List of top Questions asked in JEE Main

When 5.1 g of solid NH\(_4\)HS is introduced into a two litre evacuated flask at 27\(^\circ\)C, 20% of the solid decomposes into gaseous ammonia and hydrogen sulphide. The K\(_p\) for the reaction at 27\(^\circ\)C is \(x \times 10^{-2}\). The value of x is _________. (Integer answer)
[Given R = 0.082 L atm K\(^{-1}\) mol\(^{-1}\)]

Given below are two statements:
Statement I : Ethyl pent-4-yn-oate on reaction with CH\(_3\)MgBr gives a 3\(^\circ\)-alcohol.
Statement II : In this reaction one mole of ethyl pent-4-yn-oate utilizes two moles of CH\(_3\)MgBr.
In the light of the above statements, choose the most appropriate answer from the options given below :

The major product (A) formed in the reaction given below is :
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Potassium permanganate on heating at 513 K gives a product which is :

Which one of the following is used to remove most of plutonium from spent nuclear fuel ?

In stratosphere most of the ozone formation is assisted by :

Which one of the following tests used for the identification of functional groups in organic compounds does not use copper reagent ?

Lyophilic sols are more stable than lyophobic sols because,

The correct order of ionic radii for the ions, P\(^{3-}\), S\(^{2-}\), Ca\(^{2+}\), K\(^{+}\), Cl\(^{-}\) is:

The oxide that gives H\(_2\)O\(_2\) most readily on treatment with H\(_2\)O is :

Choose the correct statement from the following:

Which one of the following is formed (mainly) when red phosphorus is heated in a sealed tube at 803 K ?

X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n=6? The value of X is _________.

A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6 nm ?

An antenna is mounted on a 400 m tall building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range of 44 km ?

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:

If the rms speed of oxygen molecules at 0\(^{\circ}\)C is 160 m/s, find the rms speed of hydrogen molecules at 0\(^{\circ}\)C.

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

Two discs have moments of inertia I\(_1\) and I\(_2\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_1\) and \(\omega_2\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:

A player kicks a football with an initial speed of 25 ms\(^{-1}\) at an angle of 45\(^{\circ}\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take g = 10 ms\(^{-2}\))

If $\int \frac{dx}{(x^2 + x + 1)^2} = a \tan^{-1} \left( \frac{2x + 1}{\sqrt{3}} \right) + b \left( \frac{2x + 1}{x^2 + x + 1} \right) + C, x>0$ where C is the constant of integration, then the value of $9(\sqrt{3}a + b)$ is equal to _________.

If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^2}{b^2} + \frac{y^2}{4a^2} = 1$ and the co-ordinate axis is kab, then k is equal to _________.

Let the equation $x^2 + y^2 + px + (1 - p)y + 5 = 0$ represent circles of varying radius $r \in (0, 5]$. Then the number of elements in the set $S = \{q : q = p^2 \text{ and } q \text{ is an integer}\}$ is _________.

If $y^{1/4} + y^{-1/4} = 2x$, and $(x^2 - 1)\frac{d^2y}{dx^2} + \alpha x \frac{dy}{dx} + \beta y = 0$, then $|\alpha - \beta|$ is equal to _________.

If the system of linear equations
$2x + y - z = 3$
$x - y - z = \alpha$
$3x + 3y + \beta z = 3$
has infinitely many solutions, then $\alpha + \beta - \alpha\beta$ is equal to _________.