List of top Questions asked in JEE Main

If $f(x)$ satisfies the relation \[ f(x)=e^x+\int_0^1 (y+x e^x)f(y)\,dy, \] then $e+f(0)$ is equal to

The number of ways 16 oranges distributed to 4 children, each gets at least one.

Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers having product of its digits equal to 20. Then $n(S) + n(P)$ is equal to ___

Let $z=(1+i)(1+2i)(1+3i)\cdots(1+ni)$, where $i=\sqrt{-1}$. If $|z|^2=44200$, then $n$ is equal to

If the solution curve $y = f(x)$ of the differential equation $(x^2 - 4) y' - 2xy + 2x(4 - x^2)^2 = 0, x>2$, passes through the point $(3, 15)$, then the local maximum value of $f$ is ___

A small metallic sphere of diameter 2 mm and density 10.5 g/cm$^3$ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm$^3$ respectively. The terminal velocity attained by the sphere is ___ cm/s. ($\pi = \frac{22}{7}$ and $g = 10$ m/s$^2$)

In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound is

A mixed ether (P), when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which when treated with aq. NaOH give compounds (Q) and (R) give yellow precipitate with NaOI. Identify the mixed ether (P):

Given above is the concentration vs time plot for a dissociation reaction : $A \to nB$. Based on the data of the initial phase of the reaction (initial 10 min), the value of n is ____.

The work functions of two metals ($M_A$ and $M_B$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of $M_A$ : $M_B$ is in the ratio of 2.642 : 1. The work functions (in eV) of $M_A$ and $M_B$ are respectively.

Observe the following reactions at T(K).
I. $A \to$ products.
II. $5Br^- + BrO_3^- + 6H^+ \to 3Br_2 + 3H_2O$.
Both the reactions are started at 10.00 am. The rates of these reactions at 10.10 am are same. The value of $-\frac{d[Br^-]{dt}$ at 10.10 am is $2 \times 10^{-4} \text{ mol L}^{-1} \text{min}^{-1}$. The concentration of A at 10.10 am is $10^{-2} \text{ mol L}^{-1}$. What is the first order rate constant (in $\text{min}^{-1}$) of reaction I?}

Identify (P)

Which statements are NOT TRUE about $XeO_2F_2$?
A. It has a see-saw shape.
B. Xe has 5 electron pairs in its valence shell in $XeO_2F_2$.
C. The O-Xe-O bond angle is close to $180^\circ$.
D. The F-Xe-F bond angle is close to $180^\circ$.
E. Xe has 16 valence electrons in $XeO_2F_2$.

Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence of ___

The oxidation state of chromium in the final product formed in the reaction between KI and acidified $K_2Cr_2O_7$ solution is:

Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming $M^+$ ($M \to M^+ + e^-$). The cation $M^+$ is present in two different concentrations $c_1$ and $c_2$ as shown above. Which of the following statement is correct for generating a positive cell potential?