List of top Questions asked in JEE Main- 2019

Let \(f(x) = x^2\), \(x \in R\). For any \(A \subseteq R\), define \(g(A) = \{x \in R : f(x) \in A\}\). If \(S = [0, 4]\), then which one of the following statements is not true ?

Let \(f : R \to R\) be differentiable at \(c \in R\) and \(f(c) = 0\). If \(g(x) = |f(x)|\), then at \(x = c\), \(g\) is :

The region represented by \(|x - y| \le 2\) and \(|x + y| \le 2\) is bounded by a :

Let \(f(x) = e^x - x\) and \(g(x) = x^2 - x\), \(\forall\, x \in R\). Then the set of all \(x \in R\), where the function \(h(x) = (f \circ g)(x)\) is increasing, is :

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is :

If \(\Delta_1 = \begin{vmatrix} x & \sin\theta & \cos\theta \\ -\sin\theta & -x & 1 \\ \cos\theta & 1 & x \end{vmatrix}\) and \(\Delta_2 = \begin{vmatrix} x & \sin 2\theta & \cos 2\theta \\ -\sin 2\theta & -x & 1 \\ \cos 2\theta & 1 & x \end{vmatrix}\), \(x \ne 0\); then for all \(\theta \in \left(0, \frac{\pi}{2}\right)\) :

The value of \(\displaystyle\int_0^{2\pi} \left[\sin 2x\,(1 + \cos 3x)\right] dx\), where \([t]\) denotes the greatest integer function is :

If \(f(x) = \begin{cases} \dfrac{\sin(p+1)x + \sin x}{x}, & x < 0 \\ q, & x = 0 \\ \dfrac{\sqrt{x + x^2} - \sqrt{x}}{x^{3/2}}, & x > 0 \end{cases}\) is continuous at \(x = 0\), then the ordered pair \((p, q)\) is equal to

If \(a_1, a_2, a_3, \ldots, a_n\) are in A.P. and \(a_1 + a_4 + a_7 + \ldots + a_{16} = 114\), then \(a_1 + a_6 + a_{11} + a_{16}\) is equal to :

If \(a > 0\) and \(z = \dfrac{(1+i)^2}{a - i}\), has magnitude \(\sqrt{\frac{2}{5}}\), then \(\bar{z}\) is equal to :

If the length of the perpendicular from the point \((\beta, 0, \beta)\) \((\beta \ne 0)\) to the line, \(\frac{x}{1} = \frac{y-1}{0} = \frac{z+1}{-1}\) is \(\sqrt{\frac{3}{2}}\), then \(\beta\) is equal to :

If for some \(x \in R\), the frequency distribution of the marks obtained by 20 students in a test is :

Marks	2	3	5	7
Frequency	\((x+1)^2\)	\(2x - 5\)	\(x^2 - 3x\)	\(x\)

then the mean of the marks is

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation, \(x^2 + x\sin\theta - 2\sin\theta = 0\), \(\theta \in \left(0, \frac{\pi}{2}\right)\), then \(\dfrac{\alpha^{12} + \beta^{12}}{\left(\alpha^{-12} + \beta^{-12}\right)\cdot(\alpha - \beta)^{24}}\) is equal to :

If \(\displaystyle\lim_{x \to 1} \frac{x^4 - 1}{x - 1} = \lim_{x \to k} \frac{x^3 - k^3}{x^2 - k^2}\), then \(k\) is :

If a directrix of a hyperbola centred at the origin and passing through the point \((4, -2\sqrt{3})\) is \(5x = 4\sqrt{5}\) and its eccentricity is \(e\), then :

The layer of atmosphere between 10 km to 50 km above the sea level is called as :

The one that is not a carbonate ore is :

The major product of the following reaction is:

Which of the following compounds is a constituent of the polymer

?

The major products A and B for the following reactions are, respectively:

At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as
\(p = \dfrac{RT}{V - b}\)
at T.
Here, b is the van der Waals constant. Which gas will exhibit steepest increase in the plot of Z (compression factor) vs p?

10 mL of 1 mM surfactant solution forms a monolayer covering 0.24 cm\(^2\) on a polar substrate. If the polar head is approximated as cube, what is its edge length?

Assertion: For the extraction of iron, haematite ore is used.
Reason: Haematite is a carbonate ore of iron.

The maximum number of possible oxidation states of actinoides are shown by :

In an acid-base titration, 0.1 M HCl solution was added to the NaOH solution of unknown strength. Which of the following correctly shows the change of pH of the titraction mixture in this experiment?