List of top Questions asked in JEE Main- 2021

2SO$_2$(g) + O$_2$(g) $\rightarrow$ 2SO$_3$(g)
The above reaction is carried out in a vessel starting with partial pressures P$_{SO_2}$ = 250 m bar, P$_{O_2}$ = 750 m bar and P$_{SO_3}$ = 0 bar. When the reaction is complete, the total pressure in the reaction vessel is ________ m bar. (Round off to the Nearest Integer).
The total number of electrons in all bonding molecular orbitals of O$_2^{2-}$ is ________.
(Round off to the Nearest Integer).
When 400 mL of 0.2 M H$_2$SO$_4$ solution is mixed with 600 mL of 0.1 M NaOH solution, the increase in temperature of the final solution is ________ $\times 10^{-2}$ K. (Round off to the Nearest Integer).
[Use : H$^+$(aq) + OH$^-$(aq) $\rightarrow$ H$_2$O(l) ; $\Delta_r H$ = -57.1 kJ mol$^{-1}$
Specific heat of H$_2$O = 4.18 J K$^{-1}$ g$^{-1}$
density of H$_2$O = 1.0 g cm$^{-3}$
Assume no change in volume of solution on mixing.]
In a solvent 50% of an acid HA dimerizes and the rest dissociates. The van't Hoff factor of the acid is ________ $\times 10^{-2}$. (Round off to the Nearest Integer).
The equilibrium constant for the reaction
A(s) $\rightleftharpoons$ M(s) + $\frac{1}{2}$O$_2$(g)
is K$_p$=4. At equilibrium, the partial pressure of O$_2$ is ________ atm. (Round off to the Nearest Integer).
For the cell Cu(s)|Cu$^{2+}$(aq) (0.1 M)||Ag$^+$(aq) (0.01 M)|Ag(s) the cell potential E$_1$ = 0.3095 V
For the cell Cu(s)|Cu$^{2+}$(aq) (0.01 M)||Ag$^+$(aq) (0.001 M)|Ag(s) the cell potential = ________ $\times 10^{-2}$ V. (Round off to the Nearest Integer).
[Use : $\frac{2.303 RT}{F} = 0.059$]
For the first order reaction $A \rightarrow 2B$, 1 mole of reactant A gives 0.2 moles of B after 100 minutes. The half life of the reaction is ________ min. (Round off to the Nearest Integer).
3 moles of metal complex with formula Co(en)$_2$Cl$_3$ gives 3 moles of silver chloride on treatment with excess of silver nitrate. The secondary valency of Co in the complex is ________. (Round off to the Nearest Integer).
The dihedral angle in staggered form of 1,1,1-Trichloro ethane is ________ degree. (Round off to the Nearest Integer).
10.0 mL of 0.05 M KMnO$_4$ solution was consumed in a titration with 10.0 mL of given oxalic acid dihydrate solution. The strength of given oxalic acid solution is ________ $\times 10^{-2}$ g/L. (Round off to the Nearest Integer).
Let $f: \mathbb{R} \to \mathbb{R}$ be defined as $f(x+y) + f(x-y) = 2f(x)f(y)$, $f(\frac{1}{2}) = -1$. Then, the value of $\sum_{k=1}^{20} \frac{1}{\sin(k) \sin(k+f(k))}$ is equal to :
Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $6\sqrt{5}$ on the x-axis. Then the radius of the circle C is equal to :
Two sides of a parallelogram are along the lines $4x+5y=0$ and $7x+2y=0$. If the equation of one of the diagonals of the parallelogram is $11x+7y=9$, then other diagonal passes through the point :
Let \( f : [0, \infty) \rightarrow [0, 3] \) be a function defined by
\[ f(x) = \begin{cases} \max\{\sin t : 0 \le t \le x\}, & 0 \le x \le \pi \\ 2 + \cos x, & x > \pi \end{cases} \] Then which of the following is true ?
Which of the following is the negation of the statement "for all M>0, there exists x$\in$S such that x $\ge$ M" ?
The area of the region bounded by $y-x=2$ and $x^2=y$ is equal to :
Let $y=y(x)$ be the solution of the differential equation $(x-x^3)dy = (y+yx^2-3x^4)dx$, $x>2$. If $y(3)=3$, then $y(4)$ is equal to :
The point P (a, b) undergoes the following three transformations successively :
(a) reflection about the line y=x.
(b) translation through 2 units along the positive direction of x-axis.
(c) rotation through angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.
If the co-ordinates of the final position of the point P are $(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}})$, then the value of 2a+b is equal to :
Let $f: (a,b) \to \mathbb{R}$ be twice differentiable function such that $f(x) = \int_a^x g(t)dt$ for a differentiable function $g(x)$. If $f(x)=0$ has exactly five distinct roots in $(a,b)$, then $g(x)g'(x)=0$ has at least :
Let $\mathbb{N}$ be the set of natural numbers and a relation R on $\mathbb{N}$ be defined by R = $\{(x, y) \in \mathbb{N} \times \mathbb{N} : x^3 - 3x^2y - xy^2 + 3y^3 = 0\}$. Then the relation R is :
Let $\alpha = \max_{x \in \mathbb{R}}\{8^{2\sin 3x} \cdot 4^{4\cos 3x}\}$ and $\beta = \min_{x \in \mathbb{R}}\{8^{2\sin 3x} \cdot 4^{4\cos 3x}\}$.
If $8x^2+bx+c=0$ is a quadratic equation whose roots are $\alpha^{1/5}$ and $\beta^{1/5}$, then the value of c-b is equal to :
The value of $\lim_{x \to 0} \left(\frac{x}{\sqrt[8]{1-\sin x} - \sqrt[8]{1+\sin x}}\right)$ is equal to :
A student appeared in an examination consisting of 8 true - false type questions. The student guesses the answers with equal probability. The smallest value of n, so that the probability of guessing at least 'n' correct answers is less than $\frac{1}{2}$, is :
For real numbers $\alpha$ and $\beta \neq 0$, if the point of intersection of the straight lines
$\frac{x-\alpha}{1} = \frac{y-1}{2} = \frac{z-1}{3}$ and $\frac{x-4}{\beta} = \frac{y-6}{3} = \frac{z-7}{3}$
lies on the plane $x+2y-z=8$, then $\alpha-\beta$ is equal to :
If $\tan(\frac{\pi}{9})$, x, $\tan(\frac{7\pi}{18})$ are in arithmetic progression and $\tan(\frac{\pi}{9})$, y, $\tan(\frac{5\pi}{18})$ are also in arithmetic progression, then $|x-2y|$ is equal to :