List of top Questions asked in JEE Main

The integral \(\int_{\pi/6}^{\pi/4}\frac{dx}{\sin 2x\left(\tan^5x + \cot^5x\right)}\) equals :

\( \lim_{x\to 0} \frac{x\cot(4x)}{\sin^2 x\,\cot^2(2x)} \) is equal to :

If \( \int \frac{x+1}{\sqrt{2x-1}}\,dx = f(x)\sqrt{2x-1} + C \), where C is a constant of integration, then \( f(x) \) is equal to :

Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \(\frac{x^m y^n}{(1 + x^{2m})(1 + y^{2n})}\) is :

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(x^2\sin\theta - x(\sin\theta\cos\theta + 1) + \cos\theta = 0\) \((0 \lt \theta \lt 45^{\circ})\), and \(\alpha \lt \beta\). Then \(\sum_{n=0}^{\infty}\left(\alpha^n + \frac{(-1)^n}{\beta^n}\right)\) is equal to :

The number of functions f from \(\{1, 2, 3, \ldots, 20\}\) onto \(\{1, 2, 3, \ldots, 20\}\) such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :

Let \(\sqrt{3}\,\hat{i} + \hat{j}\), \(\hat{i} + \sqrt{3}\,\hat{j}\) and \(\beta\hat{i} + (1-\beta)\hat{j}\) respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is \(\frac{3}{\sqrt{2}}\), then the sum of all possible values of \(\beta\) is :

Let K be the set of all real values of x where the function \(f(x) = \sin |x| - |x| + 2(x - \pi)\cos |x|\) is not differentiable. Then the set K is equal to :

If the area of the triangle whose one vertex is at the vertex of the parabola, \(y^2 + 4(x - a^2) = 0\) and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

The area (in sq. units) in the first quadrant bounded by the parabola, \(y = x^2 + 1\), the tangent to it at the point (2, 5) and the coordinate axes is :

All x satisfying the inequality \((\cot^{-1}x)^2 - 7(\cot^{-1}x) + 10 \gt 0\), lie in the interval :

Let a function \(f : (0, \infty) \to (0, \infty)\) be defined by \(f(x) = \left|1 - \frac{1}{x}\right|\). Then f is :

Let \(S = \{1, 2, \ldots\ldots, 20\}\). A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randonly chosen subset of S is "nice" is :

The polymer obtained from the following reaction is :

Peroxyacetyl nitrate (PAN), an eye irritant is produced by :

The correct statements among (a) to (d) regarding \(\mathrm{H_2}\) as a fuel are :
(a) It produces less pollutants than petrol.
(b) A cylinder of compressed dihydrogen weighs \(\sim\) 30 times more than a petrol tank producing the same amount of energy.
(c) Dihydrogen is stored in tanks of metal alloys like \(\mathrm{NaNi_5}\).
(d) On combustion, values of energy released per gram of liquid dihydrogen and LPG are 50 and 142 KJ, respectively.

The chloride that CANNOT get hydrolysed is :

The correct match between item (I) and item (II) is :

Item-I	Item-II
(A) Norethindrone	(P) Anti-biotic
(B) Ofloxacin	(Q) Anti-fertility
(C) Equanil	(R) Hypertension
	(S) Analgesics

Match the metals (column I) with the coordination compound(s)/enzyme(s) (column II)

(Column I)	Metals	(Column II)	Coordination compounds(s) enzyme(s)
(A)	Co	(i)	Wilkinson catalyst
(B)	Zn	(ii)	Chlorophyl
(C)	Rh	(iii)	Vitamin \(\mathrm{B_{12}}\)
(D)	Mg	(iv)	Carbonic anhydrase

For the chemical reaction \(\mathrm{X \rightleftharpoons Y}\), the standard reaction Gibbs energy depends on temperature \(T\) (in K) as \(\Delta_r G^\circ\) (in kJ mol\(^{-1}\)) = \(120 - \frac{3}{8}T\).
The major component of the reaction mixture at \(T\) is :

An organic compound is estimated through Duma's method and was found to evolve 6 moles of \(\mathrm{CO_2}\), 4 moles of \(\mathrm{H_2O}\) and 1 mole of nitrogen gas. The formula of the compound is :

The major product of the following reaction is :

The major product of the following reaction is

If a reaction follows the Arrhenius equation, the plot \(\ln k\) vs \(\frac{1}{RT}\) gives straight line with a gradient (\(-y\)) unit.
The energy required to active the reactant is :