List of top Questions asked in JEE Main

In which of the following pairs of molecules/ions both the species are not likely to exist?

Copper crystallises in fcc with a unit length of $361\,pm$. What is the radius of copper atom ?

In a face centred cubic lattice, atoms of $A$ form the comer points and atoms of $B$ form the face centred points. If two atoms of $A$ are missing from the comer points, the formula of the ionic compound is :

The first ionisation potential of $Na$ is $5.1\, eV$. The value of electron gain enthalpy of $Na^+$ will be

Electron gain enthalpy with negative sign of fluorine is less than that of chlorine due to :

The surface charge density of a thin charged disc of radius $R$ is $\sigma$. The value of the electric field at the centre of the disc is $\frac{\sigma}{2 \in_{0}} \cdot$ With respect to the field at the centre, the electric field along the axis at a distance $R$ from the centre of the disc :

A solution of copper sulphate $\left(CuSO_{4}\right)$ is electrolysed for 10 minutes with a current of $1.5$ amperes. The mass of copper deposited at the cathode (at. mass of $Cu = 63u$) is :

Which of the following is the wrong statement?

Vapour pressure of pure benzene is $119$ torr and that of toluene is $37.0$ torr at the same temperature. Mole fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a mole fraction of toluene $0.50$, will be :

Which has trigonal bipyramidal shape ?

Let $x_1 , x_2,...., x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be the variance. Variance of $2x_1, 2x_2, ..., 2x_n$ is $4 \sigma^2$. Arithmetic mean $2x_1, 2x_2, ..., 2x_n $ is 4 $\bar{x}$ .

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.

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 $\frac{n(n + 1)(2n +1)}{6}$.

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

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

Let $A=\left(\begin{array}{ccc}0& 2q& r\\ p& q& -r\\ p& -q& r\end{array}\right)$. If $A{A}^T=I_3$, then $|p|$ is:

Find the numbers of distinct real roots $|x||x + 2| - 5|x + 1| - 1$ =0

Let A = [1, 2, 3, 4, 5], m be the number of relations such as 4x ≤ 5y XRY and n be the minimum number of elements to be added from A × A to make a symmetric relation. Then the value of n + m.

The resistance \( R = \frac{V}{I} \) where \( V = (200 \pm 5) \, \text{V} \) and \( I = (20 \pm 0.2) \, \text{A} \). The percentage error in the measurement of \( R \) is:

A child stands on the edge of the cliff $10 m$ above the ground and throws a stone horizontally with an initial speed of $5 \,ms ^{-1}$ Neglecting the air resistance, the speed with which the stone hits the ground will be ______$ms ^{-1}$ (given, $g=10 \,ms ^{-2}$ )