List of top Questions asked in JEE Main

Homoleptic octahedral complexes of a metal ion '${M^{3+} }$' with three monodentate ligands and $L_1, L_2, L_3$ absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is :

Ice at $-20^{\circ} C$ os added tp $50\, g$ of water at $40^{\circ}C$. When the temperature of the mixture reaches $0^{\circ}C$, it is found that $20\, g$ of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = $4.2 \; J/g/^{\circ}C$) Specific heat of Ice = $2.1 \; J/g/^{\circ}C$ Heat of fusion of water at $0^{\circ}C = 334 \; J/g$)

If $\begin {bmatrix} 1 & 1 \\ 0 & 1 \end {bmatrix}$ . $\begin {bmatrix} 1 & 2 \\ 0 & 1 \end {bmatrix} $ . $\begin {bmatrix} 1 & 3 \\ 0 & 1 \end {bmatrix}$ ..... $\begin {bmatrix} 1 & n-1 \\ 1 & 1 \end {bmatrix}$ = $\begin {bmatrix} 1 & 78 \\ 0 & 1 \end {bmatrix}$, then the inverse of $\begin {bmatrix} 1 & n \\ 0 & 1 \end {bmatrix}$ is

If $10^{22}$ gas molecules each of mass $10^{-26}$ kg collide with a surface (perpendicular to it) elastically per second over an area $1\, m^2$ with a speed $10^4$ m/s, the pressure exerted by the gas molecules will be of the order of :

If a unit vector $\vec{a}$ makes angles $\pi/3$ with $\hat{i} , \pi /4$ with $\hat{j}$ and $\theta \in (0 , \pi)$ with $\hat{k}$, then a value of $\theta$ is : -

If dichloromethane (DCM) and water ${(H_2O)}$ are used for differential extraction, which one of the following statements is correct ?

If $f\left(x\right) = \frac{2- x\cos x}{2+x \cos x}$ and $ g\left(x\right) =\log_{e}x ., \left(x>0\right) $ then the value of integral $\int\limits^{\frac{\pi}{4}}_{-\frac{\pi}{4}} g\left(f\left(x\right)\right)dx $ is :

If $\int \frac{dx}{x^{3}\left(1+x^{6}\right)^{\frac{2}{3}}}=f \left(x\right)\left(1+x ^{6}\right)^{\frac{1}{3}}+C$, where C is a constant of integration, then the function $f \left(x\right)$ is equal to-

If $ \int \frac{\sqrt{1-x^{2}}}{x^{4}} dx = A \left(x\right)\left(\sqrt{1-x^{2}}\right)^{m} + C $ , for a suitable chosen integer $m$ and a function $A(x)$, where $C$ is a constant of integration then $(A(x))^m$ equals :

If in a parallelogram $ABDC$, the coordinates of $A, B$ and $C$ are respectively $(1, 2), (3, 4)$ and $(2, 5),$ then the equation of the diagonal $AD$ is :

If $m$ is chosen in the quadratic equation $(m^2 + 1) x^2 - 3x + (m^2 + 1)^2 = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

If some three consecutive in the binomial expansion of $(x + 1)^n$ is powers of $x$ are in the ratio $2 : 15 : 70$, then the average of these three coefficient is :-

If speed $(V)$, acceleration $(A)$ and force $(F)$ are considered as fundamental units, the dimension of Young's modulus will be :

If $\sum^\limits{25}_{r=0} \left\{^{50}C_{r} . ^{50-r}C_{25-r}\right\}=K\left(^{50}C_{25}\right) $ , then $K$ is equal to :

If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be : -

If the angle of elevation of a cloud from a point $P$ which is $25\, m$ above a lake be $30^\circ$ and the angle of depression of reflection of the cloud in the lake from $P$ be $60^\circ$, then the height of the cloud (in meters) from the surface of the lake is :

If the angular momentum of a planet of mass $m$, moving around the Sun in a circular orbit is $L$, about the center of the Sun, its areal velocity is :

If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then $k$ is equal to :

If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction ${Zn(s) + cu^{2+} (aq) <=> Zn^{2+} (aq) + Cu(s)}$ at 300 K is approximately. ${(R = 8 \; JK^{-1} \; mol^{-1} , F = 96000 \; C \; mol^{-1})}$

If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observation is :

If the truth value of the statement $P \to ( \sim p \vee r)$ is false(F), then the truth values of the statements $p, q, r$ are respectively :

If three distinct numbers a,b,c are in G.P. and the equations $ax^2 + 2bx + c = 0$ and $dx^2 + 2ex + f = 0$ have a common root, then which one of the following statements is correct?

If $x = 3 \,tan \,t $ and $y = 3 \,sec \,t$, then the value of $\frac{d^2 y}{dx^2}$ at $t = \frac{\pi}{4}$, is :

If [$x$] denotes the greatest integer $\le x$, then the system of linear equations [$sin\,\theta$] x + [$-cos\,\theta$]y=0 [$cot\,\theta$] $x + y = 0$

If $\frac{z-\alpha}{z+\alpha} \left(\alpha\in R\right) $ is a purely imaginary number and $|z| = 2$, then a value of $\alpha$ is :