List of top Questions asked in JEE Main- 2019

The area (in sq. units) of the region \(A = \{(x, y) \in R \times R \mid 0 \le x \le 3,\ 0 \le y \le 4,\ y \le x^2 + 3x\}\) is :

Let \(O(0, 0)\) and \(A(0, 1)\) be two fixed points. Then the locus of a point P such that the perimeter of \(\Delta AOP\) is 4, is :

If \(\alpha\) and \(\beta\) be the roots of the equation \(x^2 - 2x + 2 = 0\), then the least value of n for which \(\left(\frac{\alpha}{\beta}\right)^n = 1\) is :

Let \(f : [0, 2] \to R\) be a twice differentiable function such that \(f''(x) \gt 0\), for all \(x \in (0, 2)\). If \(\phi(x) = f(x) + f(2 - x)\), then \(\phi\) is :

If \(f(x) = \log_e\left(\frac{1 - x}{1 + x}\right)\), \(|x| \lt 1\), then \(f\left(\frac{2x}{1 + x^2}\right)\) is equal to

The sum of the solutions of the equation
\(\left|\sqrt{x} - 2\right| + \sqrt{x}\left(\sqrt{x} - 4\right) + 2 = 0\)
\((x \gt 0)\) is equal to:

A point on the straight line, \(3x + 5y = 15\) which is equidistant from the coordinate axes will lie only in :

If \(\cos(\alpha + \beta) = 3/5\), \(\sin(\alpha - \beta) = 5/13\) and \(0 \lt \alpha, \beta \lt \frac{\pi}{4}\), then \(\tan(2\alpha)\) is equal to :

The sum of the squares of the lengths of the chords intercepted on the circle, \(x^2 + y^2 = 16\), by the lines, \(x + y = n\), \(n \in N\), where N is the set of all natural numbers, is :

Let \(y = y(x)\) be the solution of the differential equation,
\((x^2 + 1)^2\frac{dy}{dx} + 2x(x^2 + 1)y = 1\)
such that \(y(0) = 0\). If \(\sqrt{a}\,y(1) = \frac{\pi}{32}\), then the value of 'a' is :

The sum of all natural numbers 'n' such that \(100 \lt n \lt 200\) and H.C.F. \((91, n) \gt 1\) is :

The greatest value of \(c \in R\) for which the system of linear equations
\(x - cy - cz = 0\)
\(cx - y + cz = 0\)
\(cx + cy - z = 0\)
has a non-trivial solution, is :

The two monomers for the synthesis of Nylon 6, 6 are

Among the following the false statement is -

The compound that is NOT a common component of photochemical smog is :

The major product of the following reaction is –

(The reactant is a bicyclic compound (an octahydroindene: six-membered ring fused to a five-membered ring) carrying an isopropenyl group, \(\mathrm{C(CH_3)=CH_2}\), on the five-membered ring carbon that also bears an H; reagent: HCl.)

The major product of the following reaction is :
\(\mathrm{CH_3CH_2CH(Br)CH_2Br}\) (Br on the 2nd and 1st carbon; written as CH₃CH₂CH-CH₂ with Br below each of the last two carbons)
Reagents: (i) KOH alc; (ii) NaNH₂ in liq. NH₃

The major product of the following reaction is –

(Reactant: an aryl acetate, \(\mathrm{CH_3COO}\)-C₆H₄-\(\mathrm{CH_2CH_2CH_2NH_2}\), with the two substituents meta to each other. Reagents: (i) \(\mathrm{NaNO_2/H^+}\); (ii) \(\mathrm{CrO_3/H^+}\); (iii) \(\mathrm{H_2SO_4}\) (conc.), \(\Delta\).)

\(\Lambda_m^\circ\) for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S cm² mol⁻¹, respectively. If the conductivity of 0.001 M HA is 5 \(\times\) 10⁻⁵ S cm⁻¹, degree of dissociation of HA is -

The element that shows greater ability to form p\(\pi\)-p\(\pi\) multiple bonds, is :

8 g of NaOH is dissolved in 18 g of \(\mathrm{H_2O}\). Mole fraction of NaOH in solution and molality (in mol kg\(^{-1}\)) of the solution respectively are -

For a reaction consider the plot of \(\ell n\,k\) versus \(1/T\) given in the figure. If the rate constant of this reaction at 400 K is \(10^{-5}\ \mathrm{s^{-1}}\), then the rate constant at 500 K is –

(The plot of \(\ell n\,k\) against \(1/T\) is a straight line with slope \(= -4606\ \mathrm{K}\).)

The major product of the following reaction is –

(the optically active tertiary chloride \(\mathrm{CH_3-C(Cl)(CH_2CH_3)-COOCH_2CH_3}\) is heated with \(\mathrm{NaOEt}\))

If \(K_{sp}\) of \(\mathrm{Ag_2CO_3}\) is \(8\times10^{-12}\), the molar solubility of \(\mathrm{Ag_2CO_3}\) in 0.1 M \(\mathrm{AgNO_3}\) is -

The increasing order of the reactivity of the following with \(\mathrm{LiAlH_4}\) is

(A) \(\mathrm{C_2H_5CONH_2}\) (amide); (B) \(\mathrm{C_2H_5COOCH_3}\) (ester); (C) \(\mathrm{C_2H_5COCl}\) (acid chloride); (D) \(\mathrm{(C_2H_5CO)_2O}\) (anhydride)