List of top Questions asked in JEE Main- 2021

The structure of product C, formed by the following sequence of reactions is :
\( CH_3COOH + SOCl_2 \to A \xrightarrow[\text{AlCl}_3]{\text{Benzene}} B \xrightarrow[\text{}^-OH]{\text{KCN}} C \)

The major products A and B in the following set of reactions are :

Monomer of Novolac is :

Which one of the following compounds contains \(\beta\)-C\(_1\)-C\(_4\) glycosidic linkage?

The molarity of the solution prepared by dissolving \(6.3\text{ g}\) of oxalic acid (\(\text{H}_2\text{C}_2\text{O}_4 \cdot 2\text{H}_2\text{O}\)) in \(250\text{ mL}\) of water in mol L\(^{-1}\) is \(x \times 10^{-2}\). The value of \(x\) is \(\dots\dots\dots\). (Nearest integer)
[Atomic mass : H : 1.0, C : 12.0, O : 16.0]

Ge (\(Z=32\)) in its ground state electronic configuration has \(x\) completely filled orbitals with \(m_l=0\). The value of \(x\) is \(\dots\dots\dots\).

According to the following figure, the magnitude of the enthalpy change of the reaction \(A + B \to M + N\) in kJ mol\(^{-1}\) is equal to \(\dots\dots\dots\). (Integer answer)
[Given: \(x = 20\text{ kJ mol}^{-1}\), \(y = 45\text{ kJ mol}^{-1}\), \(z = 15\text{ kJ mol}^{-1}\)]

A\(_3\)B\(_2\) is a sparingly soluble salt of molar mass M (g mol\(^{-1}\)) and solubility \(x\text{ g L}^{-1}\). The solubility product satisfies \(K_{sp} = a \left(\frac{x}{M}\right)^5\). The value of \(a\) is \(\dots\dots\dots\). (Integer answer)

Consider the following cell reaction
\(\text{Cd}_{(s)} + \text{Hg}_2\text{SO}_{4(s)} + \frac{9}{5} \text{H}_2\text{O}_{(l)} \rightleftharpoons \text{CdSO}_4 \cdot \frac{9}{5} \text{H}_2\text{O}_{(s)} + 2\text{Hg}_{(l)}\)
The value of \(E_{cell}^0\) is \(4.315\text{ V}\) at \(25^\circ\text{C}\). If \(\Delta H^0 = -825.2\text{ kJ mol}^{-1}\), the standard entropy change \(\Delta S^0\) in J K\(^{-1}\) is \(\dots\dots\dots\). (Nearest integer)
[Given : Faraday constant = \(96487\text{ C mol}^{-1}\)]

For a first order reaction, the ratio of the time for \(75%\) completion of a reaction to the time for \(50%\) completion is \(\dots\dots\dots\). (Integer answer)

The number of halogen/(s) forming halic (V) acid is ____________

The number of hydrogen bonded water molecule(s) associated with stoichiometry \( CuSO_4 \cdot 5H_2O \) is ____________

The total number of reagents from those given below, that can convert nitrobenzene into aniline is ___________. (Integer answer)
I. \( Sn - HCl \)
II. \( Sn - NH_4OH \)
III. \( Fe - HCl \)
IV. \( Zn - HCl \)
V. \( H_2 - Pd \)
VI. \( H_2 - Raney \ Nickel \)}

Consider the sulphides \( HgS, PbS, CuS, Sb_2S_3, As_2S_3 \) and \( CdS \). Number of these sulphides soluble in \( 50% \ HNO_3 \) is _____________

Which of the following is not correct for relation \( R \) on the set of real numbers?

The number of real roots of the equation \( e^{4x} + 2e^{3x} - e^x - 6 = 0 \) is :

If \( a_r = \cos\frac{2r\pi}{9} + i \sin\frac{2r\pi}{9}, r = 1, 2, 3, \dots, i = \sqrt{-1} \), then the determinant \( \begin{vmatrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \end{vmatrix} \) is equal to :

If the following system of linear equations
\( 2x + y + z = 5 \)
\( x - y + z = 3 \)
\( x + y + az = b \)
has no solution, then :

Three numbers are in an increasing geometric progression with common ratio \( r \). If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference \( d \). If the fourth term of GP is \( 3 r^2 \), then \( r^2 - d \) is equal to :

The sum of 10 terms of the series \( \frac{3}{1^2 \times 2^2} + \frac{5}{2^2 \times 3^2} + \frac{7}{3^2 \times 4^2} + \dots \) is :

\( \lim_{x \to 0} \frac{\sin^2(\pi \cos^4 x)}{x^4} \) is equal to :

If the function

is continuous at \(x = 0\), then \(\frac{1}{a} + \frac{1}{b} + \frac{4}{k}\) is equal to :}