List of top Questions asked in JEE Main- 2022

A sample of 0.125 g of an organic compound when analysed by Duma’s method yields 22.78 mL of nitrogen gas collected over KOH solution at 280 K and 759 mm Hg. The percentage of nitrogen in the given organic compound is____.(Nearest integer)

Given : 1. The vapour pressure of water of 280 K is 14.2 mm Hg.

2. R = 0.082 L atm K^–1 mol^–1

If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :

A vessel contains $14 g$ of nitrogen gas at a temperature of $27°C$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be:

Take $R=8.32 J-mol^{-1}K^{-1}$

Hydrolysis of which compound will give carbolic acid?

The sum of all real value of $x$ for which $\frac{3x^2-9x+17}{x^2+3x+10}=\frac {5x^2-7x+19}{3x^2+5x+12}$ is equal to________.

While estimating the nitrogen present in an organic compound by Kjeldahl’s method, the ammonia evolved from 0.25g of the compound neutralized 2.5mL of 2M H₂SO₄. The percentage of nitrogen present in organic compound is ________

$\lim_{{x \to 0}} \limits$ $\frac{cos(sin x) - cos x }{x^4}$ is equal to :

A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100 °C, then the internal energy for vaporization in kJ mol^–1 is ________. [nearest integer]
[Assume steam to be an ideal gas. Given Δ_vapH^Θ for water at 373 K and 1 bar is 41.1 kJ mol^–1; R = 8.31 J K^–1 mol^–1]

A girl standing on road holds her umbrella at 45° with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt2$ $kmh^{–1}$, the rain drops hit herhead vertically. The speed of rain drops with respect to the moving girl is

Let
A =$\begin{pmatrix} 4 & -2 \\ \alpha & \beta \\ \end{pmatrix}$
If A² + γA + 18I = 0, then det (A) is equal to ______.

Let A be a $2×2$ matrix with $det (A) = –1$ and $det((A + I) (Adj (A) + I)) = 4$. Then the sum of the diagonal elements of A can be

If for some p, q, r ∈ R, not all have same sign, one of the roots of the equation (p² + q²)x² – 2q(p + r)x + q² + r² = 0 is also a root of the equation x² + 2x – 8 = 0, then (q² + r²)/p² is equal to _______ .

Given below are two statements: one is labelled as Assertion A and, the other is labelled as Reason R.
Assertion A: [6] Annulene, [8] Annulene and cis-[10] Annulene, are respectively aromatic, not-aromatic and aromatic.
Reason R: Planarity is one, of the requirements of aromatic systems.
In the light of the above statements, choose the most appropriate answer from the options given below.

Let S = {1, 2, 3, 4}.Then the number of elements in the set {f : S × S → S : f is onto and f(a,b)=f(b,a) ≥ a ∀ (a, b)∈ S × S is _____.

For the given reactions
Sn²⁺ + 2e^– → Sn
Sn⁴⁺ + 4e^– → Sn
the electrode potentials are;
$E^{∘}_{Sn^{2+}/Sn}=−0.140V $ and $E^{∘}_{Sn^{4+}Sn} =−0.010 V.$
The magnitude of standard electrode potential for $Sn^{4+}/Sn^{2+}$i.e.
$E^{∘}_{Sn^{4+}/Sn^{2+}}$
is _________ × 10^–2 V. (Nearest integer)

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

If $\lim_{n\rightarrow \infty}$ $\frac{(n+1)^{k-1}}{n^{k+1}}[(nk+1)+(nk+2)+....+(nk+n)]=33.\lim_{n\rightarrow \infty}\frac{1}{n^{k+1}}.[1^k+2^k+3^k+....+n^k]$
then the integral value of k is equal to _______.

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is

A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 Ω. The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determined value of R will be ___ Ω.

Let X be a binomially distributed random variable with mean 4 and variance 4/3. Then, 54 P(X≤ 2) is equal to

$\sum_{r=1}^{20}$(r²+1)(r!) is equal to

If for p ≠ q ≠ 0, the function
$f(x) = \frac{{^{\sqrt[7]{p(729 + x)-3}}}}{{^{\sqrt[3]{729 + qx} - 9}}}$
is continuous at x = 0, then

Let f(x) = [2x² + 1] and $g(x)=\left\{\begin{matrix} 2x-3,\,x<0&\\2x+3, x≥0 &\end{matrix}\right.$where [t] is the greatest integer ≤ t. Then, in the open interval (–1, 1), the number of points where fog is discontinuous is equal to _______.

Three masses M = 100 kg, m₁= 10 kg and m₂ = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m₂ moves upward with an acceleration of 2 ms^–2. The value of F is
(Take g = 10 ms^–2)

A weightless and frictionless pulleys with three masses

The ratio of specific heats

$(\frac{c_p}{c_v}) $

in terms of degree of freedom (f) is given by: