List of top Questions asked in JEE Main

If $\int\limits_{\frac{1}{3}}^{3}\left|\log _e x\right| d x=\frac{m}{n} \log e\left(\frac{n^2}{v}\right)$, where $m$ and $n$ are coprime natural numbers, then $m^2+n^2-5$ is equal to _____

Identify the correct statements about alkali metals
A. The order of standard reduction potential $\left( M ^{+} \mid M \right)$for alkali metal ions is $Na > Rb > Li$
B. $CsI$is highly soluble in water.
C. Lithium carbonate is highly stable to heat.
D. Potassium dissolved in concentrated liquid ammonia is blue in colour and paramagnetic.
E. All the alkali metal hydrides are ionic solids.
Choose the correct answer from the options given below:

Following figure shows spectrum of an ideal black body at four different temperatures The number of correct statement/s from the following is ________

[A.] $T_4 > T_3 > T_2 > T_1$
[B.] The black body consists of particles performing simple harmonic motion.
[C.] The peak of the spectrum shifts to shorter wavelengths as temperature increases.
[D.] $\frac{T_1}{\nu_1} = \frac{T_2}{\nu_2} = \frac{T_3}{\nu_3} \neq \text{constant}.$
[E.] The given spectrum could be explained using quantization of energy.

The total pressure observed by mixing two liquids A and B is 350 , mm Hg when their mole fractions are 0.7 and 0.3 respectively The total pressure becomes 410 ,mm ,Hg if the mole fractions are changed to 0.2 and 0.8 respectively for A and B The vapour pressure of pure A is _________mm ,Hg (Nearest integer) Consider the liquids and solutions behave ideally.

Sum of $\pi$-bonds present in peroxodisulphuric acid and pyrosulphuric acid is___________

The number of statement/s which are the characteristics of physisorption is __________
A. It is highly specific in nature
B. Enthalpy of adsorption is high
C. It decreases with increase in temperature
D. It results into unimolecular layer
E. No activation energy is needed

Choose the correct colour of the product for the following reaction

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Beryllium has less negative value of reduction potential compared to the other alkaline earth metals
Reason R: Beryllium has large hydration energy due to small size of $Be ^{2+}$ but relatively large value of atomization enthalpy
In the light of the above statements, choose the most appropriate answer from the options given below

The hybridization and magnetic behaviour of cobalt ion in $\left[ Co \left( NH _3\right)_6\right]^{3+}$ complex, respectively is

Let $y=y(t)$ be a solution of the differential equation$\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}$ where, $\alpha > 0, \beta>0$ and $\gamma > 0$. Then $\displaystyle\lim _{t \rightarrow \infty} y(t)$

A student has studied the decomposition of a gas AB₃ at 25^∘C. He obtained the following data.

p(mmHg)	50	100	200	400
$relative\space t_{1/2}(s)$	4	2	1	0.5

The order of the reaction is……….

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2, \sqrt{3 N}, N+2$ are in geometric progression be $\frac{k}{48}$, Then the value of $k$ is

Let the function $f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6$ have a maxima for some value of $x<0$ and a minima for some value of $x>0$ Then, the set of all values of $p$ is

Let $\Delta, \nabla \in\{\Lambda, V\}$ be such that $( p \rightarrow q ) \Delta( p \nabla q )$ is a tautology. Then

Correct statement is:

Given below are two statements:
Statement I : Pure Aniline and other arylamines are usually colourless.
Statement II : Arylamines get coloured on storage due to atmospheric reduction.
Choose the correct answer

The shortest distance between the lines $x+1=2 y=-12 z$ and $x=y+2=6 z-6$ is

Which of the following cannot be explained by crystal field theory?

Let $ f(x) = 2x^n + \lambda $, where $ \lambda \in \mathbb{R} $ and $ n \in \mathbb{N} $ . Given that $ f(4) = 133 $ and $ f(5) = 255 $, What is the sum of all the positive integer divisors of $ f(3) - f(2) $?

Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]$, where $i=\sqrt{-1}$ If $M = A ^{ T } B A$, then the inverse of the matrix $AM ^{2023} A ^{ T }$ is

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1,3,5,7,9 without repetition, is

If 5f ( x+y ) = f(x).f(y) and f(3) = 320, then the value of f(1) is

Mean & Variance of 7 observations are 8 & 16 respectively, if number 14 is omitted then a & b are new mean & variance. The value of a + b is

The mean and variance of 7 observations are 8 and 16, respectively. If one observation 14 is omitted and a and b are respectively the mean and variance of the remaining 6 observations, then $a+3b−5$ is equal to

If $a_n=\frac{-2}{4n^2-16n+15}$ and a₁ + a₂ + …… + a₂₅ = m/n where m and n are coprime, then the value of m + n is