List of top Questions asked in JEE Main- 2021

Let
\(A=[a_{ij}]\)
be a \(3\times3\) matrix, where
\(a_{ij}=\left\{\begin{matrix}1&,&\text{if } i=j\\-x&,&\text{if } |i-j|=1\\2x+1&,&\text{otherwise.}\end{matrix}\right.\)
Let a function \(f:\mathbb{R}\to\mathbb{R}\) be defined as \(f(x)=\det(A)\). Then the sum of maximum and minimum values of \(f\) on \(\mathbb{R}\) is equal to:

Let
\(A=\left[\begin{matrix}2&3\\a&0\end{matrix}\right]\)
, \(a\in\mathbb{R}\) be written as \(P+Q\) where \(P\) is a symmetric matrix and \(Q\) is skew symmetric matrix. If \(\det(Q)=9\), then the modulus of the sum of all possible values of determinant of \(P\) is equal to :

Let \([x]\) denote the greatest integer \(\le x\), where \(x\in\mathbb{R}\). If the domain of the real valued function
\(f(x)=\sqrt{\frac{|[x]|-2}{|[x]|-3}}\)
is \((-\infty,a)\cup[b,c)\cup[4,\infty)\), \(a\lt b\lt c\), then the value of \(a+b+c\) is :

If \(z\) and \(\omega\) are two complex numbers such that
\(|z\omega|=1\)
and
\(\arg(z)-\arg(\omega)=\frac{3\pi}{2}\)
, then
\(\arg\left(\frac{1-2\overline{z}\omega}{1+3\overline{z}\omega}\right)\)
is :
(Here \(\arg(z)\) denotes the principal argument of complex number \(z\))

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are :

The value of the integral
\(\displaystyle\int_{-1}^{1}\log_e\left(\sqrt{1-x}+\sqrt{1+x}\right)dx\)
is equal to:

If \(\alpha\) and \(\beta\) are the distinct roots of the equation
\(x^2+(3)^{1/4}x+3^{1/2}=0\)
, then the value of \(\alpha^{96}\left(\alpha^{12}-1\right)+\beta^{96}\left(\beta^{12}-1\right)\) is equal to :

Let \(a\) be a positive real number such that
\(\displaystyle\int_0^a e^{x-[x]}\,dx = 10e-9\)
where \([x]\) is the greatest integer less than or equal to \(x\). Then \(a\) is equal to:

Consider the above reaction. The percentage yield of amide product is __________. (Round off to the Nearest Integer).

(Given : Atomic mass : C : 12.0 u, H : 1.0 u, N : 14.0 u, O : 16.0 u, Cl : 35.5 u)

The total number of C-C sigma bond/s in mesityl oxide (\(\mathrm{C_6H_{10}O}\)) is __________. (Round off to the Nearest Integer).

The number of chlorine atoms in 20 mL of chlorine gas at STP is _________ \(10^{21}\). (Round off to the Nearest Integer).

[Assume chlorine is an ideal gas at STP

R = 0.083 L bar mol^\(-1\) K^\(-1\), \(N_A = 6.023 \times 10^{23}\)]

KBr is doped with \(10^{-5}\) mole percent of \(\mathrm{SrBr_2}\). The number of cationic vacancies in 1g of KBr crystal is ____________ \(10^{14}\). (Round off to the Nearest Integer).

[Atomic Mass : K : 39.1 u, Br : 79.9 u \(N_A = 6.023 \times 10^{23}\)]

A KCl solution of conductivity \(0.14\ \mathrm{S\ m^{-1}}\) shows a resistance of \(4.19\ \Omega\) in a conductivity cell. If the same cell is filled with an HCl solution, the resistance drops to \(1.03\ \Omega\). The conductivity of the HCl solution is ____________ \(\times 10^{-2}\ \mathrm{S\ m^{-1}}\). (Round off to the Nearest Integer).

Consider the reaction

\(\mathrm{N_2O_4(g)} \rightleftharpoons 2\mathrm{NO_2(g)}\)

The temperature at which \(K_C = 20.4\) and \(K_P = 600.1\), is ____________ K. (Round off to the Nearest Integer). [Assume all gases are ideal and \(R = 0.0831\ \mathrm{L\ bar\ K^{-1}\ mol^{-1}}\)]

On complete reaction of \(\mathrm{FeCl_3}\) with oxalic acid in aqueous solution containing KOH, resulted in the formation of product A. The secondary valency of Fe in the product A is __________. (Round off to the Nearest Integer).

A 1 molal \(\mathrm{K_4Fe(CN)_6}\) solution has a degree of dissociation of 0.4. Its boiling point is equal to that of another solution which contains 18.1 weight percent of a non electrolytic solute A. The molar mass of A is __________ u. (Round off to the Nearest Integer). [Density of water = 1.0 g cm^\(-3\) ]

The functional groups that are responsible for the ion-exchange property of cation and anion exchange resins, respectively, are :

One of the by-products formed during the recovery of \(\mathrm{NH_3}\) from Solvay process is :

Match List - I with List - II :

	List - I		List - II
(a)	Haematite	(i)	\(Al_2O_3\cdot xH_2O\)
(b)	Bauxite	(ii)	\(Fe_2O_3\)
(c)	Magnetite	(iii)	\(CuCO_3\cdot Cu(OH)_2\)
(d)	Malachite	(iv)	\(Fe_3O_4\)

Choose the correct answer from the options given below :

Match List - I with List - II.

	List - I Chemical Compound		List - II Used as
(a)	Sucralose	(i)	Synthetic detergent
(b)	Glyceryl ester of stearic acid	(ii)	Artificial sweetener
(c)	Sodium benzoate	(iii)	Antiseptic
(d)	Bithionol	(iv)	Food preservative

Choose the correct match :

The set of elements that differ in mutual relationship from those of the other sets is :

The common positive oxidation states for an element with atomic number 24, are :

For the coagulation of a negative sol, the species below, that has the highest flocculating power is :

Fructose is an example of :

The set that represents the pair of neutral oxides of nitrogen is :