List of top Questions asked in JEE Main

A magnetic needle of magnetic moment $6.7 \times 10^{-2} \, Am^2$ and moment of inertia $7.5 \times 10^{-6} \, kg \, m^2$ is performing simple harmonic oscillations in a magnetic field of $0.01\, T$. Time taken for $10$ complete oscillations is :

On treatment of $100\, mL$ of $0.1\, M$ solution of $CoCl _{3} \cdot 6 H _{2} O$ with excess $AgNO _{3} ; 1.2 \times 10^{22}$ ions are precipitated. The complex is

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is $'a'$, the closest approach between two atoms in metallic crystal will be :

The rate of a reaction quadruples when the temperature changes from $300$ to $310\, K$. The activation energy of this reaction is : (Assume activation energy and pre-exponential factor are independent of temperature; $ln\, 2 = 0.693; R=8.314 \,J$ $mol^{-1} \, K^{-1}$)

The Tyndall effect is observed only when following conditions are satisfied (a) The diameter of the dispersed particles is much smaller than the wavelength of the light used. (b) The diameter of the dispersed particle is not much smaller than the wavelength of the light used (c) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude (d) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude

The number of $S=O$ and $S-OH$ bonds present in peroxodisulphuric acid and pyrosulphuric acid respectively are :

A particle is executing simple harmonic motion with a time period $T$. At time $t = 0$, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like :

In an experiment a sphere of aluminium of mass 0.20 kg is heated upto $150^{\circ}C$. Immediately, it is put into water of volume 150 cc at $27^{\circ}C$ kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is $40^{\circ}C$. The specific heat of aluminium is : (take 4.2 Joule=1 calorie)

$XeF_6$ on partial hydrolysis with water produces a compound $'X'$. The same compound $'X'$ is formed when $XeF_6$ reacts with silica. The compound $'X'$ is :

A person trying to lose weight by burning at lifts a mass of $10\, kg$ upto a height of $1\, m$ $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies $3.8 \times 10^7 \, J$ of energy per kg which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g = 9.8 \, ms^{-2}$ :

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :

$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C$ ln $(BD)$ holds true. Then which of the combination is not a meaningful quantity ?

The artificial sweetener that has the highest sweetness value in comparison to cane sugar is :

$'n'$ moles of an ideal gas undergoes a process $A \to B $ as shown in the figure. The maximum temperature of the gas during the process will be :

Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

The number of distinct real roots of the equation, $\begin{vmatrix}\cos x&\sin x &\sin x\\ \sin x&\cos x&\sin x\\ \sin x&\sin x&\cos x\end{vmatrix}= 0$ in the interval $ \left[- \frac{\pi}{4}, \frac{\pi}{4}\right]$ is :

If the number of terms in the expansion of $\left( 1 - \frac{2}{x} + \frac{4}{x^2} \right)^n , x \neq 0$ , is $28$ , then the sum of the coefficients of all the terms in this expansion, is :

If the tangent at a point $P$, with parameter $t$, on the curve $x = 4t^2 + 3, y = 8t^3 - 1, t \in R$, meets the curve again at a point $Q$, then the coordinates of $Q$ are :

For $ x \epsilon R , f (x) = | \log 2 - \sin x|$ and $g(x) = f(f(x))$, then :

The point $(2, 1)$ is translated parallel to the line $L : x-y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is :

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3} + \frac{y^2}{4} = 4 $ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does NOT lie on it ?

If the $2^{nd}, 5^{th}$ and $9^{th}$ terms of a non-constant $A.P.$ are in $G.P.$, then the common ratio of this $G.P.$ is :

At very high pressures, the compressibility factor of one mole of a gas is given by :

$P$ and $Q$ are two distinct points on the parabola, $y^2 = 4x$, with parameters $t$ and $t_1$ respectively. If the normal at $P$ passes through $Q$, then the minimum value of $t^2_1$ is :

If $A = \begin{bmatrix}5a &-b\\ 3&2\end{bmatrix}$ and $A$ adj $A$ = $AA^T$ , then $5a + b$ is equal to :