JEE Main 2026 Paper 1 pattern · 75 Questions · 180 Min
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1. Which dimensional formula represents pressure?
Explanation: Pressure is force divided by area. [MLT^-2]/[L^2] = [ML^-1T^-2].
2. Two perpendicular vectors have magnitudes 3 and 4. What is the magnitude of their resultant?
Explanation: For perpendicular vectors, R = sqrt(3^2 + 4^2) = 5.
3. A particle moves with initial speed 2 m/s and constant acceleration 3 m/s^2. What distance does it cover during the fourth second?
Explanation: Distance in the nth second is u + (a/2)(2n - 1). For n = 4, it is 2 + 1.5 x 7 = 12.5 m.
4. A projectile is launched at 20 m/s at 30 degrees above the horizontal. Taking g = 10 m/s^2, its horizontal range is:
Explanation: R = u^2 sin(2theta)/g = 400 sin 60 degrees/10 = 20sqrt(3) m.
5. A 10 kg block rests on a rough horizontal surface with coefficient of static friction 0.20. Taking g = 10 m/s^2, the limiting friction is:
Explanation: Limiting friction is mu_s N = 0.20 x 10 x 10 = 20 N.
6. How much work is required to stretch a spring of force constant 200 N/m from its natural length by 0.10 m?
Explanation: Stored spring energy is (1/2)kx^2 = 0.5 x 200 x 0.10^2 = 1 J.
7. A body moves uniformly in a circle of radius 5 m at 10 m/s. Its centripetal acceleration is:
Explanation: Centripetal acceleration is v^2/r = 100/5 = 20 m/s^2.
8. The moment of inertia of a thin ring of mass M and radius R about an axis through its centre and perpendicular to its plane is:
Explanation: Every mass element of a thin ring is at distance R from this axis, so I = MR^2.
9. At a height equal to Earth's radius above the surface, the acceleration due to gravity is what fraction of its surface value g?
Explanation: The distance from Earth's centre is 2R, so g' = g(R/2R)^2 = g/4.
10. What gauge pressure is produced by a 5 m column of water? Take density = 1000 kg/m^3 and g = 10 m/s^2.
Explanation: Gauge pressure rho gh = 1000 x 10 x 5 = 50000 Pa = 50 kPa.
11. A gas absorbs 500 J of heat and does 200 J of work on its surroundings. What is the change in its internal energy?
Explanation: Using Delta U = Q - W for work done by the gas, Delta U = 500 - 200 = 300 J.
12. For a particle in simple harmonic motion with angular frequency omega and displacement x, its acceleration is:
Explanation: The defining relation for SHM is acceleration proportional and opposite to displacement: a = -omega^2 x.
13. A wave has frequency 200 Hz and wavelength 1.5 m. Its speed is:
Explanation: Wave speed v = f lambda = 200 x 1.5 = 300 m/s.
14. The electric field 3 m from a point charge of 2 microcoulomb in vacuum is:
Explanation: E = kq/r^2 = (9 x 10^9)(2 x 10^-6)/9 = 2000 N/C.
15. Capacitors of 6 microfarad and 3 microfarad are connected in series. Their equivalent capacitance is:
Explanation: For two series capacitors, C = C1C2/(C1 + C2) = 18/9 = 2 microfarad.
16. Three resistors of 2 ohm, 4 ohm and 6 ohm are connected in series. Their equivalent resistance is:
Explanation: Series resistances add: 2 + 4 + 6 = 12 ohm.
17. A charge of 2 microcoulomb moves at 3 x 10^4 m/s perpendicular to a magnetic field of 0.5 T. The magnetic force is:
Explanation: F = qvB = 2 x 10^-6 x 3 x 10^4 x 0.5 = 0.03 N.
18. An ideal transformer has 200 primary turns and 800 secondary turns. If the primary voltage is 200 V, the secondary voltage is:
Explanation: Vs/Vp = Ns/Np = 800/200 = 4, so Vs = 800 V.
19. A converging lens has power +2 dioptre. Its focal length in air is:
Explanation: Power P = 1/f with f in metres. Thus f = 1/2 = 0.50 m.
20. For a metal with fixed work function, the maximum kinetic energy of emitted photoelectrons is controlled by the incident light's:
Explanation: Einstein's equation is Kmax = h nu - phi. Frequency changes Kmax; intensity mainly changes the emission rate above threshold.
21. A block moving at 20 m/s stops on a horizontal rough surface. If the coefficient of kinetic friction is 0.50 and g = 10 m/s^2, enter the stopping distance in metres.
Explanation: The deceleration is mu g = 5 m/s^2. From 0 = 20^2 - 2(5)s, s = 40 m.
22. A 6 ohm resistor and a 3 ohm resistor are connected in parallel. Enter their equivalent resistance in ohms.
Explanation: 1/R = 1/6 + 1/3 = 1/2, so R = 2 ohm.
23. A 10 microfarad capacitor is charged to 100 V. Enter the stored energy in millijoules.
Explanation: U = (1/2)CV^2 = 0.5 x 10 x 10^-6 x 100^2 = 0.05 J = 50 mJ.
24. A radioactive sample initially contains 160 mg of an isotope. Enter the mass in mg remaining after three half-lives.
Explanation: After three half-lives the remaining fraction is 1/8. Thus 160/8 = 20 mg.
25. An object is placed 30 cm in front of a thin converging lens of focal length 20 cm. Enter the positive image distance in cm.
Explanation: Using 1/f = 1/v - 1/u with f = 20 cm and u = -30 cm gives 1/v = 1/20 - 1/30 = 1/60.
26. How many moles are present in 9 g of water? Use molar mass of water = 18 g mol^-1.
Explanation: Number of moles = mass/molar mass = 9/18 = 0.50 mol.
27. Approximately how many molecules are present in 0.25 mol of a molecular substance?
Explanation: Number of molecules = 0.25 x 6.022 x 10^23 = 1.5055 x 10^23.
28. What is the maximum number of electrons that can occupy the 3d subshell?
Explanation: A d subshell has five orbitals, and each orbital can hold two electrons, so its capacity is 10.
29. Which element has the highest electronegativity on the Pauling scale?
Explanation: Fluorine has the greatest effective attraction for a bonding electron pair and is the most electronegative element.
30. According to VSEPR theory, the molecular shape of NH3 is:
Explanation: Nitrogen has three bond pairs and one lone pair. The electron-pair geometry is tetrahedral and the molecular shape is trigonal pyramidal.
31. The hybridisation of each carbon atom in ethyne, HCCH, is:
Explanation: Each carbon has two regions of electron density and a linear arrangement, corresponding to sp hybridisation.
32. For an exothermic reaction carried out at constant pressure, the sign of enthalpy change is:
Explanation: An exothermic process releases heat to the surroundings, so the system's enthalpy change is negative.
33. The Kelvin temperature of a fixed amount of ideal gas is doubled at constant volume. Its pressure becomes:
Explanation: At fixed amount and volume, the ideal-gas equation gives P proportional to absolute temperature, so pressure doubles.
34. A solution contains 0.50 mol of solute in a total volume of 2.0 L. Its molarity is:
Explanation: Molarity = moles of solute/litres of solution = 0.50/2.0 = 0.25 M.
35. At 25 degrees C, the pH of 1.0 x 10^-3 M HCl, assuming complete ionisation, is:
Explanation: For this strong acid [H+] = 10^-3 M, so pH = -log[H+] = 3.
36. A catalyst increases the rate of a reaction primarily by:
Explanation: A catalyst provides an alternative pathway with lower activation energy. It does not change Delta H or the equilibrium constant.
37. Which process occurs at the anode of a galvanic cell?
Explanation: Oxidation occurs at the anode and reduction occurs at the cathode in both galvanic and electrolytic cells.
38. For a first-order reaction, the half-life is:
Explanation: For first order kinetics, t1/2 = ln 2/k, which contains no initial-concentration term.
39. The ground-state electronic configuration of Fe (atomic number 26) is:
Explanation: After the argon core, iron has eight electrons distributed as 3d6 4s2.
40. The coordination number of cobalt in [Co(NH3)6]3+ is:
Explanation: Six monodentate NH3 ligands are directly bonded to cobalt, giving coordination number 6.
41. The IUPAC name of CH3CH2CHO is:
Explanation: The molecule has a three-carbon chain and a terminal aldehyde group, so its name is propanal.
42. In the absence of peroxide, the major product formed by adding HBr to propene is:
Explanation: Normal Markovnikov addition proceeds through the more stable secondary carbocation and forms 2-bromopropane.
43. Controlled oxidation of ethanol with a mild oxidising agent gives mainly:
Explanation: A primary alcohol first oxidises to the corresponding aldehyde; ethanol therefore gives ethanal under controlled conditions.
44. Tollens' reagent is commonly used to distinguish aldehydes from ketones because aldehydes generally:
Explanation: Aldehydes reduce diamminesilver(I) ions to metallic silver, producing the characteristic silver mirror.
45. The linkage joining amino-acid residues in a protein chain is:
Explanation: The -CO-NH- amide linkage formed between amino acids is called a peptide bond.
46. 4.0 g of NaOH is dissolved to make 500 mL of solution. If its molarity is M, enter 100M. Use molar mass of NaOH = 40 g mol^-1.
Explanation: Moles = 4/40 = 0.10 mol and volume = 0.50 L. M = 0.10/0.50 = 0.20, so 100M = 20.
47. At STP, 44.8 L of an ideal gas corresponds to how many moles? Use molar volume = 22.4 L mol^-1.
Explanation: Moles = volume/molar volume = 44.8/22.4 = 2.
