List of top Questions asked in JEE Main- 2021

The major product formed in the following reaction is :

The polymer formed on heating Novolac with formaldehyde is :

Given below are two statements :
Statement I : In the titration between strong acid and weak base methyl orange is suitable as an indicator.
Statement II : For titration of acetic acid with NaOH phenolphthalein is not a suitable indicator.
In the light of the above statements, choose the most appropriate answer from the options given below :

An aqueous KCl solution of density 1.20 g \(mL^{-1}\) has a molality of 3.30 mol \(kg^{-1}\). The molarity of the solution in mol \(L^{-1}\) is _________. (Nearest integer)
[Molar mass of KCl = 74.5]

\(AB_3\) is an interhalogen T-shaped molecule. The number of lone pairs of electrons on A is _________. (Integer answer)

The Born-Haber cycle for KCl is evaluated with the following data:
\(\Delta_f H^\ominus\) for KCl = -436.7 kJ \(mol^{-1}\); \(\Delta_{sub} H^\ominus\) for K = 89.2 kJ \(mol^{-1}\);
\(\Delta_{ionization} H^\ominus\) for K = 419.0 kJ \(mol^{-1}\); \(\Delta_{electron gain} H^\ominus\) for \(Cl_{(g)\) = -348.6 kJ \(mol^{-1}\);
\(\Delta_{bond} H^\ominus\) for \(Cl_2\) = 243.0 kJ \(mol^{-1}\).
The magnitude of lattice enthalpy of KCl in kJ \(mol^{-1}\) is _________. (Nearest integer)}

Of the following four aqueous solutions, total number of those solutions whose freezing point is lower than that of 0.10 M \(C_2H_5OH\) is _________. (Integer answer)
(i) 0.10 M \(Ba_3(PO_4)_2\)
(ii) 0.10 M \(Na_2SO_4\)
(iii) 0.10 M KCl
(iv) 0.10 M \(Li_3PO_4\)

The \(OH^-\) concentration in a mixture of 5.0 mL of 0.0504 M \(NH_4Cl\) and 2 mL of 0.0210 M \(NH_3\) solution is \(x \times 10^{-6}\) M. The value of \(x\) is _________. (Nearest integer)
[Given \(K_w = 1 \times 10^{-14}\) and \(K_b = 1.8 \times 10^{-5}\)]

The following data was obtained for chemical reaction given below at 975 K:

The order of the reaction with respect to NO is _________. (Integer answer)

These are physical properties of an element
(A) Sublimation enthalpy
(B) Ionisation enthalpy
(C) Hydration enthalpy
(D) Electron gain enthalpy
The total number of above properties that affect the reduction potential is _________. (Integer answer)

The number of 4f electrons in the ground state electronic configuration of \(Gd^{2+}\) is _________. [Atomic number of Gd = 64] (Integer answer)

The ratio of number of water molecules in Mohr's salt and potash alum is _________ \(\times 10^{-1}\). (Integer answer)

The total number of negative charge in the tetrapeptide, Gly-Glu-Asp-Tyr, at pH 12.5 will be _________. (Integer answer)

The equation \(\arg\left(\frac{z - 1}{z + 1}\right) = \frac{\pi}{4}\) represents a circle with :

If \( A = \begin{bmatrix} \frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ -\frac{2}{\sqrt{5}} & \frac{1}{\sqrt{5}} \end{bmatrix} \), \( B = \begin{bmatrix} 1 & 0 \\ i & 1 \end{bmatrix} \), \( i = \sqrt{-1} \), and \( Q = A^T B A \), then the inverse of the matrix \( A Q^{2021} A^T \) is equal to :

Let \(\theta \in \left(0, \frac{\pi}{2}\right)\). If the system of linear equations
\((1 + \cos^2\theta)x + \sin^2\theta y + 4\sin3\theta z = 0\)
\(\cos^2\theta x + (1 + \sin^2\theta)y + 4\sin3\theta z = 0\)
\(\cos^2\theta x + \sin^2\theta y + (1 + 4\sin3\theta)z = 0\)
has a non-trivial solution, then the value of \(\theta\) is :

If the sum of an infinite GP \(a, ar, ar^2, ar^3, \dots\) is 15 and the sum of the squares of its each term is 150, then the sum of \(ar^2, ar^4, ar^6, \dots\) is :

Let \(f(x) = \cos\left(2\tan^{-1} \sin \left(\cot^{-1} \sqrt{\frac{1-x}{x}}\right)\right)\), \(0<x<1\). Then :

The value of \(\int_{-1/\sqrt{2}}^{1/\sqrt{2}} \left[\left(\frac{x+1}{x-1}\right)^2 + \left(\frac{x-1}{x+1}\right)^2 - 2\right]^{1/2} dx\) is :

The value of \(\lim_{n \to \infty} \frac{1}{n} \sum_{r=0}^{2n-1} \frac{n^2}{n^2 + 4r^2}\) is :

The sum of solutions of the equation \(\frac{\cos x}{1 + \sin x} = |\tan 2x|\), \(x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) - \left\{\frac{\pi}{4}, -\frac{\pi}{4}\right\}\) is :

Let \(ABC\) be a triangle with \(A(-3, 1)\) and \(\angle ACB = \theta, 0<\theta \leq \frac{\pi}{2}\). If the equation of the median through \(B\) is \(2x + y - 3 = 0\) and the equation of angle bisector of \(C\) is \(7x - 4y - 1 = 0\), then \(\tan \theta\) is equal to :

If a line along a chord of the circle \(4x^2 + 4y^2 + 120x + 675 = 0\), passes through the point \((-30, 0)\) and is tangent to the parabola \(y^2 = 30x\), then the length of this chord is :

On the ellipse \(\frac{x^2}{8} + \frac{y^2}{4} = 1\) let \(P\) be a point in the second quadrant such that the tangent at \(P\) to the ellipse is perpendicular to the line \(x + 2y = 0\). Let \(S\) and \(S'\) be the foci of the ellipse and \(e\) be its eccentricity. If \(A\) is the area of the triangle \(SPS'\) then, the value of \((5 - e^2) \cdot A\) is :

A plane \(P\) contains the line \(x + 2y + 3z + 1 = 0 = x - y - z - 6\), and is perpendicular to the plane \(-2x + y + z + 8 = 0\). Then which of the following points lies on \(P\) ?