List of top Questions asked in JEE Main

Let $ \alpha $ and $ \beta $ be the roots of $ x^2 + \sqrt{3}x - 16 = 0 $, and $ \gamma $ and $ \delta $ be the roots of $ x^2 + 3x - 1 = 0 $. If $ P_n = \alpha^n + \beta^n $ and $ Q_n = \gamma^n + \delta^n $, then $ \frac{P_{25} + \sqrt{3}P_{24}}{2P_{23}} + \frac{Q_{25} - Q_{23}}{Q_{24}} \text{ is equal to} $
A line passing through the point P$(\sqrt{5}, \sqrt{5})$ intersects the ellipse $ \frac{x^2}{36} + \frac{y^2}{25} = 1 $ at A and B such that (PA).(PB) is maximum. Then 5(PA$^2$ + PB$^2$) is equal to :
An organic compound weighing 500 mg, produced 220 mg of CO$_2$ on complete combustion. The percentage composition of carbon in the compound is ............... % (nearest integer).
(Given molar mass in g mol$^-$ of C: 12, O: 16)

The reactions which cannot be applied to prepare an alkene by elimination, are

Choose the correct answer from the options given below:

An octahedral complex having molecular composition Co.5NH$_3$.Cl.SO$_4$ has two isomers A and B. The solution of A gives a white precipitate with AgNO$_3$ solution and the solution of B gives a white precipitate with BaCl$_2$ solution. The type of isomerism exhibited by the complex is,
The first transition series metal 'M' has the highest enthalpy of atomisation in its series. One of its aquated ion (M$^{n+}$) exists in green colour. The nature of the oxide formed by the above M$^{n-}$ ion is:
A person's wound was exposed to some bacteria and then bacteria growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay ($r$) was found to be proportional with the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the 'before' and 'after' situation of the application of the medicine?
[Given: $ N $ = No. of bacteria, $ t $ = time, bacterial growth follows 1st order kinetics.]
When a salt is treated with sodium hydroxide solution, it gives gas X. On passing gas X through reagent Y, a brown coloured precipitate is formed. X and Y respectively, are:

Reaction A(g) → 2B(g) + C(g) is a first-order reaction. It was started with pure A.
The following table shows the pressure of the system at different times: 

Which of the following options is incorrect?

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height $ H $ above the first liquid. If viewed from above, the apparent shift in the position of the bottom of the container is 40 cm. The value of $ H $ is ___ cm.
A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727°C and power radiated by the wire is 94.2 W. Its emissivity is $ \frac{x}{8} $, where $ x = \ldots $

For the AC circuit shown in the figure, $ R = 100 \, \text{k}\Omega $ and $ C = 100 \, \text{pF} $, and the phase difference between $ V_{\text{in}} $ and $ (V_B - V_A) $ is 90°. The input signal frequency is $ 10^x $ rad/sec, where $ x $ is:

A, B and C are disc, solid sphere and spherical shell respectively with the same radii and masses. These masses are placed as shown in the figure.

The moment of inertia of the given system about PQ is $ \frac{x}{15} I $, where $ I $ is the moment of inertia of the disc about its diameter. The value of $ x $ is:

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:
A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)
The percentage increase in magnetic field $ B $ when space within a current-carrying solenoid is filled with magnesium (magnetic susceptibility $ \chi_{mg} = 1.2 \times 10^{-5} $) is:
Two plane polarized light waves combine at a certain point whose electric field components are $ E_1 = E_0 \sin(\omega t) $ $ E_2 = E_0 \sin(\omega t + \frac{\pi}{3}) $ Find the amplitude of the resultant wave.
A rod of length $ 5L $ is bent at a right angle, keeping one side length as $ 2L $. The position of the centre of mass of the system (Consider $ L = 10 $ cm):
If $ \epsilon_0 $ denotes the permittivity of free space and $ \Phi_E $ is the flux of the electric field through the area bounded by the closed surface, then the dimension of $ \epsilon_0 \frac{d\Phi_E}{dt} $ are that of:
Two harmonic waves moving in the same direction superimpose to form a wave $ x = a \cos(1.5t) \cos(50.5t) $ where $ t $ is in seconds. Find the period with which they beat (close to the nearest integer):
The number of points of discontinuity of the function $ f(x) = \left\lfloor \frac{x^2}{2} \right\rfloor - \left\lfloor \sqrt{x} \right\rfloor, \quad x \in [0, 4], $ where $ \left\lfloor \cdot \right\rfloor $ denotes the greatest integer function, is:
Let $ ABC $ be the triangle such that the equations of lines $ AB $ and $ AC $ are: $ 3y - x = 2 \quad \text{and} \quad x + y = 2, $ respectively, and the points $ B $ and $ C $ lie on the x-axis. If $ P $ is the orthocentre of the triangle $ ABC $, then the area of the triangle $ PBC $ is equal to:
Let $ x_1, x_2, x_3, x_4 $ be in a geometric progression. If 2, 7, 9, 5 are subtracted respectively from $ x_1, x_2, x_3, x_4 $, then the resulting numbers are in an arithmetic progression. Then the value of $ \frac{1}{24} (x_1 x_2 x_3 x_4) $ is:
From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include at least 4 batsmen and at least 4 bowlers. One batsman and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is:
The integral $ \int_0^\pi \frac{(x + 3) \sin x}{1 + 3 \cos^2 x} \, dx $ is equal to: