.008 cm2 and of lower wire is 0.004 cm2. The maximum mass that can be added to pan without breaking any wire is kg. [figure]

1. 56
2. 38
3. 96
4. 5.6

An a.c. source of angular frequency is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the source is changed to /4, (keeping the voltage unchanged) the current is found to be I/3. The ratio of resistance to reactance at frequency is

1. 67
2. 35
3. 78
4. 34

For the given logic circuit, which of the following inputs combination will make both LED-1 and LED-2 to glow? [figure]

1. A = 0, B = 1, C = 1
2. A = 1, B = 0, C = 0
3. A = 1, B = 0, C = 1
4. A = 1, B = 1, C = 0

A cube has side length 5 cm and modulus of rigidity 105 N/m2. The displacement produced by a force of 10 N in the upper face of cube is mm.

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is m. (Take g=10 m/s2 and neglect the air resistance)

A transverse wave on a string is described by y=3 (36t+0.018x+ /4 ), where x, y are in cm and t in seconds. The least distance between the two successive crests in the wave is cm. (Nearest integer) ( =3.14)

The charged particle moving in a uniform magnetic field of (3 i+2 j ) T has an acceleration (4 i- x2 j ) m/s2. The value of x is .

In the given circuit below inductance values of L1, L2 and L3 are same. The magnetic energy stored in the entire circuit is (Ut) and that stored in the L2 inductor is (Ul). Ut/Ul is . (Ignore the mutual inductance if any) [figure]

How many grams of residue is obtained by heating 2.76 g of silver carbonate? (Given : Molar mass of C, O and Ag are 12, 16 and 108 g mol-1 respectively)

1. 1.08 g
2. 2.16 g
3. 3.24 g
4. 4.32 g

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy. Choose the correct answer from the options given below:

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

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

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

What is the mole fraction of water in 10% by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1, 16, 12 and 14 g mol-1 respectively.]

1. 0.825
2. 0.032
3. 0.867
4. 0.967

M3A2 is a sparingly soluble salt of molar mass y g mol-1 and solubility x g L-1. The ratio of the molar concentration of the anion ( A3-) to the solubility product of the salt is

1. 154 y4x4
2. y5108x4
3. 108 x5y5
4. 1108 y4x4

Arrange the following resultant mixtures in increasing order of their pH values Choose the correct answer from the options given below :

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

First order gas phase reaction A B + C pi = initial pressure of gas A, pt = total pressure of the reaction mixture at time t Expression of rate constant (k) is

1. 1t pi2pi - pt
2. 1t 2pipi - pt
3. 1t pi3pi - 2pt
4. 1t 3pi4pi - pt

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

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

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

Which of the following is NOT a physical or chemical characteristics of interstitial compounds?

1. They have high melting points, higher than those of pure metals.
2. They are very soft and ionic in nature.
3. They retain metallic conductivity.
4. They are chemically inert and usually non-stoichiometric.

The correct statements about metal carbonyls are Choose the correct answer from the options given below :

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

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

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

" P " is a hydrocarbon of molecular formula:- C8H14. On ozonolysis, " P " forms "Q". "Q" on treatment with alkali under reflux condition produces "R", which on treatment with I2/NaOH gives a yellow precipitate. Acidification of the solution gives "S". The structure of "S" is given below:- [figure] The correct structure of P is

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

For the following Friedel Craft's alkylation reaction, which of the statements are correct? [figure] Choose the correct answer from the options given below :

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

Benzyl isocyanide can be obtained from 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. D and E Only

Consider compounds A, B and C with following structural formulae A = CH3-CH2-CH2-CH2-CH2-OH B = CH2=CH-CH2-CH2-CH3 C = HO-CH2-CH2-CH(OH)-CH3 For the conversion of B from A , reagent (D) required is and structural formula of product (E) obtained when C undergoes same reaction using excess reagent (D) is .

1. D: Conc. H2SO4; E: CH2=CH-CH(OH)CH3
2. D: PCC; E: HO-CH2-CH2-CH=CH2
3. D: PCC; E: CH2=CH-CH=CH2
4. D: Conc. H2SO4 or H3PO4; E: CH2=CH-CH=CH2

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

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

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

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

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 species: BrF5, XeF5-, BF4-, ICl4-, XeF4, SF4, NH4+, ClF3, XeF2, ICl2- Number of species having sp3d hybridized central atom is .

