List of top Questions asked in JEE Main- 2019

An electric field of 1000 V/m is applied to an electric dipole at angle of \( 45^\circ \). The value of electric dipole moment is \( 10^{-29} \) C.m. What is the potential energy of the electric dipole?

A particle moves from the point \( (2.0\hat{i} + 4.0\hat{j}) \) m, at t = 0, with an initial velocity \( (5.0\hat{i} + 4.0\hat{j}) \) \( \mathrm{ms^{-1}} \). It is acted upon by a constant force which produces a constant acceleration \( (4.0\hat{i} + 4.0\hat{j}) \) \( \mathrm{ms^{-2}} \). What is the distance of the particle from the origin at time 2 s?

The region between \( y = 0 \) and \( y = d \) contains a magnetic field \( \overrightarrow{B} = B\hat{z} \). A particle of mass m and charge q enters the region with a velocity \( \overrightarrow{v} = v\hat{i} \). If \( d = \frac{mv}{2qB} \), the acceleration of the charged particle at the point of its emergence at the other side is :

Let \( f(x) = \frac{x}{\sqrt{a^2+x^2}} - \frac{d-x}{\sqrt{b^2+(d-x)^2}} \), \( x \in R \), where a, b and d are non-zero real constants. Then :

If the point \( (2, \alpha, \beta) \) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane \( 2x - 5y = 15 \), then \( 2\alpha - 3\beta \) is equal to

Two lines \( \frac{x-3}{1} = \frac{y+1}{3} = \frac{z-6}{-1} \) and \( \frac{x+5}{7} = \frac{y-2}{-6} = \frac{z-3}{4} \) intersect at the point R. The reflection of R in the xy-plane has coordinates :

Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :

Let \( S_n = 1 + q + q^2 + \ldots + q^n \) and \( T_n = 1 + \left(\frac{q+1}{2}\right) + \left(\frac{q+1}{2}\right)^2 + \ldots + \left(\frac{q+1}{2}\right)^n \) where q is a real number and \( q \ne 1 \). If \( {}^{101}C_1 + {}^{101}C_2 \cdot S_1 + \ldots + {}^{101}C_{101}\cdot S_{100} = \alpha T_{100} \) then \( \alpha \) is equal to

The circuit shown below contains two ideal diodes, each with a forward resistance of \( 50\ \Omega \). If the battery voltage is 6 V, the current through the \( 100\ \Omega \) resistance (in Amperes) is :

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :

If \(\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix} = (a+b+c)(x + a + b + c)^2\), \(x \ne 0\), then x is equal to :

\( \lim_{x\to 0} \frac{x\cot(4x)}{\sin^2 x\,\cot^2(2x)} \) is equal to :

The integral \(\int_{\pi/6}^{\pi/4}\frac{dx}{\sin 2x\left(\tan^5x + \cot^5x\right)}\) equals :

If \( \int \frac{x+1}{\sqrt{2x-1}}\,dx = f(x)\sqrt{2x-1} + C \), where C is a constant of integration, then \( f(x) \) is equal to :

If 19^th term of a non-zero A.P. is zero, then its (49^th term) : (29^th term) is :

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(x^2\sin\theta - x(\sin\theta\cos\theta + 1) + \cos\theta = 0\) \((0 \lt \theta \lt 45^{\circ})\), and \(\alpha \lt \beta\). Then \(\sum_{n=0}^{\infty}\left(\alpha^n + \frac{(-1)^n}{\beta^n}\right)\) is equal to :

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \(\frac{x^m y^n}{(1 + x^{2m})(1 + y^{2n})}\) is :

Let \(\sqrt{3}\,\hat{i} + \hat{j}\), \(\hat{i} + \sqrt{3}\,\hat{j}\) and \(\beta\hat{i} + (1-\beta)\hat{j}\) respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is \(\frac{3}{\sqrt{2}}\), then the sum of all possible values of \(\beta\) is :

The number of functions f from \(\{1, 2, 3, \ldots, 20\}\) onto \(\{1, 2, 3, \ldots, 20\}\) such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :

All x satisfying the inequality \((\cot^{-1}x)^2 - 7(\cot^{-1}x) + 10 \gt 0\), lie in the interval :

Let K be the set of all real values of x where the function \(f(x) = \sin |x| - |x| + 2(x - \pi)\cos |x|\) is not differentiable. Then the set K is equal to :

The area (in sq. units) in the first quadrant bounded by the parabola, \(y = x^2 + 1\), the tangent to it at the point (2, 5) and the coordinate axes is :

Let a function \(f : (0, \infty) \to (0, \infty)\) be defined by \(f(x) = \left|1 - \frac{1}{x}\right|\). Then f is :

If the area of the triangle whose one vertex is at the vertex of the parabola, \(y^2 + 4(x - a^2) = 0\) and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :