List of top Questions asked in JEE Main

A load of mass $M\, kg$ is suspended from a steel wire of length $2\, m$ and radius $1.0\, mm$ in Searle's apparatus experiment. The increase in length produced in the wire is $4.0\, mm$. Now the load is fully immersed in a liquid of relative density $2$. The relative density of the material of load is $8$. The new value of increase in length of the steel wire is :

An organic compound $'A'$ is oxidized with ${Na2O2}$ followed by boiling with ${HNO3}$. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compound is :

The correct order of the atomic radii of $C, Cs, Al$ and $S$ is :

The correct structure of histidine in a strongly acidic solution (pH=2) is

$ {NO_2}$ required for a reaction is produced by the decomposition of $ {N2O5}$ in $ {CCl4}$ as per the equation $ { 2N2O5(g) -> 4NO2(g) + O2(g).}$ The initial concentration of $ {N2O5}$ is $3.00\, mol$ $ {L^{-1}}$ and it is $2.75\, mol$ $ {L^{-1}}$ after $30$ minutes. The rate of formation of $ {NO2}$ is :

The principle of column chromatography is :

In the figure, given that $V_{BB}$ supply can vary from $0$ to $5.0 \,V, V_{CC} = 5\,V, \beta_{dc} = 200, R_B = 100 \,k\,\Omega, R_C=l\, k\Omega$ and $V_{BE}=1.0\, V$, The minimum base current and the input voltage at which the transistor will go to saturation, will be, respectively :

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?

A plane is inclined at an angle $\alpha = 30^{\circ}$ with a respect to the horizontal. A particle is projected with a speed $u = 2 ms^{-1}$ from the base of the plane, making an angle $q = 15^{\circ}$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to : (Take $g = 10 \; ms^{-2}$)

A cylindrical plastic bottle of negligible mass is filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is $2.5\, cm$ then $\omega$ close to : (density of water = $10^3 \; kg / m^3$)

A plano convex lens of refractive index $\mu_1$ and focal length $f_1$ is kept in contact with another plano concave lens of refractive index $\mu_2$ and focal length $f_2$. If the radius of curvature of their spherical faces is R each and $f_1 = 2f_2$, then $\mu_1$ and $\mu_2$ are related as :

A string of length $1\, m$ and mass $5\, g$ is fixed at both ends. The tension in the string is $8.0\, N$. The siring is set into vibration using an external vibrator of frequency $100\, Hz$. The separation between successive nodes on the string is close to :

A travelling harmonic wave is represented by the equation $y (x, t) = 10^{-3} sin (50 t + 2x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave? The wave is propagating along the

A uniform metallic wire has a resistance of $18 \; \Omega$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is :

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation $VT = K$, where $K$ is a constant. In this process the temperature of the gas is incresed by $\Delta T$. The amount of heat absorbed by gas is (R is gas constant) :

The elastic limit of brass is $379\, MPa$. What should be the minimum diameter of a brass rod if it is to support a $400 \,N$ load without exceeding its elastic limit ?

The number of integral values of m for which the equation $(1 + m^2)x^2 - 2(1 + 3m)x + (1 + 8m) = 0$ has no real root is :

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$ then |d| equals :

The logical statement $[\sim (\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to:

Let the equations of two sides of a triangle be $3x - 2y + 6 = 0$ and $4x + 5y - 20 = 0$. If the orthocentre of this triangle is at $(1, 1)$, then the equation of its third side is :

A circle cuts a chord of length $4a$ on the x-axis and passes through a point on the y-axis, distant $2b$ from the origin. Then the locus of the centre of this circle, is :

A student scores the following marks in five tests : $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

Considering only the principal values of inverse functions, the set $A = \{ x \ge 0 : \tan^{-1} (2x) + \tan^{-1} (3x) = \frac{\pi}{4} \}$

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 :

The IUPAC symbol for the element with atomic number $119$ would be :