In an estimation of sulphur by Carius method 0.2 g of the substance gave 0.6 g of BaSO4. The percentage of sulphur in the substance is %. (Given molar mass in g mol-1 S : 32, BaSO4 : 233)

One mole of phenol is treated with dilute HNO3 at 298 K to give a mixture of products. The mixture is separated by steam distillation. The steam volatile compound (X) is separated. The increase in percentage of oxygen in (X) with respect to phenol is 10-1% (Given molar mass in g mol-1 H : 1, C : 12, N : 14, O : 16)

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below A(g) B(g) + C(g) array|c|c| 1T ( K-1) & 10 Kp \ 0.05 & 3.5 \ 0.06 & 2.5 \ 0.07 & 1.5 \ array The magnitude of H R calculated from the above data is . (Nearest integer)

If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be minutes. (Given : log 2 = 0.3010)

Let a, b C. Let , be the roots of the equation x2+ax+b=0. If - = 11 and 2- 2=3i 11, then ( 3- 3 )2 is equal to:

1. 160
2. 176
3. 194
4. 187

Let the sum of the first n terms of an A.P. be 3n2+5n. Then the sum of squares of the first 10 terms of the A.P. is:

1. 10220
2. 12860
3. 15220
4. 19780

Let A be a 3 3 matrix such that AT bmatrix1\ 0\ 1 bmatrix= bmatrix5\ 2\ 2 bmatrix, AT bmatrix0\ 0\ 1 bmatrix= bmatrix3\ 1\ 1 bmatrix, A bmatrix1\ 0\ 1 bmatrix= bmatrix3\ 4\ 4 bmatrix and A bmatrix0\ 0\ 1 bmatrix= bmatrix1\ 3\ 1 bmatrix. If (A)=1, then (adj (A2+A ) ) is equal to:

1. 16
2. 25
3. 49
4. 64

Consider the system of linear equations in x, y, z : x+2y+tz=0 6x+y+5tz=0 3x+t2y+f(t)z=0 where f : R R is a differentiable function. If this system has infinitely many solutions for all t R, then f

1. is a constant function
2. is strictly increasing on R
3. is strictly decreasing on R
4. has two critical points

n=110 ( 528n(n+1)(n+2) ) is equal to:

1. 65
2. 130
3. 220
4. 440

Let A, B, where A, B (- 2, 2 ), be the roots of the quadratic equation x2-2x-5=0. Then 20 2 ( A+B2 ) is equal to :

1. 10+ 10
2. 10-2 10
3. 10-3 10
4. 10- 10

A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:

1. 710
2. 1017
3. 1219
4. 719

The mean deviation about the mean for the data arraycccccccxi & 5 & 7 & 9 & 10 & 12 & 15\ fi & 8 & 6 & 2 & 2 & 2 & 6 array is equal to:

1. 4013
2. 4213
3. 4413
4. 4613

Let a focus of the ellipse E : x2a2+ y2b2=1 be S(4, 0) and its eccentricity be 45. If the point P(3, ) lies on E and O is the origin, then the area of POS is equal to:

1. 125
2. 145
3. 245
4. 485

Let P be a moving point on the circle x2+y2-6x-8y+21=0. Then, the maximum distance of P from the vertex of the parabola x2+6x+y+13=0 is equal to:

1. 8
2. 10
3. 12
4. 9

In an equilateral triangle PQR, let the vertex P be at (3, 5) and the side QR be along the line x+y=4. If the orthocentre of the triangle PQR is ( , ), then 9( + ) is equal to:

1. 16
2. 27
3. 36
4. 48

The sum of all the integral values of p such that the equation 3 2 x+12 x-3=p, x R, has at least one solution, is:

1. -54
2. -60
3. -75
4. -84

The square of the distance of the point P(5, 6, 7) from the line x-22= y-53= z-24 is equal to:

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

Let a= 7 i+ j- k and b= j+2 k. If r is a vector such that r a+ a b= 0 and r a=0, then |3 r|2 is equal to:

1. 44
2. 54
3. 86
4. 132

The square of the distance of the point of intersection of the lines r= ( i+ j- k )+ (a i- j ), a 0 and r= (4 i- k )+ (2 i+a k ) from the origin is :

1. 5
2. 10
3. 17
4. 26

The area of the region R= \(x, y) : xy 27, 1 y x2 \ is equal to :

1. 78 e 3- 523
2. 54 e 3- 523
3. 54 e 3- 263
4. 54 e 3+ 263

The product of all possible values of , for which x 0 ( 1- ( x) (( +1)x) (( +2)x) 2(( +1)x) )=2, is :

1. -2
2. 1
3. -1
4. 54

The value of the integral 0 e(x)x2+4 dx is:

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

Let f : R R be a differentiable function such that f ( x+y3 )= f(x)+f(y)3 for all x, y R, and f'(0)=3. Then the minimum value of the function g(x)=3+ex f(x), is:

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

The value of the integral 6 3 ( 4-cosec2 x 4 x )dx is :

1. 11 3
2. 16 3
3. 323 3
4. 643 3

Let A=\1, 2, 3, 4, 5, 6\. The number of one-one functions f : A A such that f(1) 3, f(3) 4 and f(2)+f(3)=5, is .

Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is .

If the sum of the coefficients of x7 and x14 in the expansion of ( 1x3-x4 )n, x 0, is zero, then the value of n is .

If 4+ p=111 -1 ( 2p-11+22p-1 )= , then is equal to .

Let y=y(x) be the solution of the differential equation x ( yx )dy= (y ( yx )-x )dx, y(1)= 2 and let = ( y (e12 )e12 ). Then the number of integral values of p, for which the equation x2+y2-2px+2py+ +2=0 represents a circle of radius r 6, is .