List of top Questions asked in JEE Main

\(\int e^{\sec x}\left(\sec x\tan x\, f(x) + \sec x\tan x + \sec^2 x\right)dx = e^{\sec x} f(x) + C\) then a possible choice of f(x) is :-

The area (in sq. units) of the region \(A = \left\{(x, y) : \frac{y^2}{2} \le x \le y + 4\right\}\) is :-

The total number of matrices \(A = \begin{pmatrix} 0 & 2y & 1 \\ 2x & y & -1 \\ 2x & -y & 1 \end{pmatrix}\) \((x, y \in R,\ x \ne y)\) for which \(A^{T}A = 3I_3\) is :-

A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (-8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :

The domain of the definition of the function \(f(x) = \frac{1}{4 - x^2} + \log_{10}(x^3 - x)\) is

If \(f(x) = [x] - \left[\frac{x}{4}\right],\ x \in \mathbb{R}\), where [x] denotes the greatest integer function, then

Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :-

The value of \(\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ\) is :-

If \(\cos x\,\frac{dy}{dx} - y\sin x = 6x\), \(\left(0 \lt x \lt \frac{\pi}{2}\right)\) and \(y\left(\frac{\pi}{3}\right) = 0\) then \(y\left(\frac{\pi}{6}\right)\) is equal to :-

If the function \(f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|x - \pi| + 3, & x \gt 5 \end{cases}\) is continuous at x = 5, then the value of a - b is :-

If f : R \(\to\) R is a differentiable function and f(2) = 6, then \(\displaystyle\lim_{x\to 2}\frac{\int_{6}^{f(x)} 2t\,dt}{(x-2)}\) is :-

If the sum and product of the first three term in an A.P. are 33 and 1155, respectively, then a value of its 11^th term is :-

Match the catalysts (Column I) with products (Column II).

Column I	Column II
(A) \(\mathrm{V_2O_5}\)	(i) Polyethylene
(B) \(\mathrm{TiCl_4/Al(Me)_3}\)	(ii) ethanal
(C) \(\mathrm{PdCl_2}\)	(iii) \(\mathrm{H_2SO_4}\)
(D) Iron Oxide	(iv) \(\mathrm{NH_3}\)

The ore that contains the metal in the form of fluoride is :

Consider the van der Waals constants, a and b, for the following gases.

Gas	Ar	Ne	Kr	Xe
a/ (atm dm6 mol-2)	1.3	0.2	5.1	4.1
b/ (10-2 dm3 mol-1)	3.2	1.7	1.0	5.0

Which gas is expected to have the highest critical temperature?

Excessive release of \(\mathrm{CO_2}\) into the atmosphere results in :

Aniline dissolved in dilute HCl is reacted with sodium nitrite at \(0^\circ\mathrm{C}\). This solution was added dropwise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major product is

The major product of the following reaction is :
\(\mathrm{CH_3-C\equiv CH}\ \xrightarrow[\mathrm{(ii)\ DI}]{\mathrm{(i)\ DCl\ (1\ equiv.)}}\)

The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M \(\mathrm{BaCl_2}\) in water. Assuming complete dissociation of the given ionic compounds in water, the concentration of XY (in mol \(\mathrm{L^{-1}}\)) in solution is :

Magnesium powder burns in air to give :

The major product of the following reaction is :

For any given series of spectral lines of atomic hydrogen, let \(\Delta\bar{\nu} = \Delta\bar{\nu}_{max} - \Delta\bar{\nu}_{min}\) be the difference in maximum and minimum frequencies in \(\mathrm{cm^{-1}}\). The ratio \(\dfrac{\Delta\bar{\nu}_{Lyman}}{\Delta\bar{\nu}_{Balmer}}\) is :

The standard Gibbs energy for the given cell reaction in kJ mol^-1 at 298 K is :
\(\mathrm{Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)}\),
\(E^\circ = 2\ \mathrm{V}\) at 298 K
(Faraday's constant, \(F = 96000\ \mathrm{C\ mol^{-1}}\))

The one that will show optical activity is :
(en = ethane-1,2-diamine)

The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is :