List of top Questions asked in JEE Main

The value of magnetic quantum number of the outermost electron of $\text{Zn}^+$ ion is ________. (Integer answer)
According to molecular orbital theory, the number of unpaired electron(s) in $\text{O}_2^{2-}$ is ________.
1.22 g of an organic acid is separately dissolved in 100 g of benzene ($K_b = 2.6 \text{ K kg mol}^{-1}$) and 100 g of acetone ($K_b = 1.7 \text{ K kg mol}^{-1}$). The acid is known to dimerize in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by $0.17^\circ\text{C}$. The increase in boiling point of solution in benzene in $^\circ\text{C}$ is $x \times 10^{-2}$. The value of $x$ is ________. (Nearest integer) [Atomic mass : C = 12.0, H = 1.0, O = 16.0]
The pH of a solution obtained by mixing 50 mL of 1 M HCl and 30 mL of 1 M NaOH is $x \times 10^{-1}$. The value of $x$ is ________. (Nearest integer) [log 2.5 = 0.3979]
For the reaction $\text{A} \to \text{B}$, the rate constant $k$ (in $\text{s}^{-1}$) is given by $\log_{10} k = 20.35 - \frac{2.47 \times 10^3}{\text{T}}$. The energy of activation in $\text{kJ mol}^{-1}$ is ________. (Nearest integer) [Given : R = 8.314 J K$^{-1}$ mol$^{-1}$]
$\text{CH}_4$ is adsorbed on 1 g charcoal at $0^\circ\text{C}$ following the Freundlich adsorption isotherm. 10.0 mL of $\text{CH}_4$ is adsorbed at 100 mm of Hg, whereas 15.0 mL is adsorbed at 200 mm of Hg. The volume of $\text{CH}_4$ adsorbed at 300 mm of Hg is $10^x$ mL. The value of $x$ is ________ $\times 10^{-2}$. (Nearest integer) [Use $\log_{10} 2 = 0.3010, \log_{10} 3 = 0.4771$]
In the electrolytic refining of blister copper, the total number of main impurities, from the following, removed as anode mud is ________.
Pb, Sb, Se, Te, Ru, Ag, Au and Pt.
The transformation occurring in Duma's method is given below:
$\text{C}_2 \text{H}_7 \text{N} + (2x + y/2) \text{CuO} \to x \text{CO}_2 + y/2 \text{H}_2\text{O} + z/2 \text{N}_2 + (2x + y/2) \text{Cu}$.
The value of $y$ is ________. (Integer answer)
Let \( f : \mathbb{N} \to \mathbb{N} \) be a function such that \( f(m + n) = f(m) + f(n) \) for every \( m, n \in \mathbb{N} \). If \( f(6) = 18 \), then \( f(2) \cdot f(3) \) is equal to :
If \( z \) is a complex number such that \( \frac{z - i}{z - 1} \) is purely imaginary, then the minimum value of \( |z - (3 + 3i)| \) is :
The sum of the roots of the equation, \( x + 1 - 2\log_2(3 + 2^x) + 2\log_4(10 - 2^{-x}) = 0 \), is :
Let \( a_1, a_2, a_3, \dots \) be an A.P. If \( \frac{a_1 + a_2 + \dots + a_{10}}{a_1 + a_2 + \dots + a_p} = \frac{100}{p^2}, p \neq 10 \), then \( \frac{a_{11}}{a_{10}} \) is equal to :
If \( \alpha = \lim_{x \to \pi/4} \frac{\tan^3 x - \tan x}{\cos(x + \frac{\pi}{4})} \) and \( \beta = \lim_{x \to 0} (\cos x)^{\cot x} \) are the roots of the equation, \( ax^2 + bx - 4 = 0 \), then the ordered pair \( (a, b) \) is :
The locus of mid-points of the line segments joining \( (-3, -5) \) and the points on the ellipse \( \frac{x^2}{4} + \frac{y^2}{9} = 1 \) is :
The distance of the point \((-1, 2, -2)\) from the line of intersection of the planes \(2x + 3y + 2z = 0\) and \(x - 2y + z = 0\) is :
Let \(\vec{a}, \vec{b}, \vec{c}\) be three vectors mutually perpendicular to each other and have same magnitude. If a vector \(\vec{r}\) satisfies \(\vec{a} \times \{(\vec{r} - \vec{b}) \times \vec{a}\} + \vec{b} \times \{(\vec{r} - \vec{c}) \times \vec{b}\} + \vec{c} \times \{(\vec{r} - \vec{a}) \times \vec{c}\} = \vec{0}\), then \(\vec{r}\) is equal to :
Let \(S = \{1, 2, 3, 4, 5, 6\}\). Then the probability that a randomly chosen onto function \(g\) from \(S\) to \(S\) satisfies \(g(3) = 2g(1)\) is :
The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :
The number of elements in the set \[ \left\{ A = \begin{pmatrix} a & b \\ 0 & d \end{pmatrix} : a, b, d \in \{-1, 0, 1\} \text{ and } (I - A)^3 = I - A^3 \right\}, \] where \( I \) is the \( 2 \times 2 \) identity matrix, is _________.
The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is _________.
If the coefficient of \( a^7b^8 \) in the expansion of \( (a + 2b + 4ab)^{10} \) is \( K \cdot 2^{16} \), then K is equal to _________.
If \( S = \frac{7}{5} + \frac{9}{5^2} + \frac{13}{5^3} + \frac{19}{5^4} + ... \), then 160 S is equal to _________.
Let \( f(x) \) be a cubic polynomial with \( f(1) = -10 \), \( f(-1) = 6 \), and has a local minima at \( x = 1 \), and \( f'(x) \) has a local minima at \( x = -1 \). Then \( f(3) \) is equal to _________.
If \( \int \frac{\sin x}{\sin^3 x + \cos^3 x} dx = \alpha \log_e |1 + \tan x| + \beta \log_e |1 - \tan x + \tan^2 x| + \gamma \tan^{-1} \left( \frac{2 \tan x - 1}{\sqrt{3}} \right) + C \), when C is a constant of integration, then the value of \( 18(\alpha + \beta + \gamma^2) \) is _________.
If the line \( y = mx \) bisects the area enclosed by the lines \( x = 0, y = 0, x = \frac{3}{2} \) and the curve \( y = 1 + 4x - x^2 \), then 12 m is equal to _________.