List of top Questions asked in JEE Main

Let R be the set of real numbers A = {(x, y) $\in$ R $\times$ R : y - x is an integer} is an equivalence relation on R. B = {(x, y) $\in$ R $\times$ R : x = $\alpha$y for some rational number $\alpha$} is an equivalence relation on R.

If $ {{\cos }^{-1}}\left( \frac{5}{13} \right)-{{\sin }^{-1}}\left( \frac{12}{13} \right)={{\cos }^{-1}}x, $ then $ x $ is equal to

The variance of first n even natural numbers is $\frac{n^2 - 1}{4}$. The sum of first n natural numbers is $\frac{n(n + 1)}{2}$ and the sum of squares of first n natural numbers is $\frac{n(n + 1)(2n +1)}{6}$.

Which of the following statements is true?

An artificial radioactive isotope gave ${^{14}_{7}N}$ after two successive $\beta$ -particle emissions. The number of neutrons in the parent nucleus must be :

The vector sum of two forces is perpendicular to their vector differences. In that case the forces

Probability of four sons to a couple is

The potential difference applied to an X-ray tube is increased. As a result, in the emitted radiation

Statement-I : Stability of +1 oxidation state increases as Ga< In < Tl
Statement-II : Stability of +1 oxidation state increases down the group due to inert pair effect.

Assertion: Trans But-2-ene is less polar than cis But-2-ene
Reason: Trans But-2-ene has zero dipole moment

From the given information, calculate enthalpy of formation of 2 moles of $C_6H_6$(l) at 25°C. Given: $CH(C_6H_6$(l)) = –3264.6 kJ/mol $CH(C(s))$ = –393.5 kJ/mol $fH(H_2O(l))$ = –285.83 kJ/mol

The products obtained when chlorine gas reacts with cold and dilute aqueous $NaOH$ are:

Which of the following compound is optically active?

Consider the reaction:
Fe₂0₃(s) + 3CO(g) = 2Fe(s) + 3CO₂(g)
Which of the following will not affect the equilibrium state:
(I) Addition of Fe₂O₃
(II) Addition of CO₂
(III) Decreasing mass of Fe₂O₃
(IV) Removal of CO

We have two complexes, [Fe(H₂O)₆]²⁺ and [Cu(H₂O)₆]²⁺ , the magnetic properties respectively are

If the number of neutrons in the most abundant isotope of boron is 'x' and its highest oxidation state in unsaturated compound is 'y', then find the value of (x+y).

Which metal shows the highest and maximum number of oxidation states?

The correct order of increasing $C-O$ bond length of $CO, C{O}_3^{2-}, C{O}_2$ is:

Shortest wavelength in Lyman series has wavelength of 915 À. Longest wavelength of Balmer series has a value of ?

Find the current I in the given circuit

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$ An alpha particle having certain kinetic energy has the same de-Brogle wavelength $\lambda$ The ratio of kinetic energy of proton and that of alpha particle is:

In a pond of water, a flame is held 2 m above the surface of water. A fish is at depth of 4 m from water surface. Refractive index of water is $\frac{4}{3}$. The apparent height of the flame from the eyes of fish is:

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2$ respectively. If the maximum velocities, during oscillations, are equal, the ratio of amplitudes of $A$ and $B$ is:

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the inclined plane with horizontal is θ.The magnitude of the contact force will be