List of top Questions asked in JEE Main- 2019

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is

If the fourth term in the binomial expansion of \(\left(\sqrt{x^{\left(\frac{1}{1 + \log_{10} x}\right)}} + x^{\frac{1}{12}}\right)^{6}\) is equal to 200, and \(x \gt 1\), then the value of \(x\) is :

If a point \(R(4, y, z)\) lies on the line segment joining the points \(P(2, -3, 4)\) and \(Q(8, 0, 10)\), then the distance of \(R\) from the origin is :

Let the number \(2, b, c\) be in an A.P. and \(A = \begin{bmatrix}1 & 1 & 1\\ 2 & b & c\\ 4 & b^2 & c^2\end{bmatrix}\). If \(\det(A) \in [2, 16]\), then \(c\) lies in the interval :

The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is :

A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

Suppose that the points \((h, k)\), \((1, 2)\) and \((-3, 4)\) lie on the line \(L_1\). If a line \(L_2\) passing through the points \((h, k)\) and \((4, 3)\) is perpendicular to \(L_1\), then \(\frac{k}{h}\) equals :

Let \(S(\alpha) = \{(x, y) : y^2 \le x,\ 0 \le x \le \alpha\}\) and \(A(\alpha)\) is area of the region \(S(\alpha)\). If for a \(\lambda\), \(0 \lt \lambda \lt 4\), \(A(\lambda) : A(4) = 2 : 5\), then \(\lambda\) equals

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is :

If the system of linear equations
\(x - 2y + kz = 1\)
\(2x + y + z = 2\)
\(3x - y - kz = 3\)
has a solution \((x, y, z)\), \(z \ne 0\), then \((x, y)\) lies on the straight line whose equation is :

100 mL of a water sample contains 0.81 g of calcium bicrabonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalents of \(\mathrm{CaCO_3}\) is : (Molar mass of calcium bicarbonate is 162 g mol^-1 and magnesium bicarbonate is 146 g mol^-1)

Adsorption of a gas follows freundlich adosorbed isotherm. x is the mass of the gas adsorbed on mass m of the adsorbent. The plot \(\log \frac{x}{m}\) versus \(\log p\) is shown in the given graph. \(\frac{x}{m}\) is proportional to :

The major product of the following reaction is :

In the following compounds, the decreasing order of basic strength will be :

Coupling of benzene diazonium chloride with 1 - naphthol in alkaline medium will give :

For the reaction \(2\mathrm{A} + \mathrm{B} \to \mathrm{C}\), the values of initial rate at diffrent reactant concentrations are given in the table below. The rate law for the reaction is :

[A] (mol L-1)	[B] (mol L-1)	Initial Rate (mol L-1 s-1)
0.05	0.05	0.045
0.10	0.05	0.090
0.20	0.10	0.72

Given that
\(E^{\ominus}_{\mathrm{O_2/H_2O}} = 1.23\ \mathrm{V}\);
\(E^{\ominus}_{\mathrm{S_2O_8^{2-}/SO_4^{2-}}} = 2.05\ \mathrm{V}\)
\(E^{\ominus}_{\mathrm{Br_2/Br^-}} = 1.09\ \mathrm{V}\)
\(E^{\ominus}_{\mathrm{Au^{3+}/Au}} = 1.4\ \mathrm{V}\)
The strongest oxidizing agent is :

The major product of the following reaction is :

Maltose on treatment with dilute HCI gives :

The following ligand is :

An organic compound neither reacts with neutral ferric chloride solution nor with fehling solution. it however, reacts with Grignard reagent and gives positive iodoform test. The compound is :

The major product of the following reaction is :

Which of the following amines can be prepared by Gabriel phthalimide reaction ?

If solublity product of \(\mathrm{Zr_3(PO_4)_4}\) is denoted by \(\mathrm{K_{sp}}\) and its molar solubility is denoted by S, then which of the following relation between S and \(\mathrm{K_{sp}}\) is correct ?

For the circuit shown, with R₁ = 1.0W, R₂ = 2.0 W, E₁ = 2 V and E₂ = E₃ = 4 V, the potential difference between the points 'a' and 'b' is approximately (in V):