List of top Questions asked in JEE Main

Let \(f\) be a differentiable function from \(\mathbf{R}\) to \(\mathbf{R}\) such that \(|f(x)-f(y)|\le 2|x-y|^{3/2}\), for all \(x,y\in\mathbf{R}\). If \(f(0)=1\) then \(\int_0^1 f^2(x)\,dx\) is equal to :

If \(f(x)=\int\frac{5x^8+7x^6}{\left(x^2+1+2x^7\right)^2}\,dx,\ (x\ge0)\), and \(f(0)=0\), then the value of \(f(1)\) is :

If both the roots of the quadratic equation \(x^2-mx+4=0\) are real and distinct and they lie in the interval \([1,5]\), then \(m\) lies in the interval :

Let \(S\) be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in \(S\) has area 50 sq. units, then the number of elements in the set \(S\) is :

If \(x=\sin^{-1}(\sin 10)\) and \(y=\cos^{-1}(\cos 10)\), then \(y-x\) is equal to :

Let \(f:[0,1]\to\mathbf{R}\) be such that \(f(xy)=f(x)\cdot f(y)\), for all \(x,y\in[0,1]\), and \(f(0)\neq 0\). If \(y=y(x)\) satisfies the differential equation, \(\frac{dy}{dx}=f(x)\) with \(y(0)=1\), then \(y\left(\frac{1}{4}\right)+y\left(\frac{3}{4}\right)\) is equal to :

Let \(A=\{x\in\mathbf{R}: x\) is not a positive integer\(\}\). Define a function \(f:A\to\mathbf{R}\) as \(f(x)=\frac{2x}{x-1}\), then \(f\) is :

If \(\int_0^{\pi/3}\frac{\tan\theta}{\sqrt{2k\sec\theta}}\,d\theta = 1-\frac{1}{\sqrt{2}}\), \((k\gt 0)\), then value of \(k\) is :

The isotopes of hydrogen are :

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m³ at 1000 K. Given R is the gas constant in \(\mathrm{JK^{-1}mol^{-1}}\), x is :

The alkaline earth metal nitrate that does not crystallise with water molecules, is :

The one that is extensively used as a piezoelectric material is :

The major product of the following reaction is :

The compounds A and B in the following reaction are, respectively :

The major product of the following reaction is :

The following results were obtained during kinetic studies of the reaction ;
\(2A + B \rightarrow \text{Products}\)

Experiment	[A] (in mol L-1)	[B] (in mol L-1)	Initial Rate of reaction (in mol L-1 min-1)
I	0.10	0.20	\(6.93\times10^{-3}\)
II	0.10	0.25	\(6.93\times10^{-3}\)
III	0.20	0.30	\(1.386\times10^{-2}\)

The time (in minutes) required to consume half of A is :

20 mL of 0.1 M \(\mathrm{H_2SO_4}\) solution is added to 30 mL of of 0.2 M \(\mathrm{NH_4OH}\) solution. The pH of the resultant mixture is : [\(\mathrm{pk_b}\) of \(\mathrm{NH_4OH}\) = 4.7].

According to molecular orbital theory, which of the following is true with respect to \(\mathrm{Li_2^+}\) and \(\mathrm{Li_2^-}\) ?

The major product of following reaction is :

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds \(\left[\frac{V_{rms}(\text{helium})}{V_{rms}(\text{argon})}\right]\), is close to :

The correct match between Item-I and Item-II is :

Item-I (drug)	Item-II (test)
A. Chloroxylenol	P. Carbylamine test
B. Norethindrone	Q. Sodium hydrogen carbonet test
C. Sulphapyridine	R. Ferric chloride test
D. Penicillin	S. Bayer's test

The increasing order of pka of the following amino acids in aqueous solution is :
Gly, Asp, Lys, Arg

Two complexes \(\mathrm{[Cr(H_2O)_6]Cl_3}\) (A) and \(\mathrm{[Cr(NH_3)_6]Cl_3}\) (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is :

The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexes is :

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m \((m \ll M)\). When the car is at rest, the speed of transverse waves in the string is 60 ms^-1. When the car has acceleration a, the wave-speed increases to 60.5 ms^-1. The value of a, in terms of gravitational acceleration g, is closest to :