List of top Questions asked in JEE Main- 2019

If the line \(ax+y=c\), touches both the curves \(x^2+y^2=1\) and \(y^2=4\sqrt{2}\,x\), then \(|c|\) is equal to :

If \(5x+9=0\) is the directrix of the hyperbola \(16x^2-9y^2=144\), then its corresponding focus is :

The angles A, B and C of a triangle ABC are in A.P. and \(a:b=1:\sqrt{3}\). If \(c=4\) cm, then the area (in sq. cm) of this triangle is :

The negation of the Boolean expression \(\sim s \vee (\sim r \wedge s)\) is equivalent to :

The locus of the centres of the circles, which touch the circle, \(x^2+y^2=1\) externally, also touch the y-axis and lie in the first quadrant, is :

A perpendicular is drawn from a point on the line \(\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{1}\) to the plane \(x+y+z=3\) such that the foot of the perpendicular Q also lies on the plane \(x-y+z=3\). Then the co-ordinates of Q are :

The smallest natural number n, such that the coefficient of x in the expansion of \(\left(x^2+\frac{1}{x^3}\right)^n\) is \(^{n}\mathrm{C}_{23}\), is :

The integral \(\displaystyle\int_{\pi/6}^{\pi/3}\sec^{2/3}x\;\mathrm{cosec}^{4/3}x\,dx\) is equal to :

If \(\cos^{-1}x-\cos^{-1}\dfrac{y}{2}=\alpha\), where \(-1\le x\le1\), \(-2\le y\le2\), \(x\le\dfrac{y}{2}\), then for all \(x,y\), \(4x^2-4xy\cos\alpha+y^2\) is equal to :

Let \(y=y(x)\) be the solution of the differential equation \(\dfrac{dy}{dx}+y\tan x=2x+x^2\tan x\), \(x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\), such that \(y(0)=1\). Then :

The area (in sq. units) of the region bounded by the curves \(y=2^x\) and \(y=|x+1|\), in the first quadrant is :

Lines are drawn parallel to the line \(4x-3y+2=0\), at a distance \(\dfrac35\) from the origin. Then which one of the following points lies on any of these lines ?

If both the mean and the standard deviation of 50 observations \(x_1,x_2,\ldots,x_{50}\) are equal to 16, then the mean of \((x_1-4)^2,(x_2-4)^2,\ldots,(x_{50}-4)^2\) is :

If \(\displaystyle\lim_{x\to 1}\frac{x^2-ax+b}{x-1}=5\), then \(a+b\) is equal to :

A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm\(^3\)/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :

The distance of the point having position vector \(-\hat{i}+2\hat{j}+6\hat{k}\) from the straight line passing through the point \((2,3,-4)\) and parallel to the vector \(6\hat{i}+3\hat{j}-4\hat{k}\) is :

Let \(f(x)=\log_e(\sin x)\), \((0\lt x\lt\pi)\) and \(g(x)=\sin^{-1}(e^{-x})\), \((x\ge 0)\). If \(\alpha\) is a positive real number such that \(a=(f\circ g)^{\prime}(\alpha)\) and \(b=(f\circ g)(\alpha)\), then :

Let \(\lambda\) be a real number for which the system of linear equations \(x+y+z=6,\; 4x+\lambda y-\lambda z=\lambda-2,\; 3x+2y-4z=-5\) has infinitely many solutions. Then \(\lambda\) is a root of the quadratic equation :

If \(\displaystyle\int x^5e^{-x^2}\,dx=g(x)e^{-x^2}+c\), where \(c\) is a constant of integration, then \(g(-1)\) is equal to :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is :

The sum of the real roots of the equation
\(\begin{vmatrix} x & -6 & -1 \\ 2 & -3x & x-3 \\ -3 & 2x & x+2 \end{vmatrix}=0\)
is equal to :

The correct order of catenation is :

Consider the following table :

Gas	\(a/(\mathrm{kPa\ dm^6\ mol^{-1}})\)	\(b/(\mathrm{dm^3\ mol^{-1}})\)
A	642.32	0.05196
B	155.21	0.04136
C	431.91	0.05196
D	155.21	0.4382

\(a\) and \(b\) are van der Waals constants. The correct statement about the gases is :

The synonym for water gas when used in the production of methanol is :

The regions of the atmosphere, where clouds form and where we live, respectively, are :