List of top Questions asked in JEE Main- 2019

Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of \(10^{-3}\) Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is :-

In a conductor, if the number of conduction electrons per unit volume is \(8.5\times10^{28}\ \mathrm{m^{-3}}\) and mean free time is \(25\ \mathrm{fs}\) (femto second), it's approximate resistivity is :- \((m_e=9.1\times10^{-31}\ \mathrm{kg})\)

Let P be the plane, which contains the line of intersection of the planes, \(x+y+z-6=0\) and \(2x+3y+z+5=0\) and it is perpendicular to the xy-plane. Then the distance of the point \((0,0,256)\) from P is equal to :

The common tangent to the circles \(x^2+y^2=4\) and \(x^2+y^2+6x+8y-24=0\) also passes through the point :

A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass 'm', which move at angle \(45^\circ\) with respect to the origianl direction. The speed of each of the moving particle will be :-

Two poles standing on a horizontal ground are of heights \(5\) m and \(10\) m respectively. The line joining their tops makes an angle of \(15^\circ\) with ground. Then the distance (in m) between the poles, is :-

If the two lines x + (a - 1) y = 1 and 2x + a²y = 1 \((a \in R - \{0, 1\})\) are perpendicular, then the distance of their point of intersection from the origin is :

If the tangent to the parabola \(y^2=x\) at a point \((\alpha,\beta)\), \((\beta\gt 0)\) is also a tangent to the ellipse, \(x^2+2y^2=1\), then \(\alpha\) is equal to :

The value of the integral \(\int_0^1 x\cot^{-1}(1-x^2+x^4)\,dx\) is :-

The sum of the series \(1+2\times 3+3\times 5+4\times 7+\ldots\) upto 11th term is :-

If the system of equations 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non-trival solution (x, y, z), then \(\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k\) is equal to :-

Let z \(\in\) C be such that |z| \(\lt\) 1. If \(\omega = \frac{5 + 3z}{5(1 - z)}\), then :

The area (in sq. units) of the region \(A = \left\{(x, y) : \frac{y^2}{2} \le x \le y + 4\right\}\) is :-

\(\int e^{\sec x}\left(\sec x\tan x\, f(x) + \sec x\tan x + \sec^2 x\right)dx = e^{\sec x} f(x) + C\) then a possible choice of f(x) is :-

If \(f(x) = [x] - \left[\frac{x}{4}\right],\ x \in \mathbb{R}\), where [x] denotes the greatest integer function, then

A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (-8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :

The domain of the definition of the function \(f(x) = \frac{1}{4 - x^2} + \log_{10}(x^3 - x)\) is

The total number of matrices \(A = \begin{pmatrix} 0 & 2y & 1 \\ 2x & y & -1 \\ 2x & -y & 1 \end{pmatrix}\) \((x, y \in R,\ x \ne y)\) for which \(A^{T}A = 3I_3\) is :-

If \(\cos x\,\frac{dy}{dx} - y\sin x = 6x\), \(\left(0 \lt x \lt \frac{\pi}{2}\right)\) and \(y\left(\frac{\pi}{3}\right) = 0\) then \(y\left(\frac{\pi}{6}\right)\) is equal to :-

The value of \(\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ\) is :-

Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :-

If f : R \(\to\) R is a differentiable function and f(2) = 6, then \(\displaystyle\lim_{x\to 2}\frac{\int_{6}^{f(x)} 2t\,dt}{(x-2)}\) is :-

If the function \(f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|x - \pi| + 3, & x \gt 5 \end{cases}\) is continuous at x = 5, then the value of a - b is :-

If the sum and product of the first three term in an A.P. are 33 and 1155, respectively, then a value of its 11^th term is :-

Consider the van der Waals constants, a and b, for the following gases.

Gas	Ar	Ne	Kr	Xe
a/ (atm dm6 mol-2)	1.3	0.2	5.1	4.1
b/ (10-2 dm3 mol-1)	3.2	1.7	1.0	5.0

Which gas is expected to have the highest critical temperature?