List of top Questions asked in JEE Main- 2019

An insulating thin rod of length $\ell$ has a x linear charge density $p(x) = \rho_0 \frac{x}{\ell}$ on it . The rod is rotated about an axis passing through the origin $(x = 0)$ and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is :

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 bag contains $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, the $\left(\frac{\text{mean} \; \text{of} \; X}{\text{standard} \; \text{deviation} \; \text{of} \; X }\right)$ is equal to :

If $A = \begin{bmatrix}e^{t}&e^{t} \cos t&e^{-t}\sin t\\ e^{t}&-e^{t} \cos t -e^{-t}\sin t&-e^{-t} \sin t+ e^{-t} \cos t\\ e^{t}&2e^{-t} \sin t&-2e^{-t} \cos t\end{bmatrix} $ Then $A$ is -

The area of the region $A = [(x, y): 0 \leq y \leq x|x|+1$ and $-1 \leq x \leq 1]$ in s units is :

Let $z_0$ be a root of the quadratic equation, $x^2 + x + 1 = 0$. If $z = 3 + 6iz_0^{81} -3iz_0^{93}$ , then arg $z$ is equal to :

Let $\vec{a} = \hat{i} + \hat{j} + \sqrt{2} \hat{k} , \vec{b} = b_1 \hat{i} + b_2 \hat{j} + \sqrt{2} \hat{k}$ and $\vec{c} = 5 \hat{i} + \hat{j} + \sqrt{2} \hat{k}$ be three vectors such that the projection vector of $\vec{b}$ on $\vec{a}$ , If $\vec{a} + \vec{b}$ is perpendicular to $\vec{c}$, then $| \vec{b}|$ is equal to :

Let $A(4,-4)$ and $B(9,6)$ be points on the parabola, $y^2 + 4x$. Let $C$ be chosen on the arc $AOB$ of the parabola, where $O$ is the origin, such that the area of $\Delta ACB$ is maximum. Then, the area (in s units) of $\Delta ACB$, is :

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

An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :

If $0 \le x < \frac{\pi}{2}$ , then the number of values of $ x$ for which $sin \,x-sin\,2x+sin\,3x = 0$, is

The equation of the plane containing the $\frac{x}{2} = \frac{y}{3} =\frac{z}{4} $ and perpendicular to the plane containing the straight lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{2} $ and $\frac{x}{4} = \frac{y}{2} = \frac{z}{3} $ is :

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 test particle is moving in a circular orbit in the gravitational field produced by a mass density \(\rho(r) = \frac{K}{r^2}\). Identify the correct relation between the radius \(R\) of the particle's orbit and it's period \(T\) :

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $2 \,N$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\, N$. The coefficient of static friction between the block and the plane is : [Take $g = 10\, m/s^2$]

A block of mass $10\, kg$ is kept on a rough inclined plane as shown in the figure. A force of $3\, N$ is applied on the block. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$, such that the block doesnot move downward ? (take $g = 10 \; ms^{-2}$)

A block of mass $m$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is :

A $27\, mW$ laser beam has a cross-sectional area of $10 \; mm^2$. The magnitude of the maximum electric field in this electromagnetic wave is given by [Given permittivity of space $\in_0 = 9 \times 10^{-12} $ SI units, Speed of light $c = 3 \times 10^8 \; m/s$] :

A $20$ Henry inductor coil is connected to a $10$ ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is :

A $2\, W$ carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is :

A $15\, g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ}C$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/ K mole]

A $10\, mg$ effervescent tablet contianing sodium bicarbonate and oxalic acid releases $0.25\, ml$ of ${CO_2}$ at $T$ = $298.15\, K$ and $p = 1$ bar. If molar volume of ${CO_2}$ is $25.0\, L$ under such condition, what is the percentage of sodium bicarbonate in each tablet ? [Molar mass of ${NaHCO_3 = 84 \; g \; mol^{-1}}$]

The magnetic field of an electromagnetic wave is given by : $\vec{B} =1.6 \times10^{-6} \cos\left(2\times10^{7} z +6 \times10^{15}t\right)\left(2\hat{i} +\hat{j}\right) \frac{Wb}{m^{2}} $ The associated electric field will be :-

Calculate the limit of resolution of a telescope objective having a diameter of $200\, cm$, if it has to detect light of wavelength $500\, nm$ coming from a star :