List of top Questions asked in JEE Main

A radioactive nucleus decays by two different processes. The half life for the first process is $10 s$ and that for the second is $100 s$. the effective half life of the nucleus is close to:

The activity of a radioactive sample falls from $700\, s^{-1}$ to $500\, s^{-1}$ in 30 minutes. Its half life is close to :

A wire of length $L$ and mass per unit length $6.0 \times 10^{-3} \,kgm^{-1}$ is put under tension of $540\, N$. Two consecutive frequencies that it resonates at are: $420\, Hz$ and $490 \,Hz$. Then $L$ in meters is :

Planet $A$ has mass $M$ and radius $R$. Planet $B$ has half the mass and half the radius of Planet $A$. If the escape velocities from the Planets $A$ and $B$ are $v_A$ and $v_B$, respectively, then $\frac{v_{A}}{v_{B}}=\frac{n}{4}$. The value of $n$ is :

Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ Ls carved out of it, as shown, the ratio $\frac{\left|\overrightarrow{E_{A}}\right|}{\left|\overrightarrow{E_{B}}\right|}$ of magnitude of electric field $\overrightarrow{E_{A}}$ and $\overrightarrow{E}_{B}$ respectively, at points A and B due to the remaining portion is :

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : ($1 \,HP = 746 \,W, \,g = 10\, ms^{-2}$ )

The correct order of the spin-only magnetic moments of the following complexes is : $(I)\, [Cr(H_2O)_6]Br_2$ $(II)\, Na_4[Fe(CN)_6]$ $(III)\, Na_3[Fe(C_2O_4)_3] (\Delta_0 > P)$ $(IV)\, (Et_4N)_2[CoCl_4]$

The de Broglie wavelength of an electron in the $4^{th}$ Bohr orbit is :

A crystal is made up of metal ions 'M $_{1}$ ' and 'M $_{2}$ ' and oxide ions. Oxide ions. form a ccp lattice structure. The cation '$M_1$ occupies $50 \%$ of octahedral voids and the cation 'M $_{2}$ ' occupies $12.5 \%$ of tetrahedral voids of oxide lattice. The oxidation numbers of ' $M _{1}$ ' and ' $M _{2}$ ' are, respectively:

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is

Two particles of equal mass m have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right).$ They collide completely inelastically. The energy lost in the process is :

A capacitor $C$ is fully charged with voltage $V _{0}$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{ C }{2} .$ The energy loss in the process after the charge is distributed between the two capacitors is :

A particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $l$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :

A thermodynamic cycle $xyzx$ is shown on a $V-T$ diagram. The $P-V$ diagram that best describes this cycle is : (Diagrams are schematic and not to scale)

Among statements (a)-(d), the correct ones are: (a) Decomposition of hydrogen peroxide gives dioxygen. (b) Like hydrogen peroxide,compounds, such as $KClO_3, Pb (NO_3)_2$ and $NaNO_3$ when heated liberate dioxygen. (c) 2-Ethylanthraquinone is useful for the industrial preparation of hydrogen peroxide. (d) Hydrogen peroxide is used for the manufacture of sodium perborate.

Among the statements (A)-(D), the correct ones are : (a) Lithium has the highest hydration enthalpy among the alkali metals. (b) Lithium chloride is insoluble in pyridine. (c) Lithium cannot form ethynide upon its reaction with ethyne. (d) Both lithium and magnesium react slowly with $H_2O$ .

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value ? 1. Then the expected value of X, is :

_____________If $\alpha$ and $\beta$ be the coefficients of $x^4$ and $x^2$ respectively in the expansion of $\left(x+\sqrt{x^{2}-1}\right)^{6}+\left(x-\sqrt{x^{2}-1}\right)^{6},$ then :

For $a > 0$, let the curves $C_1 : y^2 = ax$ and $C_2 : x^2= ay$ intersect at origin O and a point P. Let the line $x = b (0 < b < a)$ intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, $C_1$ and $C_2$, and the area of $\Delta OQR = \frac{1}{2},$ then 'a' satisfies the equation :

The inverse function of $f\left(x\right) = \frac{8^{2x}-8^{-2x}}{8^{2x} + 8^{-2x}}, x\epsilon \left(-1, 1\right),$ is __________.

$\displaystyle\lim_{x \to 0} \left(\frac{3x^{2}+2}{7x^{2}+2}\right)^{\frac {1}{x^2}}$ is equal to :

The mean and variance of $20$ observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was $11$. Then the correct variance is :

If a, b and c are the greatest values of $^{19}C_{p}, \, ^{20}C_{q}$ and $^{21}C_{r}$ respectively, then :

Let $\vec{a}=\hat{i}-2\,\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b}\times\vec{c}=\vec{b}\times\vec{a}$ and $\vec{c}\cdot\vec{a}=0,$ then $\vec{c} \cdot \vec{b}$ is equal to :

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4\, cm$ and $4.8\, cm$, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :