List of top Questions asked in JEE Main- 2021

Consider the above reaction and identify the Product P :

Match List - I with List - II :

Choose the most appropriate match :

The compound 'A' is a complementary base of _________ in DNA strands.

The density of NaOH solution is 1.2 g cm$^{-3}$. The molality of this solution is ________ m. (Round off to the Nearest Integer)
[Use : Atomic masses : Na:23.0 u O:16.0 u H:1.0 u, Density of H$_2$O : 1.0 g cm$^{-3}$]

The difference between bond orders of CO and NO$^\oplus$ is $\frac{x}{2}$ where x = _________. (Round off to the Nearest Integer)

For water at 100$^\circ$C and 1 bar,
(Round off to the Nearest Integer)
[Use : R=8.31 J mol$^{-1}$ K$^{-1}$]
[Assume volume of H$\_2$O(l) is much smaller than volume of H$\_2$O(g). Assume H$\_2$O(g) can be treated as an ideal gas]

1.46 g of a biopolymer dissolved in a 100 mL water at 300 K exerted an osmotic pressure of $2.42 \times 10^{-3}$ bar. The molar mass of the biopolymer is _________ $\times 10^4$ g mol$^{-1}$. (Round off to the Nearest Integer)
[Use : R = 0.083 L bar mol$^{-1}$ K$^{-1}$]

$PCl_5 \rightleftharpoons PCl_3 + Cl_2 K_c = 1.844$
3.0 moles of $PCl_5$ is introduced in a 1 L closed reaction vessel at 380 K. The number of moles of $PCl_5$ at equilibrium is _________ $\times 10^{-3}$. (Round off to the Nearest Integer)

The conductivity of a weak acid HA of concentration 0.001 mol L$^{-1}$ is $2.0 \times 10^{-5}$ S cm$^{-1}$. If $\Lambda_m^\circ(HA) = 190$ S cm$^2$ mol$^{-1}$, the ionization constant (K$_a$) of HA is equal to _________ $\times 10^{-6}$. (Round off to the Nearest Integer)

$CO_2$ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of $CO_2$ adsorbed becomes 64 times when the pressure of $CO_2$ is doubled. The value of n in the Freundlich isotherm equation is _________ $\times 10^{-2}$. (Round off to the Nearest Integer)

The number of geometrical isomers possible in triamminetrinitrocobalt(III) is X and in trioxalatochromate(III) is Y. Then the value of X+Y is _________.

In gaseous triethyl amine the "-C-N-C-" bond angle is _________ degree.

An organic compound is subjected to chlorination to get compound A using 5.0 g of chlorine. When 0.5 g of compound A is reacted with AgNO$_3$ [Carius Method], the percentage of chlorine in compound A is _________ when it forms 0.3849 g of AgCl. (Round off to the Nearest Integer)
(Atomic masses of Ag and Cl are 107.87 and 35.5 respectively)

Let $\vec{a} = \hat{i}+\hat{j}+2\hat{k}$ and $\vec{b} = -\hat{i}+2\hat{j}+3\hat{k}$. Then the vector product $(\vec{a}+\vec{b}) \times ((\vec{a} \times ((\vec{a}-\vec{b}) \times \vec{b})) \times \vec{b})$ is equal to :

If the coefficients of $x^7$ in $\left(x^2 + \frac{1}{bx}\right)^{11}$ and $x^{-7}$ in $\left(x - \frac{1}{bx^2}\right)^{11}$, $b \neq 0$, are equal, then the value of b is equal to :

Let C be the set of all complex numbers. Let $S_1 = \{z \in C : |z-3-2i|^2 = 8\}$, $S_2 = \{z \in C : \text{Re}(z) \ge 5\}$ and $S_3 = \{z \in C : |z - \bar{z}| \ge 8\}$. Then the number of elements in $S_1 \cap S_2 \cap S_3$ is equal to :

Let the plane passing through the point (-1, 0, -2) and perpendicular to each of the planes $2x+y-z=2$ and $x-y-z=3$ be $ax+by+cz+8=0$. Then the value of $a+b+c$ is equal to :

Let $\alpha, \beta$ be two roots of the equation $x^2 + (20)^{1/4}x + (5)^{1/2} = 0$. Then $\alpha^8 + \beta^8$ is equal to :

Let
A = $\{(x, y) \in R \times R | 2x^2 + 2y^2 - 2x - 2y = 1\}$,
B = $\{(x, y) \in R \times R | 4x^2 + 4y^2 - 16y + 7 = 0\}$ and
C = $\{(x, y) \in R \times R | x^2 + y^2 - 4x - 2y + 5 \le r^2\}$.
Then the minimum value of $|r|$ such that $A \cup B \subseteq C$ is

Let $y=y(x)$ be solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = 3x+4y$, with $y(0)=0$. If $y\left(-\frac{2}{3}\log_e 2\right) = \alpha \log_e 2$, then the value of $\alpha$ is equal to :

If $\sin\theta + \cos\theta = \frac{1}{2}$, then $16(\sin(2\theta) + \cos(4\theta) + \sin(6\theta))$ is equal to :

The probability that a randomly selected 2-digit number belongs to the set $\{n \in N : (2^n - 2) \text{ is a multiple of } 3\}$ is equal to :

The compound statement $(P \lor Q) \land (\sim P) \Rightarrow Q$ is equivalent to :

The value of $\lim_{n \to \infty} \frac{1}{n}\sum_{j=1}^{n}\frac{(2j-1)+8n}{(2j-1)+4n}$ is equal to :

Let a plane P pass through the point (3, 7, -7) and contain the line, $\frac{x-2}{-3} = \frac{y-3}{2} = \frac{z+2}{1}$. If distance of the plane P from the origin is d, then $d^2$ is equal to _________.