JEE Main Mock Test - 3 Free Online Test 2026

A 2.0 cm object is placed 15 cm in front of a concave mirror of focal length 10 cm. What is the size and nature of the image?

The engine of a motorboat is switched off when its speed is v0. If motorboat experiences variable acceleration as dv/dt = −βv³, where β is a positive constant and v instantaneous speed, then the speed of motorboat after t second (t = 0 when switch is off) is

In a photodiode, the conductivity increases when the material is exposed to light. It is found that conductivity changes only if the wavelength is less than 600 nm. What is the bandgap?

If the magnetic dipole moment of an atom of diamagnetic material, paramagnetic material and ferromagnetic material is denoted by μ_d, μ_p and μ_f respectively, then

Which of the following will pair up to produce stationary wave?
(1) Z₁ = A cos(kx − ωt)
(2) Z₂ = A cos(kx + ωt)
(3) Z₃ = A cos(ky − ωt)
(4) Z₄ = A cos(kz + ωt)

A particle is undergoing SHM. Displacement vs time curve is as shown in the figure.

The correct statement is

Match List - I (Electromagnetic wave type) with List - II (Its association/application) and select the correct option from the choices given below the lists :

Figure shows a cyclic process ABCDBEA performed on an ideal cycle. If P_A = 2 atm, P_B = 5 atm and P_C = 6 atm, V_E – V_A = 20 litre, find the work done (in KJ) by the gas in the complete process. (1 atm. pressure = 1 × 10⁵ Pa)

If first excitation potential of a hydrogen like atom is V electron volt, then the ionization energy of this atom will be:

Let ω is the angular velocity of the earth's rotation about its own axis and acceleration due to gravity on the earth's surface at the poles is g. An object weighed by a spring balance gives the same reading at the equator, as well as at a height h above the poles (h ≪ R). What is the value of h ?

A charge particle having charge Q is placed at the centre of hollow hemispherical sphere whose a portion is removed as shown. If the radius of the hollow sphere is R, then flux through the remaining surface is equal to Q/xε₀. The value of x is?

A tuning fork and uniform string of length 100 cm give 4 beats /s. The string is made shorter without any change in tension and the mode of oscillation, until its frequency becomes equal to that of the fork. If now the length of the string is 99 cm, and the frequency of the fork is 100nHz, find the value of n.

An ionization chamber with parallel conducting plates as anode and cathode has 5 × 10⁷ electrons and the same number of singly-charged positive ions per cm³. The electrons are moving at 0.4 m s⁻¹. The current density from anode to cathode is 4 μA m⁻². The velocity of positive ions moving towards cathode is V, find 100V in m/s.

Three identical hollow sphere, each of mass 2kg and radius 10cm are placed as shown in diagram.Consider an axis XX′ which is touching to two shells and passing through diameter of third shell. Calculate Moment of inertia of the system consisting of these three spherical shells XX′ axis in g m²?

A uniform rod of length l is acted upon by a force F in a gravity-free region, as shown in the figure. If the area of cross-section of the rod is A and it's Young's modulus is Y, then the elastic potential energy stored in the rod due to elongation is . Then find the value of n?

Identify the pair of elements with the highest and lowest electronegativity respectively

Which of the following facts regarding boron and silicon is not true?

Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 mA current. The time required to liberate 0.01 mol of H₂ gas at the cathode is (1 F = 96500C mol⁻¹)

An oxide of nitrogen is reddish brown and paramagnetic at room temperature but it decolourises and also loses its paramagnetism on freezing it. The oxide at room temperature is

T is a point on the tangent to a parabola y² = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then

The general solution of sin²θ sec θ + √3 tan θ = 0 is

The fundamental period of the function f(x) = e^{4{x}+3}, where {⋅} denotes the fractional part function is

In the figure, AB, DE and GF are parallel to each other and AD, BG and EF are parallel to each other. If CD : CE = CG : CB = 2 : 1, then the value of area (△AEG): area (ΔABD) is equal to

Let p, q, r be three statements, then (p → (q → r)) ↔ ((p ∧ q) → r), is a

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is q. If p: q = m : n, where m and n are coprime, then m + n is equal to:

If the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively, then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x - y is ______.

Let S be the set of values of λ, for which the system of equations 
6λx - 3y + 3z = 4λ²,
2x - 6λy + 4z = 1,
3x + 2y + 3λz = λ has no solution. Then is equal to ___________.