List of top Questions asked in JEE Main

Correct order of 2$^{nd}$ ionisation energy is:

In general tests of Ba$^{2+}$ and Ca$^{2+}$ give the respective tests as:

On a surface, if photon of wavelength $\lambda$ is incident, the stopping potential is $3.2$ V. If the wavelength incident is $2\lambda$, stopping potential is $0.7$ V. Find $\lambda$.

Element X is the lightest element of group 7 of periodic table which forms oxo-anion in +6 oxidation state. The colour of potassium salt of the oxo-anion is:

Select incorrect option:

The half-life of radioactive isotope Zn$^{65}$ is 245 days. Find the time after which activity of Zn sample remains 75% of its initial value.

Let $f(x)=|\log_e x|-|x-1|+5$. Statement 1: $f(x)$ is differentiable for all $x\in(0,\infty)$
Statement 2: $f(x)$ is increasing in $(1,\infty)$
Statement 3: $f(x)$ is decreasing in $(0,1)$
Which of the following is correct?

In case of meter bridge experiment balance length for $2\Omega$ and $3\Omega$ is $\ell$ and for $x\Omega$ and $3\Omega$ is $(\ell + 10)$ cm. Find $x$.

0.18 M HQ solution has molar conductivity $\frac{1}{30}$ times the molar conductivity of 0.02 M HZ solution. Find the value of pK$_a$(HQ) − pK$_a$(HZ).
[Given that $\alpha$ is very less than 1]

Statement-I: Two different aldehydes on cross aldol condensation always give four products.
Statement-II: Among benzaldehyde and acetophenone, only acetophenone reacts with semicarbazide.

In a vernier calipers 50 VSD are equal to 48 MSD. 1 MSD is equal to $0.05$ mm. Find least count of this vernier calipers.

An electron makes transition from higher energy orbit to lower energy orbit in $Li^{2+}$ ion such that $n_1 + n_2 = 4$ and $n_2 - n_1 = 2$. Determine the wavelength of emitted photon in transition (in cm).

The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{1}{\left\lfloor x \right\rfloor + 4} \, dx \] where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function, is:

Sodium extract of organic compound of 0.1 g is treated with chlorine water and \( \text{CCl}_4 \) which dissolves in organic solvent to produce a violet colour. Upon treatment with \( \text{AgNO}_3 \), a yellow ppt. of 0.12 g is produced. Calculate the percentage of halide in the organic compound.

Statement-I: Fluid exerts pressure on the surface of a solid in contact with it. Statement-II: The excess potential energy of molecules at the surface of a liquid leads to surface tension. Which of the following is correct?

An \( \alpha \)-particle with KE 7.9 MeV is projected towards a stationary target nucleus of \( Z = 79 \). Find the distance of closest approach.

If \[ \int \left( \cos x \right)^{-\frac{5}{2}} \left( \sin x \right)^{-\frac{1}{2}} \, dx \] \[ = \frac{P_1}{q_1} \left( \cot x \right)^{\frac{3}{2}} + \frac{P_2}{q_2} \left( \cot x \right)^{\frac{3}{2}} + \frac{P_3}{q_3} \left( \cot x \right)^{\frac{1}{2}} + \frac{P_4}{q_4} \left( \cot x \right)^{-\frac{3}{2}} + c \] (where \( c \) is the constant of integration), then value of \[ \frac{15P_1P_2P_3P_4}{q_1q_2q_3q_4} \] is:

If the area of the region \( \{ (x, y) : x^2 + 1 \leq y \leq 3 - x \} \) is divided by the line \( x = -1 \) in the ratio \( m : n \) (where \( m \) and \( n \) are coprime natural numbers), then the value of \( m + n \) is:

Bohr’s radius of H-atom is \( 2.12 \times 10^{-10} \) m. Calculate the energy of electron at this level.

If \[ A = \begin{pmatrix} 2 & 3 \\ 3 & 5 \end{pmatrix} \] then the value of \[ |A^{2025} - 3A^{2024} + A^{2023}| \] is:

Variates are given as \( -10, -7, -1, x, y, 2, 9, 16 \). If the mean \( (\mu) = \frac{7}{2} \) and variance = \( \frac{293}{4} \), find the mean of \( (1 + x + y), x, y, |y - x| \):

If \[ \begin{vmatrix} 0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} = \begin{vmatrix} 1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} \] then the value of \( \cos^2 \alpha + \cos^3 \beta + \cos^2 \gamma \) is: