List of top Questions asked in JEE Main- 2019

The maximum value of \(3\cos\theta + 5\sin\left(\theta - \frac{\pi}{6}\right)\) for any real value of \(\theta\) is :

If the vertices of a hyperbola be at \((-2, 0)\) and \((2, 0)\) and one of its foci be at \((-3, 0)\), then which one of the following points does not lie on this hyperbola?

A tetrahedron has vertices \(P(1, 2, 1)\), \(Q(2, 1, 3)\), \(R(-1, 1, 2)\) and \(O(0, 0, 0)\). The angle between the faces OPQ and PQR is :

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, \(y = 12 - x^2\) such that the rectangle lies inside the parabola, is :

\(\displaystyle\lim_{x \to \pi/4} \frac{\cot^3 x - \tan x}{\cos\left(x + \frac{\pi}{4}\right)}\) is :

The area (in sq. units) of the region bounded by the parabola, \(y = x^2 + 2\) and the lines, \(y = x + 1\), \(x = 0\) and \(x = 3\), is

Let \(P = \begin{bmatrix} 1 & 0 & 0\\ 3 & 1 & 0\\ 9 & 3 & 1\end{bmatrix}\) and \(Q = [q_{ij}]\) be two \(3 \times 3\) matrices such that \(Q - P^5 = I_3\). Then \(\frac{q_{21} + q_{31}}{q_{32}}\) is equal to :

If \(\lambda\) be the ratio of the roots of the quadratic equation in \(x\), \(3m^2x^2 + m(m - 4)x + 2 = 0\), then the least value of \(m\) for which \(\lambda + \frac{1}{\lambda} = 1\), is

An ordered pair \((\alpha, \beta)\) for which the system of linear equations
\((1 + \alpha)x + \beta y + z = 2\)
\(\alpha x + (1 + \beta)y + z = 3\)
\(\alpha x + \beta y + 2z = 2\)
has a unique solution, is :

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of \(\left(2^{1/3} + \frac{1}{2(3)^{1/3}}\right)^{10}\) is :

Let \(S = \{1, 2, 3, \ldots, 100\}\). The number of non-empty subsets \(A\) of \(S\) such that the product of elements in \(A\) is even is :

Let \(P(4, -4)\) and \(Q(9, 6)\) be two points on the parabola, \(y^2 = 4x\) and let \(x\) be any point on the arc \(POQ\) of this parabola, where \(O\) is the vertex of this parabola, such that the area of \(\Delta PXQ\) is maximum. Then this maximum area (in sq. units) is :

Let \(S\) be the set of all points in \((-\pi, \pi)\) at which the function, \(f(x) = \min\{\sin x, \cos x\}\) is not differentiable. Then \(S\) is a subset of which of the following ?

Let \(f\) and \(g\) be continuous functions on \([0, a]\) such that \(f(x) = f(a - x)\) and \(g(x) + g(a - x) = 4\), then \(\int_0^a f(x)g(x)\,dx\) is equal to :

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

Let \(y = y(x)\) be the solution of the differential equation, \(x\frac{dy}{dx} + y = x\log_e x,\ (x > 1)\). If \(2y(2) = \log_e 4 - 1\), then \(y(e)\) is equal to :

The correct match between Item I and Item II is :

Item I		Item II
(A)	Allosteric effect	(P)	Molecule binding to the active site of enzyme
(B)	Competitive inhibitor	(Q)	Molecule crucial for communication in the body
(C)	Receptor	(R)	Molecule binding to a site other than the active site of enzyme
(D)	Poison	(S)	Molecule binding to the enzyme covalently

The higher concentration of which gas in air can cause stiffness of flower buds?

The hydride that is NOT electron deficient :

Among the colloids cheese (C), milk (M), and smoke (S), the correct combination of the dispersed phase and dispersion medium, respectively is :

The homopolymer formed from 4-hydroxy-butanoic acid is :

Taj Mahal is being slowly disfigured and discoloured. This is primarily due to :

The relative stability of +1 oxidation state of group 13 elements follows the order :

Match the following items in column I with the corresponding items in column II.

Item I		Item II
(i)	Na2CO3.10H2O	(A)	Portland cement ingredient
(ii)	Mg(HCO3)2	(B)	Castner-Kellner process
(iii)	NaOH	(C)	Solvay process
(iv)	Ca3Al2O6	(D)	Temporary hardness

The reaction that does NOT define calcination is :