List of top Questions asked in JEE Main- 2019

The force of interaction between two atoms is given by \(F = \alpha\beta\exp\left(-\frac{x^2}{\alpha kt}\right)\); where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha\) and \(\beta\) are two constants. The dimension of \(\beta\) is :

An electromagnetic wave of intensity 50 Wm\(^{-2}\) enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be :

If the de Broglie wavelength of an electron is equal to the \(10^{-3}\) times the wavelength of a photon of frequency \(6 \times 10^{14}\) Hz, then the speed of electron is equal to : (Speed of light = \(3 \times 10^{8}\) m/s, Planck's constant = \(6.63 \times 10^{-34}\) J.s, Mass of electron = \(9.1 \times 10^{-31}\) kg)

A liquid of density \(\rho\) is coming out of a hose pipe of radius \(a\) with horizontal speed \(v\) and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be :

In a Wheatstone bridge (see fig.), Resistances \(P\) and \(Q\) are approximately equal. When \(R = 400\ \Omega\), the bridge is balanced. On interchanging \(P\) and \(Q\), the value of \(R\), for balance, is \(405\ \Omega\). The value of \(X\) is close to :

The given graph shows variation (with distance \(r\) form centre) of :

A slab is subjected to two forces \(\vec{F_1}\) and \(\vec{F_2}\) of same magnitude \(F\) as shown in the figure. Force \(\vec{F_2}\) is in XY-plane while force \(\vec{F_1}\) acts along z-axis at the point \((2\hat{i} + 3\hat{j})\). The moment of these forces about point O will be :

A particle is moving along a circular path with a constant speed of \(10\ \mathrm{ms^{-1}}\). What is the magnitude of the change in velocity of the particle, when it moves through an angle of \(60^\circ\) around the centre of the circle?

An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is \(I_0\). If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. then :

Three charges \(Q\), \(+q\) and \(+q\) are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of \(Q\) is :

If \(q\) is false and \(p \wedge q \leftrightarrow r\) is true, then which one of the following statements is a tautology ?

The value of \(r\) for which \({}^{20}C_r\,{}^{20}C_0 + {}^{20}C_{r-1}\,{}^{20}C_1 + {}^{20}C_{r-2}\,{}^{20}C_2 + \ldots + {}^{20}C_0\,{}^{20}C_r\) is maximum, is

In a triangle, the sum of lengths of two sides is \(x\) and the product of the lengths of the same two sides is \(y\). If \(x^2 - c^2 = y\), where \(c\) is the length of the third side of the triangle, then the circumradius of the triangle is :

If tangents are drawn to the ellipse \(x^2 + 2y^2 = 2\) at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :

The direction ratios of normal to the plane through the points \((0, -1, 0)\) and \((0, 0, 1)\) and making an angle \(\frac{\pi}{4}\) with the plane \(y - z + 5 = 0\) are :

The plane containing the line \(\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z-1}{3}\) and also containing its projection on the plane \(2x + 3y - z = 5\), contains which one of the following points ?

Let \(\vec{a} = \hat{i} + 2\hat{j} + 4\hat{k}\), \(\vec{b} = \hat{i} + \lambda\hat{j} + 4\hat{k}\) and \(\vec{c} = 2\hat{i} + 4\hat{j} + (\lambda^2 - 1)\hat{k}\) be coplanar vectors. Then the non-zero vector \(\vec{a} \times \vec{c}\) is :

Equation of a common tangent to the parabola \(y^2 = 4x\) and the hyperbola \(xy = 2\) is :

Let \(f_k(x) = \frac{1}{k}\left(\sin^k x + \cos^k x\right)\) for \(k = 1, 2, 3, \dots\) Then for all \(x \in \mathbb{R}\), the value of \(f_4(x) - f_6(x)\) is equal to

Let \(\left(-2 - \frac{1}{3}i\right)^3 = \frac{x + iy}{27}\ (i = \sqrt{-1})\), where x and y are real numbers, then \(y - x\) equals :

If \(x\log_e(\log_e x) - x^2 + y^2 = 4\ (y \gt 0)\), then \(\frac{dy}{dx}\) at \(x = e\) is equal to :

Let \([x]\) denote the greatest integer less than or equal to \(x\). Then \(\lim_{x \to 0} \frac{\tan(\pi \sin^2 x) + \left(|x| - \sin(x[x])\right)^2}{x^2}\)

If \(y(x)\) is the solution of the differential equation \(\frac{dy}{dx} + \left(\frac{2x+1}{x}\right)y = e^{-2x},\ x \gt 0\), where \(y(1) = \frac{1}{2}e^{-2}\), then

The maximum value of the function \(f(x) = 3x^3 - 18x^2 + 27x - 40\) on the set \(S = \{x \in \mathbb{R} : x^2 + 30 \le 11x\}\) is :