List of top Questions asked in JEE Main- 2019

The term independent of x in the expansion of $\bigg(\frac{1}{60} - \frac{x^8}{81}\bigg). \bigg(2x^2 - \frac{3}{x^2}\bigg)^6$ is equal to:

A magnetic compass needle oscillates $30$ times per minute at a place where the dip is $45^{\circ}$, and $40$ times per minute where the dip is $30^{\circ}$. If $B_1$ and $B_2$ are respectively the total magnetic field due to the earth at the two places, then the ratio $B_1/B_2$ is best given by :

A man (mass = $50\, kg$) and his son (mass = $20\, kg$) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\, ms^{-1}$ with respect to the man. The speed of the man with respect to the surface is :

A rod of mass $'M'$ and length $'2L'$ is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of $'m'$ are attached at distance $'L/2'$ from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value of ratio $m/M$ is close to :

A series $AC$ circuit containing an inductor $(20\, mH)$, a capacitor $(120 \; \mu F) $and a resistor $(60 \Omega)$ is driven by an AC source of $24\, V/50 \,Hz$. The energy dissipated in the circuit in $60\, s$ is :

The statement that is INCORRECT about the interstitial compounds is :

An amplitude modulated signal is plotted below:

Which one of the following best describes the above signal ?

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 :