List of top Questions asked in JEE Main

Number of ways of distributing 16 identical oranges among 4 persons such that each one gets at least one orange is:
Statement-I: An element ‘X’ of P-block forms a hydride H–X, which has the longest bond length, then element ‘X’ will have the shortest covalent radius.
Statement-II: An element ‘E’ of Group 15 forms hydride EH$_3$, that has least B.P. The maximum covalency of E is 4.
Choose the correct statements in respect of hydrides of group 15.
(A) Reducing power increases down the group
(B) Basic nature increases down the group
(C) Stability decreases down the group
(D) Boiling point decreases regularly down the group.
Equation of an electromagnetic wave in a medium is given by \[ E = 2\sin\left(2\times 10^{15}t - 10^{7}x\right). \] Find the refractive index of the medium.
Among the species O$_2^+$, N$_2^-$, N$_2^{2-}$ and O$_2^-$ which have same bond order as well as paramagnetic in nature.
The number of values of \( x \) satisfying \( \tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6} \) and \( x<\left[ \frac{-1}{2\sqrt{6}} , \frac{1}{2\sqrt{6}} \right] \) is:
Let \( A = \{2, 3, 5, 7, 11\} \) and a relation \( R \) is defined as \[ R = \{(x, y) : x, y \in A, 2x \leq 3y\}. \] Then the minimum number of elements to be added to relation \( R \) such that \( R \) becomes symmetric is:
The value of \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{12(3+[x])\,dx}{3+[\sin x]+[\cos x]} \] (where \([\,]\) denotes the greatest integer function) is:
Find the value of \[ \frac{6}{3^{26}} + 10\cdot\frac{1}{3^{25}} + 10\cdot\frac{2}{3^{24}} + \cdots + 10\cdot\frac{2^{24}}{3^{1}} : \]
If the system of linear equations \[ \begin{cases} 3x + y + \beta z = 3 \\ 2x + \alpha y - z = 1 \\ x + 2y + z = 4 \end{cases} \] has infinitely many solutions, then the value of \(22\beta - 9\alpha\) is:
If \[ \int (\cos x)^{-5/2}(\sin x)^{-11/2}\,dx = \frac{p_1}{q_1}(\cot x)^{9/2} + \frac{p_2}{q_2}(\cot x)^{5/2} + \frac{p_3}{q_3}(\cot x)^{1/2} - \frac{p_4}{q_4}(\cot x)^{-3/2} + C, \] where \(C\) is the constant of integration, then find the value of \[ \frac{15\,p_1p_2p_3p_4}{q_1q_2q_3q_4}. \]
If \[ I(x) = 3\int \frac{dx}{(4x+6)\sqrt{4x^2 + 8x + 3}}, \quad I(0) = \frac{\sqrt{3}}{4}, \] then find \( I(1) \):
Maximum value of $n$ for which $40^n$ divides $60!$ is
If the system of equations \[ \begin{cases} 2x + y + pz = -1 \\ 3x - 2y + z = q \\ 5x - 8y + 9z = 5 \end{cases} \] has more than one solution, then \( q - p \) is equal to:
If $y = y(x)$ satisfies
$(1+x^2)\frac{dy}{dx} + (2 - \tan^{-1}x) = 0$
and $y(0) = 0$, then the value of $y(1)$ is:
If \( a, b, c \) are in A.P. where \( a + b + c = 1 \) and \( a, 2b, c \) are in G.P., then the value of \( 9(a^2 + b^2 + c^2) \) is equal to:
A bag contains 'k' red balls and (10 - k) black balls. If 3 balls are drawn at random and they are found to be black then the probability that bag has 9 black balls & 1 red ball is
If \( (f(x))^2 = 25 + \int_0^x \left[ (f(x))^2 + (f'(x))^2 \right] \, dx \), find the mean of \( f(\ln 1) + f(\ln 2) + \dots + f(\ln 625) \):
Let \( \mathbf{a} = \sqrt{2} \hat{i} \) and \( \mathbf{b} = 5\hat{j} + \hat{k} \). If \( \mathbf{c} = \mathbf{a} \times \mathbf{b} \) and \( \mathbf{c} \) lies in the \( y \)-\( z \) plane such that \( |\mathbf{c}| = 2 \), then the maximum value of \( |\mathbf{c} \cdot \mathbf{d}| \) is equal to:
If the probability distribution is given by, \[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline p(n) & 8a-1 \, /30 & 4a-1 \, /30 & 2a+1 \, /30 & b \\ \hline \end{array} \] If it is given that \( \sigma^2 + \mu^2 = 2 \), where \( \sigma \) is the standard deviation and \( \mu \) is the mean of the distribution, then \( \frac{a}{b} \) is:
If the image of the point \( P(3, 2, a) \) reflected about the line \[ \frac{x-3}{2} = \frac{y-5}{5} = \frac{z-2}{-2} \] is \( (5, b, c) \), then the value of \( \sigma^2 + b^2 + c^2 \) is:
If sum of first 4 terms of an A.P. is 6 and sum of first 6 terms is 4, then sum of first 12 terms of an A.P. is
If the mean and variance of observations \( x, y, 12, 14, 4, 10, 2, 8 \) and 16 respectively where \( x>y \), then the value of \( 3x - y \) is
Given conic \(x^2 - y^2 \sec^2 \theta = 8\) whose eccentricity is '\(e_1\)' & length of latus rectum '\(l_1\)' and for conic \(x^2 + y^2 \sec^2 \theta = 6\), eccentricity is '\(e_2\)' & length of latus rectum '\(l_2\)'. If \(e_1^2 = e_2^2 (1 + \sec^2 \theta)\) then value of \(\frac{e_1 l_1}{e_2 l_2} \tan \theta\)
Let a function $f(x)$ satisfy \[ 3f(x)+2f\!\left(\frac{m}{19x}\right)=5x \] where $m=\sum_{i=1}^{9} i^2$. Find $f(5)+f(2)$.