JEE Main 2026 (Online) 2nd April Morning Shift

The dimensional formula of 12 0 E2 ( 0 = permittivity of vacuum and E = electric field) is MaLbTc. The value of 2a-b+c= .

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

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is 109 N/m2. The value of is . (Ignore the contribution of the load to Young's modulus error calculation)

1. 1.3
2. 1.65
3. 0.13
4. 0.25

The velocity of a particle is given as v=-x i+2y j-z k m/s. The magnitude of acceleration at point (1, 2, 4) is m/s2.

1. 6
2. 9
3. 33
4. 0

The position of an object having mass 0.1 kg as a function of time t is given as r= (10t2 i+5t3 j ) m. At t=1 s, which of the following statements are correct? Choose the correct answer from the options given below:

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

A planet (P1) is moving around the star of mass 2M in the orbit of radius R. Another planet (P2) is moving around another star of mass 4M in an orbit of radius 2R. Ratio of time periods of revolution of P2 and P1 is .

1. 12
2. 2
3. 4
4. 14

A particle is rotating in a circular path and at any instant its motion can be described as = 5t440- t33. The angular acceleration of the particle after 10 seconds is rad/s2.

1. 150
2. 120
3. 130
4. 170

A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant K=5, the percentage increase in the capacitance is . [figure]

1. 33.34
2. 66.67
3. 200
4. 400

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of Q : U : W is .

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

Two charged conducting spheres S1 and S2 of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1 and S2 spheres are ES1 and ES2 respectively. The value of ES1ES2 is .

1. 32
2. 23
3. 49
4. 94

The equation of a plane progressive wave is given by y=5 (200t- x150 ) where x and y are in cm and t is in second. The velocity of the wave is m/s.

1. 120
2. 150
3. 200
4. 300

Two short electric dipoles A and B having dipole moment p1 and p2 respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point x is making an angle of 60 with the line joining points O and x. The ratio of the dipole moments p2/p1 is . [figure]

1. 32
2. 2 3
3. 1 3
4. 3

For the given circuit (shown in part (A)) the time dependent input voltage vin(t) and corresponding output vo(t) are shown in part (B) and part (C), respectively. Identify the components that are used in the circuit between points X and Y. [figure]

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

When a coil is placed in a time dependent magnetic field the power dissipated in it is P. The number of turns, area of the coil and radius of the coil wire are N, A and r respectively. For a second coil number of turns, area of the coil and radius of the coil wire are 2N, 2A and 3r respectively. When the first coil is replaced with second coil the power dissipated in it is 2 P. The value of is .

1. 36
2. 128 2
3. 16
4. 64

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are B1 and B2 respectively, then the ratio B1B2 is . [figure]

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

For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be .

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

Refer the figure given below. 1 and 2 are refractive indices of air and lens material. The height of image will be cm. [figure]

1. 1
2. 0.5
3. 1.2
4. 0.25

For a certain metal, when monochromatic light of wavelength is incident, the stopping potential for photoelectrons is 3V0. When the same metal is illuminated by light of wavelength 2 , then the stopping potential becomes V0. The threshold wavelength for photoelectric emission for the given metal is . The value of is .

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

An electromagnetic wave travelling in x-direction is described by field equation Ey=300 (t- xc ). If the electron is restricted to move in y-direction only with speed of 1.5 106 m/s then ratio of maximum electric and magnetic forces acting on the electron is .

1. 200
2. 150
3. 400
4. 300

Angular momentum of an electron in a hydrogen atom is 3h , then the energy of the electron is eV.

1. -1.51
2. -0.85
3. -0.38
4. -0.28

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is 10-6 J. The value of is . (Take surface tension of liquid = 0.08 N/m)

1. 10
2. 7
3. 8
4. 11

In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central maximum is 10-2 degrees. The value of is .

A vessel contains 0.15 m3 of a gas at pressure 8 bar and temperature 140 °C with cp=3R and cv=2R. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is kJ. (R is gas constant)

1 μC charge moving with velocity v= ( i-2 j+3 k ) m/s in the region of magnetic field B= (2 i+3 j-5 k ) T. The magnitude of force acting on it is 10-6 N. The value of is .

A uniform wire of length l of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at l3 distance from the top is ( WA+ 2 wA ), where A is the cross sectional area of the wire. The value of is .

A tub is filled with water and a wooden cube 10 cm 10 cm 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is gram. (Take water density as 1 g/cm3 and density of wood as 0.4 g/cm3)

The mass of iron converted into Fe3O4 by the action of 18 g of steam is : (Given : Molar mass of H, O and Fe are 1, 16 and 56 g mol-1 respectively) Assume iron is present in excess :

1. 2.1 g
2. 4.2 g
3. 21 g
4. 42 g

What is the energy (in J atom-1) required for the following process ? Li2+(g) Li3+(g) + e- (Take the ionization energy for the H atom in the ground state as 2.18 10-18 J atom-1)

1. 8.72 10-18
2. 1.962 10-18
3. 1.962 10-17
4. 6.54 10-17

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 data. (i) 2Al(s) + 6HCl(aq) Al2Cl6(aq) + 3H2(g) + 1200 kJ/mol (ii) H2(g) + Cl2(g) 2HCl(g) + 164 kJ/mol (iii) HCl(g) + aq HCl(aq) + 83 kJ/mol (iv) Al2Cl6(s) + aq Al2Cl6(aq) + 663 kJ/mol The enthalpy of formation of anhydrous solid Al2Cl6 is :

1. -648 kJ mol-1
2. -1350 kJ mol-1
3. -2002 kJ mol-1
4. -1527 kJ mol-1

19.5 g of fluoro acetic acid (molar mass = 78 g mol-1) is dissolved in 500 g of water at 298 K. The depression in the freezing point of water was 1°C. What is Ka of fluoro acetic acid ? (For water, Kf = 1.86 K kg mol-1). Assume molarity and molality to have same values.

1. 10-6
2. 4 10-4
3. 3 10-5
4. 3 10-3

The solubility product constants of Ag2CrO4 and AgBr are 32x and 4y respectively at 298 K. The value of ( molarity of Ag2CrO4molarity of AgBr ) can be expressed as :

1. 2 [3]xy
2. 2 xy
3. xy
4. [3]x y

An electrochemical cell is constructed using half cells in the direction of spontaneous change: Fe(OH)2(s) + 2e- Fe(s) + 2OH-(aq) E = -0.88 V and AgBr(s) + e- Ag(s) + Br-(aq) E = +0.07 V Which of the following options is correct?

1. Overall reaction Fe(s) + 2OH-(aq) + 2AgBr(s) Fe(OH)2(s) + 2Ag(s) + 2Br-(aq)
2. E cell = -0.95 V
3. Fe is reduced in the electrochemical cell
4. E cell is an extensive property

t100\% is the time required for the 100% completion of the reaction while t1/2 is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between t100\% and t1/2 for zero and first order reactions respectively ?

1. t100\% = (t1/2)2 and t100\% = (t1/2)-
2. t100\% = 2t1/2 and t100\% = (t1/2)
3. t100\% = 2t1/2 and t100\% = (2t1/2)2
4. t100\% = (t1/2) and t100\% = 2t1/2

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

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

Which of the following sets includes all the species that will change the orange colour of K2Cr2O7 in acidic medium ?

1. Fe2+, Sn2+, I-, S2-
2. S2-, Fe3+, I-, C2O42-
3. Fe2+, NO2-, SO2, Sn4+
4. Fe3+, SO42-, S2-, Sn4+

Match List - I with List - II.

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

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

In IUPAC nomenclature, the correct order of decreasing priority of functional group is :

1. -CONH2, >C=O, -CHO, -NH2, -C C-
2. -CONH2, -COOCH3, -CHO, -NH2, -OH
3. -CONH2, -CHO, >C=O, -NH2, -C C-
4. -CONH2, -CHO, -CN, -NH2, -C C-

For the given molecule, "x", the preferred site for the attack of the electrophile is : [figure]

1. Predominantly at "r"
2. "r" and "u"
3. "p" and "s"
4. Predominantly at "u"

Match List - I with List - II.

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

Consider the three aromatic molecules (P, Q and R) whose structures have been given below : [figure] The correct order regarding the reactivity of these compounds with Ph- N N Cl under optimum but slightly acidic medium is :

1. P > Q > R
2. R > P > Q
3. R > Q > P
4. P > R > Q

Match List - I with List - II.

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

A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with K2CrO4 to give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc. HNO3 and ammonium molybdate, it resulted a canary yellow precipitate. The cation and anion present in the salt are respectively,

1. Ca2+ and SO42-
2. Ba2+ and PO43-
3. Mn2+ and PO43-
4. Ba2+ and SO42-

5.33 g of CrCl3 6H2O, which is a 1 : 3 electrolyte, is dissolved in water and is passed through a cation exchanger. The chloride ions in the eluted solution, on treatment with AgNO3 results in 8.61 g of AgCl. The ratio of moles of complex reacted and moles of AgCl formed is 10-2. (Nearest integer) [Molar mass in g mol-1 Cr : 52, Ag : 108, Cl : 35.5, H : 1, O : 16]

Consider the isomers of hydrocarbon with molecular formula C5H10. These isomers do not decolourise KMnO4 solution. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is .

One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is .

For reaction A P, rate constant k = 1.5 103 s-1 at 27°C If activation energy for the above reaction is 60 kJ mol-1, then the temperature (in °C) at which rate constant, k = 4.5 103 s-1 is . (Nearest integer) Given : log 2 = 0.30, log 3 = 0.48, R = 8.3 J K-1 mol-1, ln 10 = 2.3

At the transition temperature T, A B and G = 105 - 35 T where A and B are two states of substance X. The transition temperature in °C when pressure is 1 atm is . (Nearest integer)

Let , +2, Z, be the roots of the quadratic equation x(x+2)+(x+1)(x+3)+(x+2)(x+4)+ +(x+n-1)(x+n+1)=4n for some n N. Then n+ is equal to :

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

Let x and y be real numbers such that 50 ( 2x1+3i- y1-2i )=31+17i, i= -1. Then the value of 10(x-3y) is :

1. 20
2. 31
3. 35
4. 75

Let , R be such that the system of linear equations x+2y+z=5 2x+y+ z=5 8x+4y+ z=18 has no solution. Then is equal to :

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

Let A= bmatrix1 & 2\ 1 & bmatrix and B= bmatrix3 & 3\ & 2 bmatrix. If A2-4A+I=0 and B2-5B-6I=0, then among the two statements: (S1) : [(B-A)(B+A) ]T= bmatrix13 & 15\ 7 & 10 bmatrix and (S2) : (adj(A+B))=-5

1. only (S1) is correct
2. only (S2) is correct
3. both (S1) and (S2) are correct
4. both (S1) and (S2) are wrong

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in A B, which are divisible by 3, is :

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

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is :

1. 15400
2. 17800
3. 16800
4. 29400

The number of elements in the set S= \(r,k) : k Z and 36Cr+1= 6 (35Cr ) (k2-3 ) \, is :

1. 2
2. 4
3. 8
4. 16

If the mean of the data [figure] is 21, then k is one of the roots of the equation :

1. 2x2-23x-10=0
2. 4x2-35x+24=0
3. 2x2-19x-10=0
4. 2x2-35x+98=0

Let the mid points of the sides of a triangle ABC be ( 52, 7 ), ( 52, 3 ) and (4, 5). If its incentre is (h, k), then 3h+k is equal to :

1. 11
2. 12
3. 13
4. 14

Let an ellipse x2a2+ y2b2=1, a<b, pass through the point (4, 3) and have eccentricity 53. Then the length of its latus rectum is :

1. 4 53
2. 2 5
3. 7 53
4. 8 53

If ( 18 ) ( 5 18 ) ( 7 18 )=K, then the value of ( 10K 3 ) is :

1. 3+12 2
2. 3-1 2
3. 32
4. 12

Let S=\x [- , ] : x( x+ x)=a, a Z\. Then n(S) is equal to :

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

If the point of intersection of the lines x+13= y+a5= z+b+17 and x-21= y-b4= z-2a7 lies on xy-plane, then the value of a+b is :

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

If a and b are two vectors such that | a|=2 and | b|=3, then the maximum value of 3 | (3 a+2 b ) |+4 | (3 a-2 b ) | is :

1. 30
2. 36
3. 60
4. 72

Let a line L passing through the point (1, 1, 1) be perpendicular to both the vectors 2 i+2 j+ k and i+2 j+2 k. If P(a, b, c) is the foot of perpendicular from the origin on the line L, then the value of 34(a+b+c) is :

1. 50
2. 80
3. 100
4. 120

If x 2 (x3-5x2+ax+b ) ( x-1-1 ) e(x-1)=m, then a+b+m is equal to :

1. 5
2. 6
3. 8
4. 10

If the curve y=f(x) passes through the point (1, e) and satisfies the differential equation dy=y (2+ e x )dx, x>0, then f(e) is equal to :

1. ee
2. ee2
3. e2e
4. e2e

The number of critical points of the function f(x)= cases | xx |, & x 0\ 1, & x=0 cases in the interval (-2 , 2 ) is equal to :

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

Let [.] denote the greatest integer function. Then the value of 03 ( ex+e-x[x]! )dx is :

1. e2+e3- 1e2- 1e3
2. 12 (e2+e3- 1e2- 1e3 )
3. e2+e3- 12e2- 12e3
4. 12 (e2+e3 )- 1e2- 1e3

Let y=y(x) be the solution curve of the differential equation (1+ x) dydx+(y+1) x=0, y(0)=0. If the curve y=y(x) passes through the point ( , -12 ), then a value of is :

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

If the domain of the function f(x)= (0.6) ( | 2x-5x2-4 | ) is (- , a] \b\ [c, d) (e, ), then the value of a+b+c+d+e is .

If k=1n ak=6n3, then k=16 ( ak+1-ak36 )2 is equal to .

Let a, b, c \1, 2, 3, 4\. If the probability, that ax2+2 2 bx+c>0 for all x R, is mn, (m, n)=1, then m+n is equal to .

Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line x+y=1 is 14, then the square of the radius of C is .

If = 02 3 2 (x2+4 )dx+ 24 2x-4 dx, then 2 is equal to .