List of top Questions asked in JEE Main

Isobutyraldehyde on reaction with formaldehyde and K2CO3 gives compound ‘A’. Compound ‘A’ reacts with KCN and yields compound ‘B’, which on hydrolysis gives a stable compound ‘C’. The compound ‘C’ is

\(\begin{array}{l} I_n\left(x\right)=\int_0^x\frac{1}{\left(t^2+5\right)^n}dt, n=1, 2, 3,\cdots\end{array}\)

Then

The area enclosed by the curves 
\(\begin{array}{l} y=\text{log}_e\left(x+e^2\right),\ x=\text{log}_e\left(\frac{2}{y}\right)\text{ and }x=\text{ log }_e\ 2,\end{array}\)
above the line y = 1 is
Let y = y(x) be the solution curve of the differential equation 
\(\begin{array}{l} \frac{dy}{dx}+\frac{1}{x^2-1}y=\left(\frac{x-1}{x+1}\right)^{1/2},x>1 \end{array}\)
passing through the point (2, √(1/3)). Then √7 y(8) is
The differential equation of the family of circles passing through the points (0, 2) and (0, –2) is
Let the tangents at two points A and B on the circle\( x^2 + y^2 – 4x + 3 = 0\) meet at origin O(0, 0). Then the area of the triangle OAB is

Given below are two statements, one is Assertion (A) and other is Reason (R).

Assertion (A): Natural rubber is a linear polymer of isoprene called cis-polyisoprene with elastic properties.
Reason (R): The cis-polyisoprene molecules consist of various chains held together by strong polar interactions with coiled structure.

In the light of the above statements, choose the correct one from the options given below:

When sugar ‘X’ is boiled with dilute H2SO4 in alcoholic solution, two isomers ‘A’ and ‘B’ are formed. ‘A’ on oxidation with HNO3 yields saccharic acid whereas ‘B’ is laevorotatory. The compound ‘X’ is :
The drug tegamet is:
100 g of an ideal gas is kept in a cylinder of 416 L volume at 27°C under 1.5 bar pressure. The molar mass of the gas is ________ g mol–1. (Nearest integer). (Given : R = 0.083 L bar K–1 mol–1)
For combustion of one mole of magnesium in an open container at 300K and 1bar pressure, ΔCHΘ=–601.70kJ mol–1, the magnitude of change in internal energy for the reaction is______ kJ. (Nearest integer) (Given : R = 8.3 J K–1 mol–1)
2.5 g of protein containing only glycine (C2H5NO2) is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found to be 5.03 × 10–3 bar. The total number of glycine units present in the protein is _______.
(Given : R = 0.083 L bar K–1 mol–1)
A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ________. (Nearest integer) (Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)
[Fe(CN)6]4–
[Fe(CN)6]3–
[Ti(CN)6]3–
[Ni(CN)4]2–
[Co(CN)6]3–
Among the given complexes, number of paramagnetic complexes is_______.
(a)CoCl3⋅4NH3,(b)CoCl3⋅5NH3,(c)CoCl3.6NH3 and (d)CoCl(NO3)2⋅5NH3.Number of complex(es) which will exist in cis-trans form is/are______.
The complete combustion of 0.492 g of an organic compound containing ‘C’, ‘H’ and ‘O’ gives 0.793 g of CO2 and 0.442 g of H2O. The percentage of oxygen composition in the organic compound is_____.[nearest integer]
Let \(S={z∈C:|z−2|≤1,and(1+i)+\overline{z}(1−i)≤2}. \)Let \(|z−4i|\) attains minimum and maximum values, respectively, at z1∈s and z2∈s. If \(5(|z_1|^2+|z_2|^2=α+β√5\)  where α and β are integers, then the value of α+β is equal to _________.
Correct statement about photo-chemical smog is:

The area of the bounded region enclosed by the curve 
\(y=3−|x−\frac{1}{2}|−|x+1| \)
and the x-axis is

A commercially sold conc. HCl is 35% HCl by mass. If the density of this commercial acid is 1.46 g/mL, the molarity of this solution is :
(Atomic mass : Cl = 35.5 amu, H = 1 amu)

Let x = x(y) be the solution of the differential equation 
\(2ye^{\frac{x}{y^2}}dx+(y^2−4xe^{\frac{x}{y^2}})dy=0 \)
such that x(1) = 0. Then, x(e) is equal to

An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL–1 and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mol–1 is: (Given : R = 0.082 L atm K–1 mol–1)
If the radius of the 3rd Bohr’s orbit of hydrogen atom is r3 and the radius of 4th Bohr’s orbit is r4. Then
Consider the ions/molecules \(O^{2+}, O_2, O_2^-, O_2^{2-}\)For increasing bond order the correct option is
The \(\left(\frac{\partial E}{\partial T}\right)_p\) of different types of half cells are as follows:
ABCD
1 × 10-42 × 10-40.1 × 10-40.2 × 10-4

(Where E is the electromotive force)
Which of the above half cells would be preferred to be used as reference electrode?