List of top Questions asked in JEE Main- 2019

Let \([x]\) denote the greatest integer less than or equal to \(x\). Then \(\lim_{x \to 0} \frac{\tan(\pi \sin^2 x) + \left(|x| - \sin(x[x])\right)^2}{x^2}\)

Let \(f : \mathbb{R} \to \mathbb{R}\) be defined by \(f(x) = \frac{x}{1+x^2},\ x \in \mathbb{R}\). Then the range of f is :

Let \(f(x) = \begin{cases} -1, & -2 \le x \lt 0 \\ x^2 - 1, & 0 \le x \le 2 \end{cases}\) and \(g(x) = |f(x)| + f(|x|)\). Then, in the interval \((-2, 2)\), g is :

A square is inscribed in the circle \(x^2 + y^2 - 6x + 8y - 103 = 0\) with its sides parallel to the coordinate axes. Then the distance of the vertex of this square which is nearest to the origin is :

If one real root of the quadratic equation \(81x^2 + kx + 256 = 0\) is cube of the other root, then a value of \(k\) is

The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is \(\frac{27}{19}\). Then the common ratio of this series is :

The straight line \(x + 2y = 1\) meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

The area (in sq. units) of the region bounded by the curve \(x^2 = 4y\) and the straight line \(x = 4y - 2\) is :

The electrolytes usually used in the electroplating of gold and silver, respectively are :

The reaction that is NOT involved in the ozone layer depletion mechanism in the stratosphere is :

Among the following reactions of hydrogen with halogens, the one that requires a catalyst is :

The correct match between item 'I' and item 'II' is :

Item 'I' (compound)	Item 'II' (reagent)
(A) Lysine	(P) 1-naphthol
(B) Furfural	(Q) ninhydrin
(C) Benzylalcohol	(R) KMnO4
(D) Styrene	(S) Ceric ammonium nitrate

The major product of the following reaction is

An ideal gas undergoes isothermal compression from 5 \(\mathrm{m^3}\) to 1 \(\mathrm{m^3}\) against a constant external pressure of 4 \(\mathrm{N\,m^{-2}}\). Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capacity of Al is 24 \(\mathrm{J\,mol^{-1}\,K^{-1}}\), the temperature of Al increases by :

The major product of the following reaction is :

The pair that contains two P - H bonds in each of the oxoacids is

In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing one molecule of \(\mathrm{CO_2}\) is :

Which of the following tests cannot be used for identifying amino acids?

A reaction of cobalt (III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A (violet coloured) and B (green coloured). A can show optical activity, but B is optically inactive. What type of isomers does A and B represcent?

For an elementary chemical reaction, \(\mathrm{A_2} \underset{K_{-1}}{\overset{K_1}{\rightleftharpoons}} 2\mathrm{A}\), the expression for \(\frac{d[A]}{dt}\) is

The major product obtained in the following reaction is :

The major product of the following reaction

The difference in the number of unpaired electrons of a metal ion in its high spin and low-spin octahedral complexes is two. The metal ion is :

What will be the major product in the following mononitration reaction ?

Elevation in the boiling point for 1 molar solution of glucose is 2 K. The depression in the freezing point for 2 molal solution of glucose in the same solvent is 2 K. The relation between \(K_b\) and \(K_f\) is