List of top Questions asked in JEE Main

A current of \(30\,\text{A}\) each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of \(8\,\text{cm}\). The magnetic field at the mid point between the two wires is _____ \(\mu\text{T}\). \(\left(\frac{\mu_0}{4\pi}=10^{-7}\,\text{}^2\right)\)

The electric potential as a function of \(x,y\) is given by \(V=5(x^2-y^2)\,\text{V}\). The electric field at the point \((2,3)\) m is _____ V/m.

A spring stretches by \(2\,\text{mm}\) when it is loaded with a mass of \(200\,\text{g}\). From equilibrium position the mass is further pulled down by \(2\,\text{mm}\) and released. The frequency associated with the system and the maximum energy in the spring are _____ Hz and _____ J, respectively. (Take \(g=10\,\text{m/s}^2\)).

If \(2\) mole of an ideal monoatomic gas at temperature \(T\) is mixed with \(6\) mole of another ideal monoatomic gas at temperature \(2T\) then the temperature of mixture is :

A cylindrical vessel of \(40\,\text{cm}\) radius is completely filled with water and its capacity is \(528\,\text{dm}^3\) (\(\text{dm}=\text{decimetre}\)). The vessel is placed on a solid block of same height as vessel. If a small hole is made at \(70\,\text{cm}\) below the top of water level, then the horizontal range of water falling on the ground in the beginning is ______ cm.

Figure represents the extension (\(\Delta l\)) of a wire of length \(l\), suspended from the ceiling of the room at one end and with a load \(W\) connected to the other end. If the cross-sectional area of the wire is \(10^{-5}\,\text{m}^2\) then the Young’s modulus of the wire is _____ N/m\(^2\).

Two identical bodies \(A\) and \(B\) of equal masses have initial velocities \(\vec v_1 = 4\hat{i}\,\text{m/s}\) and \(\vec v_2 = 4\hat{j}\,\text{m/s}\) respectively. The body \(A\) has acceleration \(\vec a_1 = 6\hat{i} + 6\hat{j}\,\text{m/s}^2\) while the acceleration of body \(B\) is zero. The centre of mass of the two bodies moves in ______ path.

For an electromagnetic wave propagating through vacuum, \( \vec{k},\vec{E}\) and \( \omega \) represent propagation vector, electric field and angular frequency respectively. The magnetic field associated with this wave is represented by :

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \(P,V,T\). Heating is started from left side until pressure changes to \( \frac{27P}{8} \). If initial volume of each compartment was \(9\) litres then the final volume in right-hand side compartment is _____ litres. (for this ideal gas \(C_P/C_V=1.5\)).

A body of mass \(1\,\text{kg}\) moves along a straight line with a velocity \(v=2x^2\). The work done by the body during displacement from \(x=0\) to \(x=5\,\text{m}\) is _____ J.

A solid sphere (A) of mass \(5m\) and a spherical shell (B) of mass \(m\), both having the same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of \(A\) and \(B\), they start rolling without slipping with accelerations \(a_A\) and \(a_B\) respectively. The ratio of \(a_A\) and \(a_B\) is _____.

Match List-I with List-II.

Choose the correct answer.

The percentage error in the calculated volume of a sphere, if there is \(2%\) error in its diameter measurement, is _____.

Which of the following is NOT a physical or chemical characteristic of interstitial compounds?

Correct statements from the following are:
A. Nitrogen in oxidation states from \(+1\) to \(+4\) disproportionates in acid medium.
B. Nitrogen has the ability to form \(d\pi - p\pi\) multiple bonds with itself and other elements with small size and high electronegativity.
C. N-N single bond is stronger than P-P single bond.
D. Nitrogen has highest density in its group due to small size.
E. The maximum covalency of nitrogen is four since it has only four valence orbitals for bonding.

Given below are two statements:
Statement I: The correct order of electronegativity of fluorine, oxygen and nitrogen is \(F>O>N\).
Statement II: The oxidation state of oxygen in \(OF_2\) is \(+2\) and in \(Na_2O\) is \(-2\).

Arrange the following resultant mixtures in increasing order of their pH values}
A. \(10 \text{ mL } 0.2 \text{ M Ca(OH)}_2 + 25 \text{ mL } 0.1 \text{ M HCl}\)
B. \(10 \text{ mL } 0.01 \text{ M H}_2\text{SO}_4 + 10 \text{ mL } 0.01 \text{ M Ca(OH)}_2\)
C. \(10 \text{ mL } 0.1 \text{ M H}_2\text{SO}_4 + 10 \text{ mL } 0.1 \text{ M KOH}\)

\(M_3A_2\) is a sparingly soluble salt of molar mass \(y \text{ g mol}^{-1}\) and solubility \(x \text{ g L}^{-1}\). The ratio of the molar concentration of the anion (\(A^{3-}\)) to the solubility product (\(K_{sp}\)) of the salt is:

What is the mole fraction of water in \(10%\) by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1, 16, 12 and \(14 \text{ g mol}^{-1}\) respectively.]

Identify the correct statements from the following :}
A. Heisenberg uncertainty principle is applicable to electrons.
B. The size of \(2p_x\) orbital is less than the size of \(3p_x\) orbital.
C. The energy of \(2s\) orbital of H atom is equal to the energy of \(2s\) orbital of Li.
D. The electronic configuration of Cr is \([Ar] 3d^5 4s^1\)

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
A. \(n=3, l=2, m=+1\)
B. \(n=4, l=0, m=0\)
C. \(n=6, l=1, m=0\)
D. \(n=5, l=1, m=+1\)
E. \(n=2, l=1, m=+1\)

How many grams of residue is obtained by heating \(2.76 \text{ g}\) of silver carbonate? (Given : Molar mass of C, O and Ag are 12, 16 and \(108 \text{ g mol}^{-1}\) respectively)

In the given circuit below inductance values of \(L_1, L_2\) and \(L_3\) are same. The magnetic energy stored in the entire circuit is \((U_t)\) and that stored in the \(L_2\) inductor is \((U_j)\). \(U_t / U_j\) is ____. (Ignore the mutual inductance if any).

The charged particle moving in a uniform magnetic field of \((3\hat{i} + 2\hat{j}) \text{ T}\) has an acceleration \((4\hat{i} - \frac{x}{2}\hat{j}) \text{ m/s}^2\). The value of \(x\) is ____.

A transverse wave on a string is described by \(y = 3\sin(36t + 0.018x + \pi/4)\), where \(x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is ____ \text{cm}. (Nearest integer) (\(\pi = 3.14\))}