48. At 25 degrees C, a solution has pOH = 4. Enter its pH.
Explanation: At 25 degrees C, pH + pOH = 14. Hence pH = 14 - 4 = 10.
49. Enter the percentage of a first-order reactant remaining after two half-lives.
Explanation: The remaining fraction after two half-lives is (1/2)^2 = 1/4, which is 25 percent.
50. A charge of 96500 C is passed through AgNO3 solution. Enter the mass of silver deposited in grams. Use F = 96500 C mol^-1 and molar mass of Ag = 108 g mol^-1.
Explanation: The charge is 1 F, so 1 mol of electrons deposits 1 mol of Ag. The deposited mass is therefore 108 g.
51. If n(A) = 20, n(B) = 15 and n(A intersection B) = 5, then n(A union B) is:
Explanation: n(A union B) = n(A) + n(B) - n(A intersection B) = 20 + 15 - 5 = 30.
52. The modulus of the complex number 3 + 4i is:
Explanation: |3 + 4i| = sqrt(3^2 + 4^2) = 5.
53. The sum of the roots of x^2 - 7x + 10 = 0 is:
Explanation: For ax^2 + bx + c = 0, the sum is -b/a. Here it is -(-7)/1 = 7.
54. The discriminant of x^2 + 4x + 4 = 0 is:
Explanation: The discriminant b^2 - 4ac = 16 - 16 = 0.
55. The determinant of the matrix with rows (2, 3) and (1, 4) is:
Explanation: The determinant is 2 x 4 - 3 x 1 = 5.
56. For any square matrix A of order n, multiplication by the identity matrix I_n gives:
Explanation: The identity matrix is the multiplicative identity, so AI_n = I_nA = A.
57. The 10th term of the arithmetic progression 5, 8, 11, ... is:
Explanation: a_10 = a + 9d = 5 + 9 x 3 = 32.
58. The fifth term of the geometric progression 2, 6, 18, ... is:
Explanation: Here a = 2 and r = 3. The fifth term is ar^4 = 2 x 81 = 162.
59. The coefficient of x^2 in the expansion of (1 + x)^5 is:
Explanation: The coefficient is the binomial coefficient C(5,2) = 10.
60. How many distinct arrangements can be made using all letters of the word LEVEL?
Explanation: There are five letters with L repeated twice and E repeated twice, so the number is 5!/(2!2!) = 30.
61. Two fair coins are tossed. The probability of obtaining exactly one head is:
Explanation: The equally likely outcomes are HH, HT, TH and TT. Two of four have exactly one head, so the probability is 1/2.
62. The value of lim(x approaches 0) sin(3x)/x is:
Explanation: sin(3x)/x = 3[sin(3x)/(3x)], and the bracketed limit is 1.
63. The derivative of x^2 e^x with respect to x is:
Explanation: By the product rule, d(x^2e^x)/dx = 2xe^x + x^2e^x = e^x(x^2 + 2x).
64. The slope of the tangent to y = x^2 at x = 2 is:
Explanation: dy/dx = 2x, which equals 4 at x = 2.
65. The value of the integral of 3x^2 from x = 0 to x = 1 is:
Explanation: An antiderivative is x^3. Evaluating from 0 to 1 gives 1.
66. The solution of dy/dx = 2x satisfying y(0) = 3 is:
Explanation: Integrating gives y = x^2 + C. The condition y(0) = 3 gives C = 3.
67. The perpendicular distance of the point (5, -2) from the y-axis is:
Explanation: Distance from the y-axis is the absolute value of the x-coordinate, |5| = 5.
68. The radius of the circle x^2 + y^2 - 6x + 4y - 12 = 0 is:
Explanation: Completing squares gives (x - 3)^2 + (y + 2)^2 = 25, so the radius is 5.
69. If two non-zero vectors a and b are perpendicular, then:
Explanation: a dot b = |a||b|cos 90 degrees = 0.
70. The distance between the points (1, 2, 3) and (4, 6, 3) is:
Explanation: Distance = sqrt((4-1)^2 + (6-2)^2 + (3-3)^2) = sqrt(9 + 16) = 5.
71. Enter the sum of the first 20 positive integers.
Explanation: The sum is n(n + 1)/2 = 20 x 21/2 = 210.
72. The determinant of the matrix with rows (x, 2) and (3, 4) is 10. Enter x.
Explanation: The determinant is 4x - 6. Solving 4x - 6 = 10 gives x = 4.
73. Enter the area under y = x from x = 0 to x = 4.
Explanation: The area is the integral of x from 0 to 4: [x^2/2]_0^4 = 8.
74. Enter the magnitude of the vector 2i - 3j + 6k.
Explanation: Magnitude = sqrt(2^2 + (-3)^2 + 6^2) = sqrt(49) = 7.
75. Enter the shortest distance from the point (2, -1, 4) to the xy-plane.
Explanation: The xy-plane is z = 0. The perpendicular distance is the absolute value of the z-coordinate, |4| = 4.