List of top Questions asked in JEE Main- 2019

Let \(f:\mathbb{R}\to\mathbb{R}\) be a continuously differentiable function such that \(f(2)=6\) and \(f'(2)=\frac{1}{48}\). If
\(\int_{6}^{f(x)} 4t^{3}\,dt=(x-2)\,g(x)\),
then \(\lim_{x\to 2} g(x)\) is equal to :

If the area (in sq. units) of the region \(\{(x, y) : y^2 \le 4x,\ x + y \le 1,\ x \ge 0,\ y \ge 0\}\) is \(a\sqrt{2} + b\), then \(a - b\) is equal to :

The equation \(|z - i| = |z - 1|\), \(i = \sqrt{-1}\), represents :

If \(\alpha\) and \(\beta\) are the roots of the equation \(375x^2 - 25x - 2 = 0\), then \(\lim_{n\to\infty}\sum_{r=1}^{n}\alpha^r + \lim_{n\to\infty}\sum_{r=1}^{n}\beta^r\) is equal to :

If \(e^y + xy = e\), the ordered pair \(\left(\frac{dy}{dx}, \frac{d^2y}{dx^2}\right)\) at \(x = 0\) is equal to :

The coefficient of \(x^{18}\) in the product \((1 + x)(1 - x)^{10}(1 + x + x^2)^9\) is :

If \(B = \begin{bmatrix} 5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & -1 \end{bmatrix}\) is the inverse of a \(3 \times 3\) matrix A, then the sum of all values of \(\alpha\) for which det(A) + 1 = 0, is :

If m is the minimum value of k for which the function \(f(x) = x\sqrt{kx - x^2}\) is increasing in the interval [0,3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to :

If the data \(x_1, x_2, \ldots\ldots, x_{10}\) is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :

If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = \(\begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix}\), then AB is equal to :

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :

Consider the differential equation, \(y^2\,dx + \left(x - \frac{1}{y}\right)dy = 0\), If value of y is 1 when x = 1, then the value of x for which y = 2, is :

The value of \(\sin^{-1}\left(\frac{12}{13}\right) - \sin^{-1}\left(\frac{3}{5}\right)\) is equal to :

If \(\int_0^{\pi/2} \frac{\cot x}{\cot x + \operatorname{cosec} x}\,dx = m(\pi + n)\), then \(m \cdot n\) is equal to

The correct statement is :

Number of stereo centers present in linear and cyclic structures of glucose are respectively :

The number of pentagons in \(\mathrm{C_{60}}\) and trigons (triangles) in white phosphorus, respectively, are :

A hydrated solid X on heating initially gives a monohydrated compound Y. Y upon heating above 373 K leads to an anhydrous white powder Z. X and Z, respectively, are :

The correct match between Item-I and Item-II is :

	Item - I		Item - II
(a)	High density polythene	(I)	Peroxide catalyst
(b)	Polyacrylonitrile	(II)	Condensation at high temperature & pressure
(c)	Novolac	(III)	Ziegler-Natta Catalyst
(d)	Nylon 6	(IV)	Acid or base catalyst

Which of the following is not a correct method of the preparation of benzylamine from cyanobenzene ?

The correct option among the following is :

The highest possible oxidation states of uranium and plutonium, respectively are :

The major product obtained in the given reaction is :

The INCORRECT statement is :